Kampala International University Uganda

 BACHELOR OF COMMERCE

MODULE 6
INTRODUCTION TO MICROECONOMICS 
BY
Tindyebwa Wilberforce, Phd CANDIDATE,M.A ECON,BAE(Econ)

INTRODUCTION
Unit 1
Introduction
1.1	Fundamental Questions in Economics
1.2	Purpose and principles of economic theory
1.3	Assumptions in Economics
1.4	Fundamental Economic Problems Scarcity, Choice and  Opportunity Cost
1.5	Production possibility curve, scarcity, choice and opportunity  cost
1.6	Implication of a Concave PPC
Review Questions
Unit 2
Market Analysis
2.1	Introduction
2.2	Demand Analysis
2.3	  Supply Analysis
3.4	 Market Equilibrium and Deviations from Equilibrium
2.5	Equilibrium in a Market
2.6	Consumer’s Surplus
2.7	 Producer’s Surplus
2.9	Consumer Sovereignty
Review Questions
Unite 3
Elasticity
3.1	Introduction
3.2	Elasticity of Demand
3.3	 Uses of Price Elasticity of Demand
Review Questions
Unite 4
Theory of Consumer Behaviour
4.1	Introduction
4.2	Cardinal Utility Theory
4.3	Total Utility (TU)
4.6	Indifference Curve Approach (Ordinal Utility Theory)
4.7	An Indifference Map
4.8	Implications of other slopes of indifference curves
4.9	A Budget Line
4.10	Consumer Equilibrium
4.11	 Engel Curve
4.12	 Price Consumption Curve (PPC)
4.13	 Price Effect, Substitution Effect and Income Effect
Review Questions
Unit 5
Production Theory
5.1	Introduction
5.2	The Theory of a Firm
5.3	Basic Concepts in Production Theory
5.4	Production Decision of a Firm
5.5	Equilibrium in Production
Review Questions
Unit 6
Theory of Costs
6.1	Introduction
6.2	Types of Costs
6.3	Variation of Costs in the Short run
6.4	Economies and Diseconomies of Scale
Review Questions
Unit 7
Profit Maximization
7.1	Introduction
7.2 	Total Revenue (TR)
7.3	 Marginal Revenue (MR)
7.4	 Relationship between Total Revenue and Marginal Revenue
7.5	 Profit (п)
Review Questions
Unit 8
Market Structures
8.1	 Introduction
8.2	Perfect Competition
8.3	Monopoly
8.4	Equilibrium of  Monopolist
8.5	Income Distribution under Monopoly
8.6	Monopolist and Consumer Sovereignty
8.7	Price Discrimination
8.8	Monopolistic Competition
Review Questions
Unit 9
Pricing of Factors of Production
9.1 	Introduction
9.2	Factor Pricing in Perfectly Competitive Markets
9.3  The Supply of Labour by an Individual Worker
9.4  The Market Supply Curve of Labour
Review Questions

INTRODUCTION 

Unit 1
Introduction
Many things take place in the daily life and hardly do we notice that they are backed by economic concepts. For instance taxi operators tend to hike fares during rush hours and during Christmas seasons and reduce fares the rest of the period without realizing that they are applying the laws of demand and supply. Politicians during political campaigns promise tax reductions, reducing the general price level, solving un-employment well knowing that they are the greatest evils of a society probably worse than wars. Private health workers give treatment to both the poor and the rich depending on the amount of money that they own, hence practicing price discrimination. These examples and a lot more are economics issues and are quite common in our societies. Non economists have tended to misrepresent the study of economics as a study of economizing, hence have always referred Economists as people who are squirrel which indeed might not be the case. At this point therefore, it is imperative to first understand what the study of economics is all about.

 Definition of Economics
Several definitions have been offered by different Economists; however all tend to agree
on one thing that it is the “study of how scarce resources are and how they can be used to satisfy human wants or needs”. In other words, Economics is the study e how scarce resources can be rationally or optionally exploited and distributed to satisfy human wants and needs. Scarce resources ar such things that command price even though they may be in abundance. These may include things such as raw materials, energy and labour, that can be used to produce goods and services that satisfy human wants and needs.

Branches of economics
Economics is divided into two major parts; Microeconomics and Macroeconomics. However, as you will find out, there are several other branches such as monetary economics, public finance, industrial economics, agricultural economics, and the most recent ones such as resource economics, health and environment economics among many others.
Microeconomics is the study of the economic actions of individuals and small groups of economic agents such as consumers, producers and resource owners. It is that part of economics that looks at the functioning of small economic units such as resource owners and business firms. One fundamental assumption is that Economic agents maximize their interests, for instance consumers maximize satisfaction / utility, producers maximize profits, so economic agents are assumed to be rational. Microeconomics therefore examines these rational Economic agents by providing conditions under which those interests are maximized. It is also concerned with the analysis of price determination which is an emphasis of a market. A market therefore is a central concept in microeconomics.

On the other hand, Macroeconomics looks at the economy as a whole. It aggregates all the economic agents; the consumers, resource owners and producers or business firms. It addresses the major problems of an economy which include; economic growth, unemployment, inflation and balance of payment problem. Macroeconomics suggests policy options that may be followed to solve the key Economic problem. The solutions are variant because the Social, Political, Economic and natural setting of Economies differ, besides the variations in the school of thought i.e. classical, Keynesians, Monetarists, Structural neo-Keynesian, national expectations schools, real business cycle school) may lead to divergences in solutions! Economic policies due to unresolved Economic debates.

Economics is further subdivided into: positive economics and normative economics.
  
Positive Economics
This deals with issues that can be observed or it deals with scientific explanations of the working of the economy. It looks at the world as it is and different from what it should be. It aims at explaining how society makes decision about say consumption, production and exchange of goods and services. Positive economics therefore refers to objective economic statements that explain that if certain conditions hold then certain things can be expected to happen, since things are arrived at through Economic research where theoretical models are subjected to Econometric analysis so as to arrive at a deduction. For instance, a statement such as “income inequality can be reduced through a system of income taxes”, is a positive statements. This is because such a statement can be subjected to research. Another positive statement can be “Currency depreciation or devaluation leads to increased exports” Another positive statement can be “Currency depreciation or devaluation leads to increased exports”.

Normative economics
This offers recommendation based on personal value judgment. It tries to explain how the world should be. It does not involve scientific proof or research. Therefore normative statements are subjective in nature, for instance, a statement such as “An income tax system is a good thing”, is a normative statement. Because its goodness depends on the perceptions of the individuals who say so most likely it is expected to be good to those who do not pay it.

1.1	Fundamental Questions in Economics
The study of Economics attempts to answer the following key questions which societies are always faced with given the ever limited/scarce resources;
1.	What to produce? This addresses the type of the commodity, whether it is the consumer durables or non-durables. Societies are always faced with the problem of deciding on what to produce. If resources were in abundance this problem would never arise but since resources are scarce, society has to choose between producing; cars, TV-sets, tractors (consumer durable) and producing rice, beer, (non-durable) or how to mix the two in order to maximize utility.
2.	How to produce? This is concerned about the production technique and it tries to identify those cost minimizing, hence efficient technique of production. By efficiency we mean optimal resource utilization. During production, firms use factors of production such as labour, capital, entrepreneur skills and land. But these factors are in limited supply hence scarce. Accordingly, there is need to choose that in put mix that will minimize cost so as to achieve the major objective or interest of firms which is profit maximization.
3.	For whom to produce? This question addresses the targeted market, whether production is for the low income or high-income groups, for the young or the old people. The aim here is to produce for those who need the good most since they obtain more satisfaction and are willing to demand more hence pay a higher price for the good which in turn maximizes the producer’s profits.
4.	When to produce? Society is always faced with the problem of choosing between producing now for consumption or delaying production and having it later. For instance consider harvesting (cutting) a forest. Should it be done now or leave it for the future generation?
5.	Where to produce? This question is concerned with the location of the firm, i.e. Is it near the source of raw material or near the source of energy, near transport system or near the market? This may be influenced by the perish-ability of the good or on the loyalty of the society to the political regime if the producer is government. What we mean here is that some political regimes tend to locate investments in area where they are popular.

However, solutions to the above questions are answered differently depending on the type of the economic system: Whether traditional, capitalist, socialist or mixed economy.

1.2	Purpose and principles of economic theory
In economics, when making conclusion, previous events are essential. All economic questions can be analyzed by examining the decisions of individuals and the outcome of the decision. For instance we stated that positive statements can be subjected to empirical analysis. What we mean is that such statements can be proved scientifically. The Scientific proof is based on theory. For example we stated that “Currency depreciation / devaluation leads to increased exports.” A model is built basing on the underlying theory, data is collected on these variables over a period of time together with that of exports, then we have exports as the dependent variable and the rest as independent variable, then we use statistical packages (computer soft wares) such as STATA, PC-Give, Eviews, SAS, SPSS etc to analyze the data.

The methodology for the analysis of data involves the use of statistical methods and econometrics. The basic framework for the analysis involves an economic model. An economic model is a simplified small-scale version of some aspect of the economy. Economic models can be expressed in different forms such as:

(i)	Equations; For instance;
For instance; 
	Qdx	=	Q(Px, Py, T, Y, Yd, Pn, A)

The above is a demand function and it states that the quantity of a commodity X (i.e. Qdx) demanded depends on factors such as;

Px	=	price of the commodity X.
Py	=	price of related commodities that may either be substitutes or complements.
T	=	Tastes and preferences of the consumers
Y 	=	Income of the consumers
Yd 	= 	Income distribution of the population. 
Fn	= 	the size of the population
A	 = 	other factors.

(ii) Graph
An econometric model could as well be expressed in a graphical form, for instance a demand function could be simplified for graphical purposes to assume that quantity demanded depends only on the price of the commodity. This would then give rise to a graphical demand model or curve. This form however, reduces the economic model to only two variables; the depended variable and the independent variable (because a graph has only two axes). For instance in our above example, quantity demanded is the dependent variable and price of the commodity in question as the independent variable.

(iii) In words
An economic model can as well be expressed in words for instance, “when the price of a commodity increases, its demand falls”. Such a statement implies that quantity demanded and price of the commodity are related, specifically they are inversely or negatively related.
Stages in Model building
Generally, there are two major stages in model building:

i) Identifying the factors that are likely to affect the variable in question; for instance suppose the task is to find out how the quantity of beef demanded, responds to changes in its price. We would therefore, need to build a model for quantity of beef demanded. We however note that the quantity of beef demanded at any particular time period is affected by several factors other than its price such as price of its related commodities which include both compliments (i.e. commodities that have to be consumed together rather simultaneously at any one time such as tomatoes, cooking oil, salt etc. and substitutes (i.e. commodities that can be consumed in place of another due to the income constraint such as fish, chicken, beans, peas and others). Another factor that affects the quantity of beef is tastes and preferences of the consumers. Other factors include; consumers’ incomes, religion of the consumers (for instance Hindus do not eat beef Moslems do not eat pork). Time-period is another factor of demand (for instance, around Christmas, people tend to purchase more beef), size of the family (population), past quantities of beef purchased and many other factors. The above analysis can be summarised by the following equation.

Qdb 	= 	Q(Pb, P,, T, Y, PT, A)
Where:
Qdb 	=	Quantity demanded of beef
Pb 	=	Price of beef
Py	=	 Price of related commodities e.g. fish
T 	= 	Tastes and preferences
Y 	= 	Consumer’s income
PT 	= 	Time period
A 	= 	Other factors.

ii) The second stage involves data collection on the identified variables. Data on the variables that can be measured (quantifiable) e.g. price of beef, income of the consumer’s price of related goods, is collected and it is then subjected to economic analysis using either statistical or econometrics techniques, so as to estimate the actual strength of each independent variable postulated in the model. The intention is to determine how each independent variable affects the dependent variable.

For instance suppose the price of beef changes by 10 percent, by what percentage will quantity demanded of beef change? Alternatively, suppose the consumer’s income changes by 10 percent, by what percentage will the quantity demanded of beef change or suppose the price of fish changes by a given percentage , by what percentage will quantity of beef change. The Econometric results of the model also enable us to tell whether fish is a substitute or compliment to beef and whether a weak or strong substitute or compliment.

1.3	Assumptions in Economics
Economists use assumption so that they can easily explain a phenomenon particular that may be explained by a number of factors. In which case if all variables or factors were allowed to change, we could hardly be in position to tell the impact and direction of factor on the given phenomenon or variable. These assumptions are used so as to try to reflect the most important aspects of behaviour in models. This enables economists to study the behaviour of an aspect and hence draw conclusions or predictions whenever there is a change in one variable. Time and again, economists use a statement “Ceteris paribas”. This is a key assumption in economics; it is a Greek statement, which means, “Other factors kept constant”. It enables the researcher to imagine that other factors that affect the aspect under investigation (dependent variable) do not change, instead only one factor (independent variable) changes. This enables the researcher to draw conclusions, which we would otherwise not have done if other variables or factors changed as well.

For instance, let us consider quantity demanded of beef. We know that the amount of beef purchased by an individual or house hold is influenced by several factors as we saw earlier. It would therefore be difficult to tell the impact of a change in price of beef on quantity demanded if other factors since as consumer’s income, size of the house hold, price of other goods such as fish changed as well. Therefore to be in position to tell the level of impact and direction of impact of change in price of beef on the quantity of beef demanded. We would assume that other factors that affect the quantity of beef do not change at that particular time period.

Assumptions and models therefore are used to simplify the examination of a problem under discussion. However, two problems are likely to occur during construction of a model, and these are;

(i)	 Over simplification: This may remove an important aspect of the situation under discussion. For instance, consider a demand function Qd = Q(P) which assumes that price is the only determinant of quantity demanded. This model is over simplified and may lead to false results.

(ii)	Under simplification: When a model is under simplified, it leaves the important aspects obscured by too much detail, for instance,

Qdb 	= 	Q(P, P,,Y, T, Q, A, R, S, E, M, P0, Y0)
Where
Qdb 	= 	Quantity of beef demanded
P 	=	Price of beef
R 	= 	Religion of the consumers
Py 	= 	Price of other goods e.g fish
S	= 	Sex of the consumers
Y 	=	Income of the consumer
E 	= 	Education of the consumers
T 	= 	Tastes of the consumer
M 	=	 Marital Status of the consumers
Q 	= 	Quality of beef
P0 	=	Population distribution
A 	= 	Age of the consumers and
Y0 	= 	Income distribution –

We note that some factors for instance age, education, sex, marital status etc may not be good determinants of quantity of meat demanded. So such variables tend to eclipse the key determinants.

1.4	Fundamental Economic Problems Scarcity, Choice and 	Opportunity Cost

Scarcity
Resources and commodities of decision makers no matter how large they may be are always limited, thus less than people’s desires. As a result, everyone has some hard decision to make. In order to obtain something of value another good has to be given out. A good is said to be an economic good when it is not free. And such a good is said to be scarce, so scarcity gives rise to price. For that matter, due to limited income, when one gets money or expects to get money, she may list down the different items, their quantities and prices that she intends to purchase. She then makes sure that the total amount to be spent is less or equal to the income. During the actual purchase, a rational consumer starts with the most pressing want, and then the less pressing are subsequently purchased. Such a list of priorities is what is referred to as the Scale of Preference. A scale of preference is common among students going to colleges, heads of families even a State. It is because of scarcity that man or woman makes a scale of preference or sets priorities otherwise he would acquire any commodity at any one time. At the aggregate level, all countries in the world whether poor or rich, make budget proposals each year which is a result of scarcity of resources.

Choice
Choice arises out of scarcity and it simply means making the right decision.. Because of the scarcity of resources, man must make a scale of preference. As noted above, a scale of preference is where items are arranged according to order of priority. Here, the most preferred or pressing need is placed in the first position then another item is place in the second position until the last item which is least pressing. When a consumer chooses the first item, then the second, he or she is said to be making choice.
Opportunity Cost:
When a consumer uses her scale of preference to make choice, it implies that she is making a decision to satisfy/choose one set of wants. But this necessarily means sacrificing some other set. It is apparent that the consumer is making choice because her resources cannot enable her to acquire all that she needs. In other words, it is because of her limited, rather scarce resources (e.g. income) that she chooses commodity A and leaves B for the meantime. By making choice therefore, she is sacrificing commodity B for A. It is this sacrifice which is referred to as Opportunity cost in economics. Therefore, opportunity cost refers to the alternative foregone of one good for another. For instance, if a consumer purchases a house instead of 3 cars using his limited income then the opportunity cost of a house is 3 cars. So opportunity cost is a real cost, and it arises out of scarcity and choice.

 Production Possibility Curve (PPC)
A production possibility curve or production possibility frontier (PPC or PPF) is a curve that joins together the different combinations of two goods or services that can be produced by a country or any other economic entity such as a firm when all its resources are filly and efficiently utilized.

When defining a PPF, the following assumptions are crucial:
a)	Two commodities are produced e.g. cars and maize or capital goods and consumer goods.
b)	Technology is fixed.
c)	Resources are given or fixed.
d)	Resources are fully utilized.
e)	Technology is efficiently used.
igure 1.1: The production Possibility Curve / Frontier 
	Cars
                            C1		A	.F
                            C2		B

                            C3		E	  C

                            C4		D
	PPF
	M1     M2       M3   M4        Maize

Points along the PPC such as A, B, C or D show the maximum physical combination of cars and maize which can be produced when all resources are fully utilized and when technology is efficiently utilized. Along a PPC, an increase in the production of one commodity say maize can only be done at the cost (sacrifice) of another commodity, cars (i.e. moving from point A to B on the graph). In other words, to increase the out put of maize, that of cars has to be reduced. This implies that a PPC has a negative slope specifically it is concave to the origin and its slope increases as one moves down the curve.

A point inside the PPC for instance point E, shows a combination of maize and cars that can be produced by the economy using less of the available resources and technology. So such a point is not desirable because it is a point of under utilization of resources. In other words, at point E, the firm or economy can increase the production of either maize or cars or both without affecting the output of the other commodity. For instance, moving from point E to point A on the PPC, the economy increases the amount of cars from C3 to C1 and leaves the quantity of maize unaffected at M1. Alternatively the economy could move from point E td C on the PPC and by so doing, it increases the output of maize from M1 to M3 leaving that of cars unaffected (i.e. at C3.). The economy can as well decide to increase the output of both maize and cars by moving from point E to any point between A and C say point B. At point B on the PPC, the output of maize and cars increases from M1 to M2 and C3 to C2 respectively.
So if an economy or firm produces inside its PPC, then it implies that either there is under employment of resources or there is use of inefficient technology or both.

It is believed that many developing countries produce inside their PPC and this is because:
•	A lot of their natural resources e.g. mineral are unexploited.
•	They have poor production techniques.
•	Are always embedded in political instabilities, which discourage production.

On the other hand, a point outside a PPC for instance point F in the above diagram, is desired by every economy or firm because it shows greater output of both maize and cars over and above *hat the economy can potentially produce. However, such an output level can not be achieved due to resource and technological constraints. For such an output level to be achieved, then there must be either one of the following or a combination of these factors:

•	Discovery of new resources e.g. new mineral deposits, land reclamation etc.
•	Discovery of new technology
•	Grants and donation.

Let consider a simple example of an individual with fixed amount of land on which she produces maize and beans. Given the available land, production techniques say hoe, type of seeds used, and labour, the maximum combinations of maize and beans that she can produce is given by points along the PPF such as A,B,C,D. At the prevailing conditions, the individual can never produce beyond the PPF, however, she can move to a point outside the PPF say point F if and only if any of the following or a combination of the following takes place.

•	He reclaims some land if she happens to live next to a forest or swamp, so as to increase on the size of her land holdings: This is similar to discovery of new resource.
•	A relative or friend donates her more land.
•	She uses fertilizers or better farming techniques such as tractors, pesticides hybrid seeds etc: This is similar to adopting new production techniques mentioned before.
Finally, a movement from a point inside a PPC e.g. point E toward a point on the PPC from a point on the PPC to a point outside the PPC shows economic growth.
1: Shifts in the PPC
s noted above, a movement from a point on the PPC to a point outside the PPC shows economic growth. This therefore involves a shift in the PPC outwards to the right. However, there are two types of shifts; un-biased shift and biased shift.
Unbiased shift
Under this form, the PPC shifts parallel to the original one implying that the innovation discovery of the new resource equally encourages the production of both commodities as shown below.
Figure 1.2: Unbiased shift in the PPF

	Cars

	PPC2
	0	PPC1
	Maize 
Such a shift can be as a result of either discovery of new resources or new technology or both as long as they equally favour production of both cars and maize. 

Based shift 
In this case the shift in the PPC is not parallel to the original one as shown below. 
Figure 1.3: Biased shift 

Cars 	        Cars 

	0	0
	Maize 	Maize 
	(a)	(b)
Figure (a) shows that the discovered resources or technology favours maize production and none or very little of cars. For instance a discovery of fertilizers or land reclamation would favour to a greater extent maize production than car production. On the other hand figure (b) shows that the discovered resources or technology favours production of cars and none or very little of maize production. 

Relationship between Production Possibility Curve, Scarcity, Choice and Opportunity Cost
Introduction
In the preceding section, we introduced some of the economic concepts. We recall that a production possibility curve (PPC) is sometimes referred to as production possibility frontier (PPF) or production transformation curve. In this section we shall look at the inter-relationship between these four concepts i.e PPC, scarcity, choice and opportunity cost.

1.5	Production possibility curve, scarcity, choice and opportunity 	cost
We have seen that a PPC reflects the maximum quantities of two commodities that can be produced by an economy. Also we have seen that, the slope of a PPC is negative. We however, note that this upper limit (maximum quantities) is as a result of the limited resources. So, due to scarcity of resources, there must be a limit on the output level that an economy can produce. Also the negativity of the PPF signifies that because resources are scarce, to increase the output of one commodity, say maize that, of another (cars) has to be reduced. This is as a result of the competition for the scarce factor inputs.

From the definition of the PPF, we further note that the economy has several alternative commodity combinations that it can produce at any one time. The question however, is at what particular point on the PPF, should the economy produce? In other words, should it be commodity combinations A or B or C? (Refer to figure 1.1). The decision of a firm or economy to produce at any point on the PPC depends on the choice of the society. If the society wants more cars than maize, then the economy should produce at point A. If on the other hand the society wants more maize than cars, then it should produce at point D and so forth. Choice is therefore determined by the social cost welfare of the society, and the type of the economic system, (this shall be discussed in the next chapter).

Now if the society chooses to produce at either A or B on the PPC, it produces more of one commodity than another. For instance, if it chooses to produce at point B instead of A (i.e. M2, of maize and C2 of cars), it means that society will consume M1 M2 more of maize and C1, C2 less of cars. This implies that society is sacrificing C1 C2 less of cars for more M, M2 of maize. So the opportunity cost of producing M1 M2 more of maize is C1, C2 of cars foregone.

 Slope and Shape of a Production Possibility Frontier
The proceeding section arbitrarily imagined that the PPC is concave to the origin much as it laboured to justify the negativity of the slope of the curve, it did not justify the concavity of the curve. We therefore need to understand why the curve takes a concave shape and not any other.

The slope of a PPC is referred to as the Marginal Rate of Product Transformation of commodity X and Y (i.e. MRPTx,y). It shows the quantities of commodities Y (e.g. cars) that must be given up in order to produce an additional unit of commodity X (maize). We recall that the PPC has a negative slope. This means that for a firm or an economy, to increase the production of one commodity, it has to forego the production of some units of the other commodity.

Mathematically we can derive the slope of the PPC as follows;
We recall that an economy can not produce beyond the boundaries of the PPC; given the prevailing conditions therefore combinations along the PPC show the maximum output combinations possible. This means that the change in output along the PPC is zero i.e. given the economy’s output function as;

Q	=	Q(X,Y).

This means that output (Q) depends on the quantities of commodities X and Y produced. Since change in output is zero along a PPC, then, we now use calculus to obtain total derivative which is;
		Dq	=	

As noted above the change in total output is zero. Rearranging we get; 		

This finally gives us;

			=  MRPTY.X

MRPTY.X means Marginal Rate of Product Transformation of commodity Y for X. It is the slope of Production possibility frontier.
The negative sign means that the slope of the PPF is negative, meaning that to increase the amount of commodity X, that Y has to be reduced and vise versa. But a negative slope could imply a number of different shapes of a curve such as, convex, linear or concave. We next look at the different shapes of a PPF and their possible implications.
1.6	Implication of a Concave PPC
Diagrammatically, a concave PPC takes the following shape.

Figure 1.4: A Concave PPF
	Cars
                            C1		A	
                            C2		B

                            C3		E	  C

                      C4  

    		D
	
	M1     M2       M3   M4        Maize

We assume that the graph is drawn on the same scale for both axes; we note that at point A. (i.e. towards the Y axis), the economy or firm produces more cars than maize so cars are abundant. Also at a point towards the X-axis such as D, the economy/firm produces more maize; hence maize becomes more abundant towards the X-axis.

The gradient of the PPC or the Marginal Rate of Product Transformation between points A arid B i.e. MRPTA,B is given as:     
But this is smaller in absolute terms than the slope between points C and D which is;
				
The above illustration implies that along any concave curve, the slope of the curve increases (in absolute terms) down the curve. This therefore means that for a firm or an economy to produce more units of another commodity X (maize), it has to fore-go more resources that were initially used to produce commodity Y (cars). In other words, the opportunity cost for a firm/an economy increases as it reallocates resources from the production of one commodity to another. This can be seen to mean that; it becomes increasingly more difficult to transform cars into maize. During the production of cars, raw materials such as steel, rubber, sophisticated technology and others are used. The concave curve therefore assumes that it is difficult and indeed it becomes increasingly difficult or costly to transform steel machines, rubber raw materials, motor vehicle engineers and the elated highly trained personnel into fertilizer production, hoes and farmers so as to increase maize production. Ideally, the curve seems to be more realistic because when we compare an engineer, or an accountant working with a motor vehicle plant, we realistically note that it is very difficult to transform such personnel into competent maize farmers. 

Implication of a Convex PPC
Let us now consider a convex PPC given by figure 1.5. The slope of the curve is given by a change in the vertical axis divided by a corresponding change in the horizontal axis. If we consider two sets of points A, B and C, D their responding slopes are; 
	 And  , respectively. 
Figure 1.5: A Convex PPF

	Cars 
	     C1	A

	C2	B

	C
                          C3			 D
             
             C4
	0  
			M1    M2 	       M3       M4			Maize 

Contrary to the concave PPC, along the convex curve the slope of the PPF (i.e. MRPT) diminishes (in absolute terms) down the curve. This therefore means that the   MRPT diminishes down the curve. The fall in the gradient implies that the opportunity cost decreases as more of ope commodity is produced. Technically this means that it becomes increasing easier to transfer resources from the production of commodity Y (cars) to the production of another commodity X (maize). In other words, that resources that were initially being used to produce cars e.g steel, computers, factory engineers can easily be transformed to those that are used to produce maize e.g. fertilizers, hoes etc. This appears to be unrealistic because different commodities require different production technique and different inputs. These may not favour the production of another commodity at all.

  Implication of a linear PPC
A linear PPC has a constant slope which means that the MRPT is constant.

Figure 1.6: A Linear PPF / PPC

	Cars 

	A
	 C1

                      C2                                      B
	Linear PPF
                        0
	M1              M2	Maize 
 
The slope of the line at A and B and any other point is the same: Technically, the curve assumes that it is equally difficult to produce commodity Y or X. In other words such a curve assumes that resources or factor inputs used in the production of Y (cars), and X (maize) are the same. It further means that a fixed number of cars are equivalent to a given quantity of maize. But this is indeed unrealistic because factor inputs used to produce cars are very different from those used to produce maize hence may not be comparable.

Generally however, we need to agree that as a commodity becomes scarce, it tends to be dearer to the producer and consumer, “ceteris paribus”. This therefore means that the firm or economy will incur a higher opportunity cost when it tries to transform the scarce commodity into an abundant one. In other words, as we move down the PPF, the’ commodity on the Y-axis becomes more and more scarce hence dearer than that on the X-axis which now becomes more abundant. This analysis justifies why a PPC is concave to the origin.
	
1.7	Economic Systems
 
Introduction
An economic system refers to the means by which decisions involving economic variables are made in a society. It should be noted that the fundamental economic questions are answered differently depending on the economic system. Basically there are four general types of economic systems namely: The Traditional economy, the Command economy, the pure Capitalism and mixed systems.

 The Traditional Economic System
In primitive economies or in the early stages of economic development the organization, production and distribution is frequently governed by tribal rules or customs. The economy is ‘embedded’ in the social structure of the community and people often perform economic tasks for non- economic gains. Production is communal and what is to be produced is determined either by the heads of communities or predetermined by social norms and rules. Distribution is done by heads of communities but not market forces. And resources are communally owned.

 The Command or Centrally Planned Economy
This economic system is governed by an authoritarian central government. So, such an economy operates on orders from those in power. Decision making or ownership of factors of production is by government. This system is also referred to as centrally planned because in this system the fundamental economic questions of what, how for whom and where td produce decisions, are made on a collective or group basis. In addition there is collective ownership of factors of production. In this system there is very little freedom of choice. The central planners determine the occupation of workers, the quantities of each type of good or service to be produced and the distribution of income. The fundamental economic questions of; what, how, when, for whom and where to produce, are all determined by the state. Particularly, the question of how to produce, such States always prefer labour intensive techniques to capital intensive ones.

 Pure Capitalism
This is characterized by freedom of choice exercised by consumers and producers in the market for goods, services and resources. There is private ownership of goods and the factors of production such as labour. It is also characterized by perfect competition with o government intervention in the market and production process.

In purely market economies the fundamental economic questions of what, how, when, where and for whom to produce are determined by forces of demand and supply which set prices for goods and services. Individuals in the free markets pursue their own interests, trying to do as well for themselves as they can without any government intervention and in the end they too benefit the society. This is what Adam Smith referred to as the “invisible hand”. Examples of economies that are close to market economies include U.S.A. The United Kingdom, Japan, Germany, France and other developed economies.

 Mixed Economy
This lies between the two extremes that is the command and capitalist economies. In mixed economies government and the private sector interact in solving economic issues. Government controls a significant share of the economy, through; taxation, transfer payment and provision of public goods and services. The private sector on the other hand, provides the private goods and services.

We should however, note that in the real sense, there is no country which is purely command economy or purely capitalist. Indeed all countries are mixed economies, but the degree of government-private sector participation differs. There are those which are more centrally planned while others are more market oriented. Nevertheless, among the mixed economies are the less developed countries such as Uganda, Kenya, India, the “Tiger” i.e. Taiwan, Hong Kong, South Korea, Thailand, Singapore”, Latin American countries and virtually all African countries.

 Answers to the Fundamental Economic Questions under Pure Capitalism
a) What to produce?
Under the capitalist system, what is to be produced is determined by the consumers’ demand through their offers to purchase goods and services at various prices and also by the available factors of production and their prices. It is through this system of prices that order is maintained in the market place and production of goods and services that society wants is stimulated. For instance, if consumers express their desire to have bicycles, computers, snacks, beer, by offering prices that cover the production costs and a profit margin and also if the factors of production, that is; technology, raw materials and other factors -of production are available, the goods will be produced. According to Adam Smith, in a market economy, it appears as if an “invisible hand” is guiding the economic activity so that the wishes of the society are fulfilled, even as individuals work to further their own interests.

The concept of the invisible hand emphasizes that individuals pursue different tasks which involve inventions and innovations all aimed at promoting one’s interests. For instance, by an individual putting up a school, the major objective is to earn income. But in so doing, he benefits the society by providing education and employment opportunities. Also when an individual puts up a shop, the objective is to get profit, but in the process, he avails the society with the essential commodities and also takes the services closer to the community which saves time and money that would have been incurred when moving to a far away place where such services could be got. Smith (1976), in his book of “The wealth of Nation”, states that “By pursuing his own interest an individual frequently promotes that of the society more effectually than when he really intends to promote it”.

b) How to Produce: Under the capitalist system, producers will aim at producing goods and services at the lowest possible cost. Thus how to produce will depend on the available techniques and availability of; natural resources, capital, labour and their relative cost. Producers will use the cheaper technology to produce goods and services so as to maximize their profits.

c) For Whom to Produce: Under the capitalist system, who gets the goods and services that are produced is determined in the market place. The goods and services produced are for those people who are willing and able to purchase that is those who express effective demand for the goods and services. Production will be based on the demand for goods and services, therefore goods and services produced will be for those who can afford to buy them.

The outcomes of these transactions reflect the distribution of income and wealth. In other words, under the capitalist or free enterprise economy, the distribution of income and wealth depends on the ownership or distribution of talents, abilities and factor endowments.

d) When to produce: In a pure capitalist system, this decision is determined by individuals such as consumers, workers, owners of firms and managers of firms. Producers will aim at maximizing profits while consumers aim at maximizing satisfaction. Thus consumers will consume in those periods which maximize their satisfaction, while producers will produce in those periods when their profits are maximized. So for what ever decision each individual consumer or firm takes, the long-term implication of the current decisions is open to question.
Summary
Basically there are four types of economic system: Traditional, market oriented, centrally planned, and mixed economic ‘system, Price and resource allocation are determined differently in the four systems. Whereas demand and supply forces (market forces) determine the price and resource allocation and a market system, the central government sets the price and allocates the resources under centrally planned system and both market forces and government set price and allocate the resource in the mixed economy.

Also we must note here that there is no state or economy that is purely market oriented or centrally planned. Instead all economies are mixed. However, the degree of mixing differs from state to state.

1.8	Price Mechanism
This is defined as an economic organization in which scarce resources are allocated according to prices. The resources include: the factors of production, what to produce and consume. 

Conditions / assumptions
The allocation of resources refers to the movement of resources from unwanted regions to wanted region.

The unwanted regions are the ‘resources which are being used to produce what is not demanded or desired by consumers. The wanted regions are the resources which are used to produce what is demanded.

Conditions for Price Mechanism 
In order for price mechanism to operate in an economy there should be the following conditions:
•	Prices in a market should be determined by the forces of demand and supply. There should be free market forces. 
•	There should be no government influence in a market. Such an economy should be a free enterprise economy or unplanned economy or Liaises faire. 
•	There should be consumer’s sovereignty. This means that a consumer shou1d be a king in a market. He is the one to determine what to produce, how much to produce and when to produce. 
•	There should be perfect competition. This is where there are many producers and sellers competing for consumers. 
•	Production should be according to demand. What is produced is what is demanded. 
•	Factors of production should be perfectly mobile. It is easy to move factors from one area of production to another.
•	Factors of production are perfectly substituted.
•	Producers have a large freedom in the market on what to buy, when, how and how much.

How Price Mechanism Allocates Resources 
Resource allocation refers to the process of moving resources from unwanted -regions to wanted regions, this is when producers are rational by minimizing losses so as to maximize profits. When the above conditions are present price mechanism will allocate resources in the following ways: 

Under price mechanism, the aim of the of the consumer is to maximize utility. This means that the consumer wants to get the highest satisfaction from every unit of money spent. This will imply that the consumers will always buy from the cheapest sources. 

The aim of the producers is to maximize profits and this is done by:
•	Minimizing the costs of production. 
•	Charging low prices as possible.
•	Minimizing any losses. 
•	Attracting many customers, so as to increase on market sales. 

Since producers produce at different costs of production, there will be efficiency firms and inefficient firms. And an inefficient firm is that firm which produces at a higher cost of production and therefore charges lower prices. 

Assuming that there are two firms A and B. Firm A is efficient and firm B is inefficient. Firm A will compete with firm B through price competition i.e. by reducing prices since firm A is smaller. 

Firm B will reduce prices up to a point where it will be out competed. The efficient firm therefore, will employ the resources formerly used by the inefficient firm that has closed down. In this way, the resources would have moved from unwanted region (firm B) to the wanted region (firm A). This is referred to as resource allocation. 

Similarly, price mechanism allocates resources according to the demand for a commodity. When there is an increase in demand, consumers are indirectly informing the producers to produce more of a commodity. This is referred to as casting of votes. Producers will also increase the production of a commodity where more votes have been casted. The increase in production will be according to the increase in demand for example suppose the producer produces two conmiodi1ies namely beaus and peas, if there is an increase in demand for beans, the producer will produce more of beans. This is done by diver1ing resources from the production of peas so as to produce more beans. By using resources formerly used to produce peas so as to produce beans is resource allocation, Resources will move frond unwanted regions (production of peas) to wanted regions(production of beans). However, it should e noted that the producer should put in the mark the amount of output equal to the number of votes increase in demand.

Advantages of Price Mechanism 
•	Price mechanism determines what to produce. The producers do produce according to demand. If the demand for a commodity is higher, producers will move their resources to the production of such a commodity. 
•	Under price mechanism, there is no wastage of resources. Since production is according to demand, there is no liability of losses. Losses would occur if what is produced is not demanded but this is not so under price mechanism. 
•	Under price mechanism, there is consumer sovereignty. A consumer is a king in a market which reduce exploitation. Consumers will know what to buy and when to buy it. 
•	In price mechanism, producers are efficient. They minimize costs of production so as to maximize profits. There is an advantage in that consumers will buy goods cheaply from the market. 
•	Price mechanism determines whom to produce for and when. Producers will produce for those with high demand for a commodity. In answering the question of when to produce, producers will produce when demand has increased. 
•	Producers can fully utilize resources under price mechanism. If there is high demand for a commodity a lot of resources is used and this will ensure full employment (utilization) of resources. 
•	Price mechanism help in resource allocation to where they are best wanted. When prices increase due to1ncrease in demand resources will be diverted to those areas of production.
•	Price mechanism encourage producers to produce mores .When price increases, more will be produced.
•	Price mechanism encourage arbitrage hence equally  distributed benefits.
•	Price mechanism gives freedom to producers to make independent decisions that are free of government influence.
•	There is no monopoly under price mechanism. Hence competition helps in improving quality and charging low prices.

Disadvantages
•	Price mechanism may lead to unemployment. Due to perfect competition, some firms may be out competed. Those people formerly employed may remain jobless. Even though the efficient firm uses the resources of the inefficient one but not all of them will be used. 

•	Instability in prices and incomes. Price mechanism operates under perfect competition where there is price competition. Producers continue attracting customers by lowering prices hence leading to price fluctuations. In case of income instability, firms which are out competed will reduce on the level of earnings which all will affect the incomes of employers. Similarly when labour remains unemployed, there is a reduction in the level of income. 

•	Price mechanism may not produce public goods. These are goods that are demanded by the poor population for example public buses, roads, hospitals, etc, these are produced cheaply and supplied at no profits. The producers under price mechanism who are profit motivated will not produce them since they don’t give them enough profits. In this way the poor are ignored. 

•	Price mechanism may encourage producers to produce luxuries. This is because production is according to demand and since the rich people have  high demand or can offer high prices or can cast more votes that the poor, what will be produced only will for the rich. 

•	Price mechanism may encourage income inequality. Some people may become rich or better of than others for example if some people become unemployed due to price mechanism, those will remain employed will earn a higher income. While some become rich, others become poor. Similarly, since production is according to the rich, the poor are ignored. This also encourages income inequality. 

•	Price mechanism may encourage over utilization of resources. Due to high demand for a commodity producers will divert all their resources to the production of that commodity. This consequently will lead to resource exhaustion for example fish extinction, deforestation and soil exhaustion.  

•	Price mechanism may not maintain the standards of living of people. One commodity may be produced and consumers will suffer from the range of choice. This is because many goods where demand is low cannot be produced. Dependence on few goods affects standards of living of people.  

•	Price mechanism may not utilize all ho resources in a country. This is because resources are not evenly distributed. What may be demanded may not necessitate to use all resources e.g even if the demand for beans increases, riot all land will be used to produce beans. 
•	The assumption under price mechanisms are un-realistic. In today’s world, there is no consumer sovereignty nor is there perfect competition. Similarly it is not obvious that if a firm is out competed it simply closes down. Some times a firm may continue operating even though it is earning normal profits. 
•	 Inability of price mechanism to cope up with the structural changes with in the economy. Structural changes mean the movement of one structure of economy from one state to another for example a shift from subsistence production to monetary production, a change from traditional methods to modern methods, a shift from illiteracy to literacy  etc the reason for the inability is that structural changes require governments’ effects where some costs are made without immediate returns. The move from susistance production to monetary will require the government to meet the cost of education supply farmers with cheap inputs etc such cannot be met by price mechanism.

Factors That May Limit Price Mechanism To Allocate Resources
•	Consumer’s ignorance: This means lack of proper or perfect knowledge in market. This is the knowledge pertaining to prices, availability of goods when they are available end how to buy them. It is usually created by advertising and business propaganda. A consumer may be deceived that a commodity due is going to buy is cheap and of high quality when it is not ignorance in a market will limit price mechanism allocate resources because consumers may not know when the goods are available. They may be produced but not be consumed. Consumers may demand what is not produced and producers may produce. 

•	Un equal distribution of income: In the real world, there is income inequality. The poor live together with the rich. This limits price mechanism because the rich tend to dominate the market such that production goes to the demand of the rich. In the way, the poor will not determine resource allocation and if they are the majority in the country, price mechanism will be limited. 
•	Interference of the government or government influence in an economy. Due to failure to cope with the structural changes in the economy or producing cheap consumer goods, the government interference by setting up her own enterprises to supply cheap goods and services for example construction of roads, hospitals, schools. These compete with price mechanism whereby resources may go to the government because of being at cheaper cost. As a result, price mechanism will be rendered a failure.
•	Price control: This means the fixing of prices by the government upon which sellers should sell their commodities and buyers or consumers pay for them. Under price control, there is no free movement of prices to determine allocation of resources. 
•	Unemployment: Price mechanism leads to unemployment of labour and other resources. When one firm is out competed, it simply closes down. The resources formerly employed may remain unemployed. If this happens, labour will have a fluctuation in income which will affect price mechanism. Those who are formerly casting votes will not do so when they become unemployed.  
•	Price mechanism lads to a divergence between a private benefit and a social benefit. The former refers to the benefit which to the individual and the latter one refers to the benefits which are connected to the whole public. Price mechanism therefore will put private benefits on the expense of social benefits e.g. if there is an increase in demand for fish, individuals (fish mongers) may increase the supply of fish leading to fish extinction. However, this is a private benefit on the expense of a social benefit or public benefit. If resources are exhausted, price mechanism will stop allocating resources since there are not there. 
•	Lack of consumer’s sovereignty in the market. In the real world, consumer’s sovereignty is determined by income. This means that there are very few customers who are kings in the market. Such are the ones that allocate resources but not all consumers. Producers are not influenced by the demand of the consumers are price takers but not the price givers.
•	Influence of a monopoly. Monopoly refers to a market situation where there is one seller / too many buyers or consumers. His commodities have no substitutes that are competitors. A monopolist has powers to determine the price and the output. He is not influenced by the consumers in price determination. He is the price giver while consumers are price takers. Therefore, price mechanism does not apply in such a market.   

 Review Questions
1.	Clearly explain how the fundamental economic question are addressed in a capitalist economic system
	(a) Define Economics,
(b) Distinguish between;
i) Microeconomics and Macroeconomics,
ii) Positive Economics and Normative Economics.
2.	Clearly state the fundamental questions that Economics addresses.
3.	Distinguish between scarcity, choice and opportunity cost.
4.	(a) What is a production possibility frontier (PPF)?
	(b) What factors may lead to a shift in a PPF?
5.	Clearly explain the relationship between a PPF, scarcity, choice and opportunity cost.
6.	What is the Economic implication of the following shapes of a PPF?
(i)	Convex PPF, Concave PPF, Linear but down ward sloping PPF

Unit 2
Market Analysis

2.1	Introduction
The fundamental economic questions of what, how, when, where and for whom to produce rely mainly on markets. A market is a place where buyers and sellers come into close contact. It can take place in offices, internet, geographical place, etc. It is in markets that prices are determined. Prices act as a guide to the solutions to the fundamental economic questions. In a perfectly competitive market, supply and demand forces also referred to as market forces determine the price of a commodity. This chapter forms the basis for most economic aspects and branches of economics that involve the study of price mechanism. Price of a service or good can be in different forms e.g. exchange rate, interest rate, wage rate, producer price, commodity price etc. We shall discuss this chapter in two parts; demand analysis and supply analysis.

 2.2	Demand Analysis
Several concepts are considered under the theory of demand such as factors of demand and mechanism of demand, the demand schedule and curve, shifts in the demand curve, individual demand curve and market demand curve. In simple terms, demand refers to the desire to have or own some thing. This may not necessary be backed by ability to pay for the good at different prices (effective demand) which is shown by a demand schedule. Effective demand on the other hand refers to the quantity of a commodity that a consumer is willing and able to purchase at a given price. It is shown by a demand schedule. However let us first look at the general expression of demand usually given by a demand function.

 The Demand Function
This explains the relationship between quantity demanded of a commodity and factors that affect it. It can be expressed implicitly as Qd = Q(Xi): i = 1,2,...,n where X is a vector of factors that affect demand such as own-price, price of other goods, consumer’s income, tastes and preferences of the consumer and other factors. At any one time, the quantity of a commodity that a consumer will effectively demand or purchase depends on several factors. These include;
•	Price of the Commodity: This is considered to be the major factor of quantity demanded of any good or service. Indeed the relationship between the price of the good in question (under investigation) and the corresponding quantity demanded gives rise to a demand curve. Generally, a consumer is likely to demand more of a commodity when its price falls and less of the commodity when its price rises. This is true for a normal good. This is because given fixed income of a consumer; she can be able to purchase more units of a commodity only when its price falls ceteris paribus.

•	Income of the consumer: Another major factor of demand is the consumer’s income. Time and again, we observe richer individuals purchasing goods such as fiiel, meat, telephone, credit cards, and drinks to mention but a few in large quantities while the poor usually buy in smaller quantities of any good. And when one’s income level change, his/her expenditure pattern change as well. Usually, more of a normal commodity will be demanded when the consumers’ income increases and less of it will be demanded at lower incomes. However for an inferior commodity, less of a commodity is demanded at higher income levels of a consumer and more of commodity will be demanded when the consumers’ income falls.

•	Price of related commodities: Related commodities can either be compliments or substitutes. Complimentary commodities refer to those commodities that have to be consumed at the same time e.. coffee and sugar, car and fuel, beef and tomatoes, beef and salt, etc. On the other hand substitute commodities are those that may not be consumed at the same time or those where consumption of a commodity may stop the consumer from consuming the other. For instance riding a motorcycle or bicycle, taking tea or coffee, eating fish or beef. The last combination (i.e. fish and beef) suggests that substitute commodities are not always necessary mutually exclusive.

For instance let us consider two goods; X and Y. Supposing that they are compliments, from our previous discussion, an increase in price of commodity Y would lead to less of Y demanded. But since the two goods X and Y have to be consumed at the same time, then, a reduction in quantity of X demanded will necessarily lead to less of quantity Y demanded. Now if X and Y are substitute commodities, an increase in price of X leads to an increase in quantity demanded of good Y. This is because, when price of good X rises, less of it shall be demanded and since good Y can play the same role as X, then the consumer will substitute the now expensive good X by purchasing more units of the cheaper good Y. Therefore other factors fixed, the lower the price of a complement the greater the quantities demanded of another good. And the lower the price of a substitute, the less the quantity demanded of another good.

•	Tastes and Preferences of the Consumer: Many commodities are consumed due to consumer’s tastes and preferences and any change in tastes may adversely affect the quantity demanded. Such goods may include food, fashions, cars, drinks and many others. Preferences can either be natural or under influence from peers. Generally, however, a consumer’s tastes and preferences can change at any one time and will affect the quantity demanded of the good in question. For instance supposing that tastes change in favour of a commodity, then, more of that commodity will be demanded. On the other hand, less of the commodity will be demanded when the tastes and preferences change in disfavour of a particular commodity. This is very common with fashions and food. For instance in Uganda, the demand for fish from people around Lake Victoria fell drastically in 1994 after viewing the dead bodies of the Rwandese killed during the 1994 Rwandan genocide, floating on the lake.

•	The expected price of the commodity: If the future price of the commodity in question is expected to fall, consumers will demand less of the commodity now. On the other hand, more of the commodity will be demanded or purchased when its price is expected to rise. This is however, common with goods that are not perishable. For goods whose consumption can be postponed or goods that can easily be stored for future consumption, price expectation matters a jot on the decision to consume now.

•	Seasons of the Year: Some goods tend to be consumed during certain seasons, so their demand is likely to rise during such seasons. For instance, during wet seasons, people demand more umbrellas and rain coats. Also during Christmas or Edi season, more Christmas cards or Edi cards are demanded.

•	Religion and Culture: The quantity demanded of a commodity, may also be affected by religion and culture of the consumers. For instance, the demand for pork is likely to be low in a society where there are many Muslims. Also in some African societies, certain commodities are prohibited, meaning that the consumption is a taboo; while some cultures promote the consumption of certain commodities or certain fashions of goods (such as dresses such as Busuuti or gomesi in the central region of Uganda). So in a society where more of the consumers, customary promote the consumption of a particular commodity, then more of it will be demanded and vice-versa.

•	Sex: This is also another important factor of demand. It is worth noting that certain commodities are consumed by a particular sex group. For instance shirts, skirts, bras and others. Particularly, the demand for bras is likely to be high in a society where there are more female than male, keeping other factors constant. So we would expect the demand of bras to be high in a girls’ hostel and that of shirts to be high in a boys’ hostel.
•	Level of Education: there are certain commodities that are consumed by a certain group of people, where the grouping is based on education levels. For instance the demand for scholastic materials such as pens, reams of paper, exercise books etc is likely to be low in a place where very few people go to school and vice versa. Also the demand for university text books will be very low or zero in a location where there are no university students. Therefore it would be unprofitable if one located a stationary shop in a place where there are no schools.
•	Marital Status: There are certain goods that are consumed mainly by married couples for instance wedding rings, some style of dress for instance Busuuti* in some parts of Uganda. So the demand of such commodities is likely to be high in a place where there are many married people. Indeed it would be unprofitable if one located a busuuti shop in a secondary school premises.
•	Age: This is also an important factor of demand. There are certain commodities that are consumed by certain age brackets. Such goods include; hairstyles, dresses, alcohol and others. We find that the demand for a certain hair style, jeans, “mini-skirts” is high among the teenagers than among the old “ceteris paribus”.
•	Number of consumers: Quantity demanded can also be influenced by the size of the population, but more so by the income distribution of the society. Producers will always want to locate in places that are more populated than in sparsely populated places. This is one major reason why countries integrate to form trade blocks. Large markets tend to attract foreign investors because they expect higher turnovers. Like wise on the local scene, many traders tend to locate their businesses in towns other than rural areas because of high population hence higher demand in towns than rural areas.
•	Location of consumer: The location factors may either be geographical or due to level of economic activity. For instance if individuals are located in hot places such as places at lower altitudes tropical places e.g. Accra, Dar es Salaam, Mombasa, etc goods such as blankets may face a lower demand while Air conditioners face a higher demand. On the other hand, we would expect the demand for sweaters, coats to be high in the cooler parts of a country than in hotter areas. Similarly, the demand for electrical appliances will be very low in areas where there is no electricity and it will be high in a location where there is electricity. As regards to the level of Economic activities, we would for instance expect the demand for fertilizers and pesticides to be high in crop growing areas than in other areas.

From the above analysis we can then write a general demand function as

Qd 	=	(P,PY,Y,T,S, Pt+1,Rc,Sx,E,M,A,Nc,L
P 	=	Price of the commodity
PY 	=	Price of other related commodities.
Y 	= 	Income of the consumers.
T 	= 	Tastes and preferences of the consumers.
S 	= 	Season of the year
Pt+1 	=	The expected price of the commodity.
Rc 	= 	Religion and cultural factors
Sx	= 	Sex
E 	= 	Level of education
M 	= 	Marital Status
A 	= 	Age
Nc 	= 	Number of consumers
L 	=	Location of the consumers.

A Demand curve
From the above analysis, we have seen that there are a number of factors that affect the demand for a commodity at any particular time. However, when defining a demand curve we assume that “ceteris paribus”, quantity demanded is determined by the price of the commodity. A demand curve therefore, is a graphical relationship between the quantity of a commodity demanded and the price of the commodity, assuming that other factors are kept constant.

A demand curve is derived drom a demand schedule, which refers to a tabular relationship between price of a commodity and its quantity demanded at the respective prices. For illustration purposes, we can assume the following hypothetical demand schedule, (Table 3.1 and figure 3.1).

Table 3.1: A Demand Schedule 
Price in $	Quantity demanded (units)	
100	0	
90	1	
80	3	
70	5	
60	8	
50	13	
40	20	
30	30	

When the above information is plotted on graph the resulting curve is known as a demand curve. A normal demand curve. A normal demand curve has a negative slope; an illustration is shown in figure 3.1 below. 

Figure 1:  A Demand Curve 

	Price

	P1

	Demand curve
	 P2

	0	Q1         Q2	Quantity 

The above figure shows that there is an inverse relationship between quantity demanded and the price of the commodity, for a normal good. But in a situation where more of a good is demanded when its price increases then such a good is said to be a giffen good, (as we shall see later under consumer choice in chapter five).

A giffen good therefore is that good whose demand increases as its price increases where as this good is not a luxury, The reason for this positive relationship (see figure. 3.2) between the price and demand of the commodity is that; as the price increases, the consumer is left with no other alternative but buying this good in order to satisfy his basic needs.

Figure 2: A demand curve of a Giffen good

	  P2

	P1

	Q1         Q2            Quantity demanded 

A giffen good is an extreme case of inferior goods, where an inferior good is that good whose demand falls as income of a consumer increases. All giffen goods are inferior in nature but not all inferior foods are giffen.

3.13: Change in Quantity Demanded
This is brought about by a change in the price of the commodity ceteris paribus. It is illustrated by a movement along the same demand curve as shown by figure 3.3. From the figure, at a higher price P1, a consumer demands less quantity Q1 (point A). When the price falls to P2, the consumer will now demand more quantity Q2 (at point B). So a movement from point A to B (i.e. along the same demand curve) shows a change in quantity demanded. We note here that all other factors that affect demand are assumed not to change but we allow only the price of the commodity to vary.
Figure 3.3: Change in Quantity Demanded
	Price 

	P1	 A
	Demand curve 
	P2	B

	0
	Q1          Q2	Quantity demanded 

3.1.4: Change in Demand
This occurs when there is a change in any other factor that determines quantity demanded other than the price of the commodity in question. Such factors may include change in the income of the consumer, price of a related commodity, tastes of the consumer and others factors. Change in demand is shown by a shift in the demand curve upwards to the right or downwards to the left, depending on the direction of change of the concerned variable (Figure 3.4).
Figure 3.4: Change in Demand 
	Price	D1
	D2    D0    

                             P0

	D1
      D2    D0  

	0             Q2        Q0        Q1              Quantity 
At a constant price P0 a change in other factors which affect demand of the commodity, shifts the demand curve to either D1 or D2, from D0 depending on the direction of change in the variable. If the change increases demand then the demand curve shifts outwards to D1 but if the change reduces demand of the commodity, then the demand curve shifts inwards to D2. For instance increase in the consumers’ income other factors kept fixed would shift the demand curve outwards to the right and vice versa. Also if the consumer’s tastes change in favour of the commodity, its demand curve shifts outwards to the right and vice versa.

3.1.5: The Market Demand Curve
Market demand simply refers to the total demand of a commodity in a market at each price level in a given time period. The market demand curve is therefore derived from individual demand curves and it is the horizontal summation of all the individual demand curves in the market.

For instance supposing that there are two consumers of a commodity in a market, whose respective demand schedules are as shown below in table 3.2.

Table 3.2: Consumer Market 
Price in $	Consumer A	Consumer B	Market Demand 	
100	1	2	3	
90	3	4	7	
80	5	7	12	
70	8	10	18	
60	12	15	27	
50	16	24	40	

From the table, we note that at a price of $ 90 consumer A demands 3 units while B demands 4 units therefore the total demand or market demand is 7 units at that price. Similarly, at a price of $70, consumer A demands 8 units while B demands 10 units, giving a total demand of 18 units. This is shown graphically in figure 3.5 below.

Figure 3.5: Market and Individual demand curve 

Price 				Price 				   Price 

					         
   70	  70	70
	DM

	DA	DB
     0	 0	0
	8          Quantity                      10               Quantity                    18            Quantity 
(a)  A’s Demand curve		(a) B’s Demand curve		 (c) Market Demand curve

Since the market demand curve is the horizontal summation of all individual demand curves of a commodity in a market, it is flatter (more elastic) than any individual demand curve.

2.3	  Supply Analysis 
Introduction
By the term quantity supplied, we refer to the quantity a ay which a producer is willing to bring to the market at the prevailing price. The factors that influence supply, differ from one commodity to another. For instance those that determine the supply of beef are different from those of maize and also different from those of an industrial commodity such as bread or cars, although there are some factors that are common to all commodities such as price of the commodity, cost of production and others.

Quantity Supplied
Quantity supplied, is the quantity of a commodity produced and available for sale in a market at any given time and price. Quantity supplied is determined by several factors, which include the following;
i)	Price of the commodity,
ii)	Cost of producing the commodity,
iii)	Price expectations, 
iv)	Price of other commodities (substitutes or complements),
v)	Taxes on the commodity,
vi)	Number of producers,
vii)	Level of technology,
viii)	The production period,
ix)	Natural hazards (in the case of agriculture products),
x)	Government policy,
xi)	Political climate, and
xii)	 Availability of factors of production.

Price of the commodity
This is the major determinant of quantity supplied of any commodity. Producers are willing to put more of a commodity on the market when its price goes up and less when its price falls. This is also known as the law of supply. Economic research has shown that supply is more responsive to price than to any other factor. In other words, to induce producers to produce more, the price of the commodity should be raised. 

Cost of Production
During a production process, several factor inputs are employed, these include, raw materials, labour, energy, capital and others For a producer to use such factors there mist be payment (reward for the factors of production) for them. These rewards constitute costs. 

The extent of costs should be in line with the consumer’s ability to pay for the produced commodity and also in line with the producers’ ability to afford the cost Nevertheless, cost is a disincentive to production Accordingly, the higher the cost of production, the less the quantity supplied of a commodity at any period and vice versa.

Price Expectation
A producer, who involves himself in market research, is always out to know the trend of prices for his commodity. The expected price is affected by the expected demand which in turn is influenced by the number of consumers, that may change due to increase in awareness about the commodity that may arise from advertising, or it may change due to periods of the year for instance Christmas season, students going back to schools, change in the population due to migration and immigration (refugees problem), change in weather and others. The producer will supply more now, if he expects price to fall in future and vice versa.

Price of other goods:
Quantity supplied of commodity may also be influenced by the price of related goods; such goods may either be complements or substitutes. If the price of substitute goods is low, the producer will supply less but if the price of the complementary goods is low, she will supply more.

Taxes on the commodity 
Increase in taxes raise the cost of production, thus negatively impact on production. Therefore at high levels of tax, a producer tends to supply less of a commodity to the market.

Number of producers
Indeed in a market where there is single producer also called monopoly (refer to market structures-: Chapter 9) the level of output is less, while where there are many producers, i.e. perfect competition, the level of output is high. Therefore, the smaller the number of producers the lower the level of output, and the greater the number of producers the greater the level of output.

Level of technology
The level of technology influences the degree of misuse (waste) of raw materials, and production capacity of the firm. Indeed remote technology yield less output hence less is supplied. While advanced technology leads to little inputs wasted, greater production capacities hence more output supplied to the market.

Production period
This is also known as gestation period. It refers to the amount of time taken to produce a particular good. Production periods vary from commodity to commodity, indeed some commodities take a little time to be produced, hence a availed to the market in large quantities in a short time period, for instance industrial commodities provided the raw materials are a available. But some commodities such as agriculture goods particularly perennial goods take years to be prodi.ced For instance suppose the price of coffee increased a hundred fold, quantity supplied may not change in the short run because there is a time lag in coffee production. Therefore, the lower the production period, the greater the quantity supplied and vice versa.

Natural hazards
These are uncontrollable factors that may include; floods, drought and a general change in climate. Such factors affect production especially of agricultural commodities although there may be less or no effect on industrial commodities unless the key factor inputs are agricultural produces. Accordingly, where ever such calamities occur, less output shall be supplied.
Government policy
Government can encourage or discourage production of particular commodity. Government can openly campaign for more production of a particular good by either subsiding its production, providing seeds in case of crops, and ensuring availability of ready market either local or international. In such a case more output shall be supplied. On the other hand, government can out-rightly ban production of a particular good for instance cocaine and impose penalties to those who promote the production of such a good.

Political climate
Political climate affects all sorts of production, whether agricultural or industrial. In areas where there are wars, little or no production takes place. Accordingly, there is less supply of any commodity in such a region. Similarly conducive political environment encourages production hence more output can be supplied.

Availability of factors of production
Availability of factor inputs directly affects the level of production particularly for industrial commodities where factor of inputs are less available, less output-is produced hence supplied.

Season; (time period of year)
Some commodities are supplied in particular season. For instance Christmas cards, Edi cards, success cards or seasonal cards in general. Also many agricultural crops tend to be harvested around the same period. Such as beans, coffee, maize, millet, coffee etc therefore quantity supplied of such commodities is high in particular season and low the rest of the periods.

 The Supply Curve
‘From the above discussion, we have seen that there are many factors that influence the quantity supplied of any commodity. However, if we now assume that other factors do affect the level of supply other than price of the commodity so that we investigate effect of the changes in the price of the commodity on the quantity supplied. If this relationship is expressed in the table form, we call such a table the supply schedule, other words, a supply schedule is a table that shows the relationship between price of commodity and quantity supplied at the various prices. Table 3.3 shows a hypothetical supply schedule.
Table 3.3: The Supply Schedule 
Price in $	Quantity Supplied 	
0	0	
100	2	
200	5	
300	10	
400	16	
500	24	
600	34	
The supply schedule shows the producer’s willingness to supply different quantities of the quantity at the given prices to the market. Generally, a producer is much willing to supply more when price is higher. When the information from the supply schedule is transferred to a graph, we get a supply curve. A supply curve therefore is a graphical representation of a supply schedule. 
Figure 3.6: The Supply Curve 
	Price
	s

	P2

	P1
	s

	Q1          Q2                 Quantity 
Generally when price is low, the producer is willing to supply less to the market and at higher price the producer supplies more. This leads to the law of supply that states that “The higher the price of a commodity, the greater the quantity supplied ceteris paribus”. Accordingly, a normal supply curve has a positive slope (i.e. is up-ward sloping). However, there are instances when the supply curve is down-ward sloping thus contradicting the law of supply. Such a down-ward sloped supply curve is usually referred to as an abnormal supply curve.
Figure 3.7: The Abnormal Supply Curve 

	Price 	s

                             P1

	  P2

          s

	Q1         Q2	Quantity 

Just as it is not common to have an up-ward sloping demand curve (abnormal demand curve) it is equally not common to have a down-ward sloping supply curve. Instances where we can get a down-ward sloping supply curve include, supply of perishables. For instance consider production of perishable commodities such as passion fruits, pineapples, tomatoes especially in developing countries where there are small peasant farmers with no cold-room. At the beginning of the season, the harvest is low, so price tends to be high. But as time goes on the level of harvest increases and since farmers do not store the produce so that they can regulate its supply, they will supply more of the increased amount of their harvests although the price shall be failing continuously. Therefore more and more quantity shall be supplied yet the price shall be falling more and more, hence leading to a down ward sloping supply curve.

 Change in Quantity Supplied
From the proceeding section, the law of supply is based on the assumptions that other factors of supply do not change, such that when price of the commodity changes, quantity supplied also change in the same direction as the price change. This is referred to as change in quantity supplied and is shown by a movement along the same supply curve. In other words, change in quantity supplied is caused by a change in the price of the commodity other factors kept constant as shown in figure 3.8.
Figure 3.8: Change in Quantity Supplied 

	Price 	S
	P2
	B

                       P1		A

	S

	Q1         Q2	Quantity 
An increase in price from p1 to p2 leads to an increase in quantity supplied from Q1 to Q2. This is equivalent to a movement from point A to B along the same supply curve.

 Change in Supply:
If we now allow other factors of supply to change while the price of the commodity is kept fixed, then more quantity shall be supplied at the same price if there is an increase in the factor that favour supply, such as increased number of producers, better technology, availability of raw material. etc. On the other hand, less shall be supplied at a given price when there is an increase the factor that disfavour production such as; cost of production, natural hazards, fall in the number of producers etc. This is known as change in supply and is shown by a shift in the supply curve as shown in figure 3.9 below.

Figure 3.9: Change in Supply 

Price 	S1

	S2
                   P2		B
     B’

	 P1                   A         A’

	S1  S2

	Q1    Q1’    Q2     Q2’          Q	uantity 

At the same price P1 quantity supplied will increase from Q1 to Q1’ when there is for example an increase in number of producers. Similarly at the same price P2 quantity supplied increases from Q2 to Q2’. Joining the new points A’ and B’ leads to a new supply curve S2’.

 The Market Supply Curve 
The market supply curve is derived from the individual supply curves which in turn are derived from individual supply schedules total market supply of a commodity is obtained by summing up the individual supplied at each price, and the market supply curve is obtained by a horizontal summation of all the individual supply curves.

For instance let us consider a market where there are only two producers A and B with their respective supply schedules shown below;

Table 3.4: Total or Market Supply 
Price in $	Supply by A	Supply by B	Market Supply 	
0	0	0	0	
100	1	2	3	
200	2	4	6	
300	4	7	11	
400	7	12	19	
500	12	20	32	
600	20	30	50	

The fourth column (market supply) is obtained by summing the second column (supply by producer A). We can now represent the above table in a graphical form and is given by figure 3.10.

Figure 3.10: The Market Supply Curve

Price 	SA	Price 	Price 

	   SM
    
 500                                         500		500

	200	200
     200

	0	0	0
	  2        12	Quantity         4        20       Quantity 	6           32      Qty

(a)	Firm A			(b) Firm B			(c) Market 
(b)	

From figure 3.10, SA is the supply curve of firm A, and SB is the supply curve of firm B while SM is the market supply curve. SM is obtained by a horizontal summation of SA and SB Indeed the market supply curve is more elastic than the individual supply curves since it is an aggregate of all firms’ supply curves in the market.

3.4	 Market Equilibrium and Deviations from Equilibrium
 Introduction
The term equilibrium simply refers to a state of stability. Equilibrium states are found in many areas and situations either social, political, biological, chemical, physical, economical etc. As we shall see later in this book, there are several equilibrium states in economics: in a market, consumer behavior, production, etc. for now we shall concentrate on market equilibrium. A commodity market is said to be in equilibrium when the quantity demanded equals to that supplied. This simply means that what ever is demanded is supplied at the right time and price and neither the producer nor the supplier is rationed. Therefore when a market is in equilibrium there is neither a shortage (excess demand) nor a surplus (excess supply).

In the last two chapters we studied about a consumer (demand curve) and a producer (supply curve). We however, note that these two, co-exist and are found in a market. In this chapter therefore, we shall look at a market and see how the two relate to one another under different situations. We shall also state the different types of equilibrium, determine quantitatively, the equilibrium price and quantity given a demand and supply equations. In addition, we shall see what happens to the equilibrium point whenever there is a change in demand or supply. In the same chapter, we shall see that government policy may distort the equilibrium position of a market leading to either surplus or shortage. You will note that under this case, a new equilibrium is not achieved neither is the old one re-instated. Such policies may take the form of minimum pricing policy or maximum pricing policy.

 2.5	Equilibrium in a Market
A market is said to be in equilibrium when quantity supplied is equal to quantity demanded. It occurs when both the consumer (demand curve) and producer (supply curve) co-exist interact using forces of demand and supply (market forces) to yield the market price and quantity (equilibrium price and quantity). At tat point, there is no tendency of any of the variables to change since equilibrium is considered to a state of stability.

Graphically the point of equilibrium is defined by the point of intersection of the market demand curve and supply curve. The price and quantity at the equilibrium point are referred to as equilibrium price and equilibrium quantity respectively.

Figure 3.11: Market Equilibrium 

	Price 	SS

                        Pe

           DD

	0
	Qe	Quantity 

In the above figure, Pe is equilibrium price and Qe is equilibrium Quantity. In this case the forces of demand and supply are said to be in equilibrium. This simply means that both the producer and consumer are equally satisfied because whatever the consumer demands is supplied by the producer and whatever is supplied is demanded hence there is no rationing in the market. There are two different types of equilibriums i.e. stable equilibrium and unstable equilibrium.

Under stable equilibrium, any distortion in the market system say arising from change in the commodity price, the system will re-organize itself such that it regains its initial position. This occurs either when the demand and supply curves have normal shapes or when  both are upward sloped but the supply curve is more elastic than the demand curve as shown below.

Figure 3.12(a): Stable Equilibrium 

	Price 	S

	P1
	P0                                Q                              

	   P2

	D
	 	Q2s  Q1d Qe      Q1s Q2d          Quantity 	

From figure 3.12(a) above, the equilibrium price and quantity are Pe and Qe respectively. When price rises to P1 quantity demanded falls to Q1d while that supplied rises to Q1S. This leads to a surplus of the commodity on the market. If the surplus can not be stored or if the cost of storage is high and the level of waste is great, it will force the producers to cut the prices. So market forces originating from the supply side will push down the commodity price. As price starts to fall, quantity supplied falls while that demanded starts to rise. The processes will continue until equilibrium price Pe is reestablished where quantity demanded will be equal to that supplied and the surplus will be no more.

On the other hand suppose the commodity price fell bellow the equilibrium price level to P2, quantity demanded would increase to Q2d while that supplied would fall to Q2s in accordance to the laws of demand and supply respectively. But since quantity demanded exceeds that supplied, there will be excess demand (shortage) in the market given by. In this case we say that consumers are rationed because they are willing to purchase more than what the producers are supplying.
A shortage will force the consumers to compete amongst themselves by offering higher prices for the commodity. In other words market forces originating from the demand side will push up the price of the commodity. But as price starts to rise, quantity demanded starts to fall meaning that some consumers may either drop off or those remaining will demand less at higher prices. In addition, as price rises, quantity supplied will also start to rise. The process continues until the initial equilibrium is re-established where quantity demanded equals to that supplied meaning that there is no more shortage. 

Figure 3.12(b): Stable equilibrium 
                          Price 	D

	S
	P1
	Pe	        e

	P2

                                                     Q2s       Q2d     Qe   Q1d         Q1s             Quantity 

Alternatively, if the demand curve is abnormal (up-ward slopped) but more inelastic (Steeper) than the supply curve, there will be stable equilibrium.

For instance consider price P1, which is higher than the equilibrium price Pe. The quantity supplied at that price Q1S is higher than quantity demanded Q1d. This means that the producers are rationed since their willingness to supply exceeds the actual demand by the consumers at price P1, therefore this leads to a surplus on the market, given by Q1d Q1s. The excess supply on the market forces the producers to reduce prices. But as price falls, both quantities demanded and that supplied fall. The process will continue until the equilibrium price Pe and quantity Qe are attained.
Similarly, at a lower price say P2, quantity demanded exceeds quantity supplied (see diagram) leading to a shortage given by Q2s Q2d .But a shortage will force consumers to offer higher prices. As price rises, both demand and supply increases although supply increases at a higher rate than the demand (This is because the supply curve is more elastic than the demand curve). The process will continue up to point ‘e’ where the equilibrium price and quantity are attained.

On the other hand, under unstable equilibrium, any distortion in the price, will instead lead to explosion of the system. So the initial position is never regained. This occurs when either the demand curve or supply curve or both have abnormal shapes.

Figure 1.13(a): Unstable Equilibrium 

                          Price 	S

	D
	P1
	Pe	        e

	P2

                                                     Q2s       Q2d     Qe   Q1d         Q1s             Quantity 

As we saw earlier, it is possible to have an upward slopped demand curve although it is referred to as an abnormal curve. For instance, consider upward slopped demand and supply curves but when the demand curve is more elastic than the supply curve. At price say P1 higher than the equilibrium level, (Pe), quantity demanded (Q1d) exceeds quantity supplied Q1S leading to a shortage given by Q1s Q1d.  But from our earlier analysis a shortage would lead to higher prices, since consumers compete for the limited amount of goods. In this case however, increase in prices instead lead to increase in both demand and supply, hence worsening the shortage. So the system moves further away from the equilibrium point.
Similarly, if we consider a price lower than the equilibrium level, say P2. At that price, the quantity supplied Q2S exceeds that demanded Q2 hence leading to excess supply or surplus on the market. But from our earlier analysis, a surplus leads to reduced prices by the producers. In this case however, when prices are reduced so as to clear the surplus, both quantities supplied and demanded fall, leading to increased surplus.

We note from the diagram that the surplus worsens because the reduction in quantity demanded is greater than that of quantity supplied because the demand curve is more elastic than the supply curve.

Another case of unstable equilibrium occurs when both the demand curve and the supply curve are down ward slopped( i.e. when we have an abnormal supply curve) and the supply curve is more elastic than the demand curve, as shown in figure 3.13 below.
Figure 3.13(b): Unstable Unequilibrium  

	S	D
	P1
	Pe	e

	P2

	S
	SD

	0	 Q1s   Q1s    Qe        Q2d        Q2s     Quantity 

Using the above diagram, if we consider a price level P1 higher than the equilibrium level Pe, at that price, quantity demanded exceeds that supplied hence leading to a shortage. The shortage will prompt consumers to offer higher prices, but instead as price increases, the shortage widen. Similarly, at a price level say P2 lower than the equilibrium level, quantity supplied Q2s exceeds that demanded Q2d leading to a surplus. The surplus would force the producers to offer lower prices, but instead as price is reduced, the surplus widens hence driving away the system from the equilibrium point.

In summary, we can note the following;
a) Stable market equilibrium can be attained when;
•	The demand and supply curves have normal shapes
•	Both the demand and supply curves are upward slopped but the supply curve is more elastic than the demand curve.
•	Both the demand and supply curves ate downward sloped out the demand curve is more elastic than the supply curve.

b) Unstable equilibrium occurs when;
•	Both the demand and supply curves are upward sloped but the demand curve is more elastic than the supply curve.
•	Both the demand and supply curves are downward sloped but the supply curve is more elastic than the demand curve.

 Mathematical Derivation of Equilibrium price and Quantity 
Supposing that the demand and supply functions arc given as;

	Qd	=	a – bP
	Qs	=	=c + dP.

Where; a, b, c, and d are positive constants. P is price, Qd and Qs are quantity demanded and quantity supplied respectively.

At equilibrium Qd  =  Qs

Now equating quantity demanded and quantity supplied, we get

	-c + dp  =  a – bp

Collecting like terms together we get,
		bp  dp  =  a + c
		P(b + d)  =  a + c

	=  P  	=	a + c
			b + d
Substituting for P in any of the quantity equations, for instance the supply equation we get:
	Qe  =  =c +  d
Expanding we get:
	Qe  =  
Therefore, equilibrium quantity: Qe =  
Example 1

Given the following demand and supply functions as;
Qd = 36 - 4P and Qs = -12 + 12P respectively.

To find equilibrium quantity and price we equate quantity demanded to that supplied such that:

At equilibrium, Qd = Qs such that we get;
36 - 4P = -12+12P

Then collecting like terms together we get,
16P = 48
Therefore the equilibrium price is;
P	=	3

Now substituting for price P = 3 in any of the quantity equations, say the demand equation we get the level of equilibrium quantity i.e. using the demand equation;
Qe =36 - (4 x 3)

Hence equilibrium quantity is, Qe = 24.

Therefore equilibrium price Pe = 3 and equilibrium quantity Qe 24.

2.6	Consumer’s Surplus
On many occasions a consumer goes to a market without knowing the actual price of a commodity. He may for instance anticipate paying a higher price but ends up paying less. If such a situation occurred, he could use the balance either to purchase other commodities, purchase more of the same commodity or save it. It is this difference which is referred to as the consumer surplus.

Definition
Consumer’s surplus is the difference between the amount of money that a consumer would be willing and able to spend on a commodity and the amount that he actually spends on a commodity for the same quantity. But the amount of money actually spent on the commodity is equal to the product of the market price and quantity purchased while the total willingness of the consumer to purchase the commodity is given by the area under the demand curve. Graphically therefore consumer’s surplus is given by the area bellow the demand curve but above the price level. This concept can be illustrated using a demand curve or a demand schedule as below.

Figure 3.13: Consumer’s Surplus 
	Price 
	A
	SS

	Pe	B

	C	DD

	0	Qe			Quantity 

From the above diagram, the consumer’s willingness to pay is shown by the area under the demand curve. At equilibrium, the consumer will demand quantity Qe (given by the intersection of the demand and supply curve) at price Pe. She will therefore pay an amount of money equal to area OPeBQe. However, the consumer is willing to pay an amount of money equal to area OABQe for quantity Qe. Therefore, the difference between these two expenditures which is equal to area PeAB is the consumer’s surplus. If the demand curve is linear, then consumer’s surplus is equal to the area of a triangle PeAB. A student should however note that a demand curve is not always linear, in which case finding the area would call for finding the integral with lower limit being price Pe and upper limit being price at point A.

Example
Consider the following demand and supply functions;
Qd	=	36 - 4P
Qs	=	-l2 + l2P
At equilibrium Qd = Qs, solving for equilibrium price and equilibrium quantity, we get P = 3 and Q = 24.

Now at the point where the demand curve touches the price axis, quantity demanded is zero. If we now substitute for Q = 0 in the demand equation, we get;
36 - 4P = 0 such that price at point A is P = 9.

This means that when the market price is $ 9, quantity demanded will be zero. Now using the triangle method:

Consumer’s surplus equals to the areas of the triangle below the demand cuive but above the price level, (see figure 3.13).

But area of a triangle is given by tl4 formula; A = ½ bh, where b=base and h is the height. And in our example, base b = 24 while height is 6. This gives consumer’s surplus equal to; ½ x 6 x 24 = $72. 

Alternatively we would use the integral method since the integral of a function gives the area below that function. So we integrate the demand function with respect to price, between lower limit being market price and upper limit being price at the point where quantity demanded is zero that is;

	Consumer surplus 	=	
				=	
				=	162 – 90
				=	72

The student should note that the triangle method is applicable only if the function is linear otherwise the integral method is preferred since it can be used in both linear and non-linear functions.

Finding the Consumer’s Surplus using a Demand Schedule
We can directly determine the amount of consumer’s surplus from a demand schedule. For instance, using the following hypothetical demand schedule. 

Table 3.3: A demand Schedule 
Price in $	0	
90	2	
80	5	
70	9	
60	16	
50	25	
40	35	
30	48	
20		

Recall that a demand schedule reveals that consumer’s willingness and ability to pay for a commodity. Supposing that the market price of the commodity is $40, then the consumer will demand 25 units, and would pay $1000. However, from the above demand schedule, and assuming that the market price is $40, we can note the following;

•	 The consumer will purchase zero units of the commodity if its price is at $90 hence she would pay nothing at this price.
•	The consumer is willing to pay a per unit price of $80 for the first two units (i.e. the 1st  and 2nd ) so she would pay a total of $160 although she actually pays at a market price of $40 per unit hence paying a total of $80 for these two units.
•	 The consumer will buy more units only it’ the price is reduced further, Indeed she is willing to buy at a price $70 the next three units (i.e. the 3rd 4tha and 5th) Hence she is illing to pay a total amount of $210 (i.e. 70*3). But since she actually buys at the market price of $ 40, she instead pays a total of $120.
•	 For the next four units (i.e. the  6th, 7th, 8th, and 9th) she is willing to purchase at a price of $ 60, so she is willing to pay a total of $240. But since the market price is $40, she instead actually pays $160 for the four units.
•	When the price is reduced further to $ 50, the consumer would purchase an additional seven units (i.e. the 10th, 11th, …., 16th) So she is willing to pay a total of $350 for these seven units. But since the market price is $40, she actually pays a total of $ 280 for the seven units.
•	 Finally the consumer is willing to purchase at a price of $ 40, the next nine units (i.e. the 17th, 18th, up to the 25th). So she is willing to pay a total amount of $360 and since the market price is $40, per unit, she indeed pays a total amount of $360 for these nine units.
We note that prices below $40 e.g. $30 and $20 are not considered because they are not achieved, since the market price is $40. The above analysis can be summarised as follows.

Willingness to pay ($)				Actually 	paid(S)
90 x 0  =  0						40 x 0 = 0
80 x 2  =  160					40 x 2  = 80
70 x 3  =  210					40 x 3  =  120
60 x 4  =  240					40 x 4  =  160
50 x 7  =  350					40 x  7  =  280
40 x 9  =  360					40 x 9  =  360
Total $ 1320					Total $1000

Consumer’s surplus is equal to total willingness to pay less total actual payment, i.e. $1320-$1000 = $320

2.7	 Producer’s Surplus
Unlike a consumer who in his mind sets a maximum price at which to purchase a commodity (perhaps basing on his income, tastes and expected utility), which is referred to as ‘willingness to pay’, a producer on the other hand sets a minimum price that she can accept in exchange for the commodity mainly (basing on the cost of production and the profit margin) which is referred to as ‘willingness to accept’. The minimum price should be such that it can cover the cost of production and perhaps enable her realize some profits. However, if she happens to sell her commodity at a price higher than the acceptable minimum, then the difference in revenue is what is referred to as producer’s surplus.

Definition:
Producer’s surplus is the difference between the amount of money that a producer actually receives upon, the sale of a commodity (product of quantity sold and market price) and the minimum amount of money that she would be willing to accept for the same quantity. Producer’s surplus can be illustrated by the use of a supply curve or supply schedule as shown below.

Figure 3.13: Producer’s Surplus 

	A	S

                               Pe                         B

	C	D

	0
	Qe			Quantity 

The minimum acceptable is shown by the area below the supply curve. This is because the supply curve is equivalent to the upward rising portion of the marginal cost (MC) curve. (see perfect competition market structure in chapter 9). 

Quantity Qe is purchased at a unit price of Pe, implying that the producer receives total revenue given by area OPeBQe (price times quantity). But she is willing to accept minimum revenue given by the area under the supply curve OCBQe. Therefore the producer’s surplus is the difference between the amounts of money that the producer receives: OPeBQe and the minimum amount of money that he would be willing to CBQe which is equal to area CPeB, i.e.

Producers surplus 	=	OPeBQe - OCBQe CPeB.

Graphically, therefore, producer’s surplus is equal to the area above the supply curve (marginal cost curve) but below the price level. 

Determining the Producer’s Surplus
We can determine the value of the producer’s surplus using either the supply schedule or supply curve if the market price is known. Precisely, if the supply curve is linear, then producer’s surplus is equal to the area of a triangle above the supply curve but below the price level. For instance, consider the following demand and supply functions; 

	Qd  =  36 – 4p

	Qs  =  -12 + 12p

As we saw earlier, the equilibrium price and quantity are 3 and 24 respectively. We next need to determine the price level at which quantity supplied is zero, i.e. the point of intercept of the supply function. Now using the supply action, substituting Qs = 0, we get price P = 1. This means that when price is unit quantity supplied is zero, so the height of the triangle is 2, while the base is 24 as shown in the figure 3.14 below. 

Figure 3.14: Finding Producer’s Surplus  

	Price 	9	
	SS
                                                                       e
	3

	DD

	0                           24
	Quantity 

Using the triangle method, producer’s surplus is equal to; ½ x 2 x 24 = $24.

Alternatively given a supply function, we can use the integral approach to find the value of producer’s surplus. Using the above supply equation, producer’s surplus will be equal to 

	=   
This gives us;

By substitution, this simplifies to give, 18 + 6 = $24. 

We can also obtain the value of producer’s surplus from a supply schedule just as we obtained consumer’s surplus from a demand schedule. For instance consider the following hypothetical supply schedule. 

Table 3.4: Supply Schedule 
Price in $	Quantity 	
10	1	
20	3	
30	7	
40	12	
50	20	
60	30	
70	42	
80	58	

Recall that a supply schedule shows a producer’s willingness and ability to sale a given quantity of a commodity at the given price. The producer’s willingness reflects the additional cost (marginal cost) of production. In other words, as long as the producer can recover the marginal dost of production, then she may be willing to provide the good for sale. Any revenues to the producer over and above the minimum willingness marginal cost) would imply a surplus to the producer.

From the above supply, schedule, supposing that the market price of the commodity is set at $60, the producer would supply 30 units and would earn total revenue of $1800.

However, if we refer to the supply schedule, we can note the following.
•	At a price of $10, the producer is willing to supply only one unit, hence she is willing to earn $10, but since the market price is $60 she actually receives $60 from that unit.
•	At a higher price of $20, the producer supplies a total of three units. This means that since she was willing to supply only one unit at a price of $10, then she is willing to supply the additional two units (i.e. the 2nd, 3rd) at a price of $20. Therefore she is willing to accept a total of $40 as revenue from these two units.
•	The producer is willing to supply the additional four units (i.e. 4th, 5th, 6th, and 7th ) at a price of $30; hence she is willing to accept total revenue of $120 from these four units. But since the market price is $60, then she actually earns $240.
•	At a price of $40, the producer supplies an additional five units (i.e. 8th, 9th up to the 12th), so she is willing to accept a total of $200 but since the market price is $60, she actually earns $300 from the additional five units.
•	When price increases to $50, the producer supplies additional eight units (i.e. 13th, 14th, up to the 20th unit). She is therefore willing to accept total revenue of $400, but since the market price is $60, she actually receives total revenue of $480 from these eight units.
•	Finally, at a price of $60, the producer will supply an additional ten units (i.e. the 21st 22nd up to the 30th), so she is willing to accept total revenue of $ 600 from this unit and since the market price is $60, she indeed earns $600 from these ten units.
•	The producers would wish selling at a higher price such as $70 and $80 but such prices are not achievable because the market price she set at $60.

We can represent the above analysis in a simple table as shown below. 

Actual Earnings 	Willingness to Accept 	Producer’s Surplus 	
60* = 60	10* 1 = 10	50	
60* 2 = 120	20* 2 = 40	80	
60* 4 = 240	30* 4 = 120	120	
60* 5 = 300	40* 5 = 200	100	
60* 8 = 480	50* 8 = 400	80	
60* 10 = 600	60* 8 = 600	0	
Total $ 1800	$1,370	$430	

We shall note here that unlike consumer’s surplus that is given by total willingness to pay, less total actual, producer surplus on the other hand is given by the total actual less total willingness to accept. 

 Externalities
These are social costs and benefits that accrue to a society arising from a market activity. An external effect therefore arises when the utility or production of one person is dependent upon the activities of other persons. There are of two forms of externalities; positive and negative externalities.

 Negative externalities
This occurs when society or third party suffers from a market activity. For instance if a factory or firm produces acid or emits, pollutants to the environment, it is likely that society will suffer from that pollution.

Let us illustrate using simple but common examples. Consider a river and a factory located up-stream while down-stream there are fisher men. If the factory produces pollutants and discharges it into the river without treating it, (hence does not incur abatement costs), the pollutant will have a disastrous effect on the livelihood of fish, whose population will therefore fall leading to reduced fish -catch. This implies that the activities of the factory owner negatively impact on those of the fisherman.

Another example of negative externality is production of loud music in the neighbouring apartment during late hours in the night. This may lead to discomfort to the neighbour. Similarly, if a health clinic or school is located next to a metal workshop or stone-quarry or factory where too much noise is produced, the noise might have serious negative impact on the health of the patients, or on the understanding ability of the pupils in class.

The easier way of solving a negative externality is to impose a tax on the producer of the externality. This method however, has two major limitations;
i)	It is difficult to determine the amount of tax that is equivalent to the amount of damage.
ii)	Would it be fair to tax the externality producer if she was the first to establish her business in the area?

Therefore, there is need to determine the rightful property- rights owner.
In other words, who owns the property rights? Is it a factory owner or a fisher man? That is, is the polluter free to pollute or the pollutee has right to pollution-free environment? When ownership of property is known, then the property rights owner should be compensated for the damage. This means that if the factory owner (polluter) has the right to pollute, the fisher man should compensate her (bribe her) for the reduction in the production of the output hence pollution. On the other hand, if the fisherman has the right to fish (has ownership over the river) then the polluter should compensate him for the reduction in the amount of fish catch resulting from her pollution activities.

Positive Externality
At times externalities may be of benefit to other parties; consumers and producers; yet the producers of such externalities may not be compensated. Indeed there are several market activities that may benefit society. For instance consider two neighbours where one plays a ‘sweet’ music during a convenient time of the other neighbour who can not afford yet he is interested in the music. The neighbour who can not afford and yet is interested in the music will have free access to the music and the one who plays the music is not compensated.

Also consider two neighbours, where one has a flower garden and the other does not own one yet likes it. The one who does not own the flowers will enjoy looking at the owners in the neighbourhood at no cost.

Some positive externalities however, may be of benefit to both parties. In other words. 5oth parties or individuals or firms may be producers of externalities and beneficiaries. For instance, consider two individuals located in the neighbourhood; one owns a bee-farm and the other owns an orchard-farm. Orchards produce flowers from which bees collect nectar to make honey which in turn is sold by the bee-farmer. So an expansion of the orchard farm will be of great benefit to the production of honey by the bee-farmer. Similarly, bees are important during the process of pollination of the orchard flowers which result in orchard fruits. Therefore either way the activities of one individual benefit the other individual’s activities.

Unlike negative externalities where a tax may be imposed so as to reduce the production of the externality, in case of positive externalities, a subsidy should be given to the producer of the externality so as to promote the production of the externality.

 Deviation from Equilibrium
There are cases when a disturbance to the initial equilibrium, may lead to a permanent disequilibrium or lead to a new equilibrium point with new equilibrium price and quantity different from the initial ones. In the latter case neither the demand nor the supply curve shifts but instead price is set at a certain level that may either be above or below the equilibrium level. While in the ‘former case either the demand curve or the supply curve or both shifts to form a new equilibrium point. One good example of the first case is price legislation; a situation where government may fix price below equilibrium level (price ceiling) or above the equilibrium level (price floor).

As stated earlier, the second case involves a shift of either the demand curve or supply curve. But we recall that the demand or supply curve can only shift if there is a change in any other factor other than price of the commodity. For illustration purpose, we shall consider change in tastes as the demand shifting factor. This is also described by the term “consumer’s sovereignty”. For the case of a shift in the supply curve, we shall consider imposition of tax or subsidy on the production of a good.

 2.8	Price legislation
There are situations when government fixes prices of some commodities with a purpose of either enabling its poor citizens to acquire the basic goods such as salt, soap, sugar particularly during scarcity of such basic goods or to protect the producers of certain goods.
Price legislation is of two forms, either price is fixed below the equilibrium level which is known as price ceiling (or maximum price legislation) or price is fixed above the equilibrium level (minimum price legislation).

 Price Ceiling (Maximum Price Legislation)
This is usually done so as to avail essential commodities to every one especially the poor at reasonable prices. This can be done when there is a commodity crisis in a country which exists particularly during wars. Government may want to check on the producers by fixing a maximum price below the equilibrium price, so as to protect its citizens against exploitation by producers. Producers are not allowed to sell at any price above the fixed level, but can sell at any price below the fixed price; therefore, the fixed price acts as the maximum possible at which any producer can sell the good and hence maximum price legislation policy. The major causes of such crisis are; wars, drought, floods or any other natural calamity.
Figure 3.15: Price Ceiling (Maximum Price)

	Price 	SS

                                                                 e
	Pe

	Pc	DD

                                 0
	 Qs            Qe                Qd      Quantity 
Referring to the above diagram, government fixes price at Pc which is below equilibrium level Pe. At a lower price P, quantity demanded Qd exceeds that supplied Qs and since it is a government policy, market forces are not in position to push up the price back to the equilibrium level, hence leading to a persistent shortage given by QsQd. One major problem with this policy is that, the existence of the shortage on the market may lead to creation of “black markets “, which might further lead to corruption and bribery.

 Price Support/Price floor (Minimum price Legislation)
Price support is said to have occurred when the price of a commodity is fixed above the equilibrium price. This is mainly done because government feels sympathetic with the producers of the particular commodity. Producers are allowed to sell at any price but not below the fixed price (hence minimum price), leading to a surplus on the market as shown in figure 3.16 below.

Figure 3.16: Price Floor (Minimum Price Legislation)

	Price 	SS

                                                                 e
	Pe

	Pc	DD

                                 0
	 Qs            Qe                Qd      Quantity 

If government fixes a higher price P than the equilibrium re,, quantity supplied would exceeds that demanded, leading to excess supply hence a surplus on the market. But since it is a government policy, the surplus Qd Qs will stay on the market. This is so because market forces (forces of demand and supply) are disabled by government intervention.

 2.9	Consumer Sovereignty
In a free market system, the fundamental economic question of what to produce is answered by knowing the consumer’s needs and wants which are in turn influenced by consumer’s tastes. Quite often we observe new commodities, styles, brands entering a market while others leave the market or are reduced this is caused by changes in consumers’ taste. Therefore by the term consumer sovereignty, we refer to a situation where the consumer is a “King” in the market. This means that the producers tend to “obey” the consumer by producing more of what consumers desire more and less of the undesirable commodity. The processes have a dual effect on the production of the two goods: The producers of the now wanted commodity benefit while those of the unwanted one lose. Production techniques are adjusted to meet the new demands of the consumers and resource owners also have to adjust to the new demand or else they are phased out. The adjustment process is categorized into 3 phases or stages; instantaneous, short run and long run.

To illustrate this concept we shall use the following example. Consider two substitute commodities A and B and assuming that initially the markets for commodities A and B are in equilibrium. If we suppose that the consumer’s tastes change in favor of commodity B, we would expect more quantities of B to be demanded hence produced and less of A to be demanded hence produced. Resource owners will also have to adjust such that they produce more inputs that are used in the production of commodity B and less of those used to produce commodity A. Changes in demand and production levels will have an impact on the prices of these two commodities and those of factor inputs (cost). We can illustrate the adjustment processes by identifying three stages:
Instantaneous, short run and long run for both the commodity market and factor market of the two commodities A and B.

First, we shall consider the market for commodity B. Since the consumer’s tastes for commodity B have improved and using our knowledge of the concepts of change in demand and change in quantity demanded, an improvement in consumer’s tastes all equal (other factors kept constant) will lead to an out-ward shift in the demand curve. Assuming that the market is initially in equilibrium, three effects can be identified;

Instantaneous effects
At the very instant of the sudden change in consumer’s tastes, quantity supplied does not change because the time is too short for the firm to adjust its technology and factor input requirements to match the increased demand for the commodity. Therefore, a shift in the demand curve only leads to an increase in the commodity price with the same original equilibrium quantity. This is shown in figure 3.17 below: Point e0 is the original equilibrium, with respective equilibrium price and quantity given by Po and Q0. A change in tastes in favour of the commodity shifts the demand curve outwards to from D0D0 to D1D1. At the instant, quantity supplied remains fixed at Q0, but with the increased demand and fixed quantity Q0 price rises to P0’. We should however, note that point e0’ is not an equilibrium point because quantity supplied is not equal to that demanded.

Short run effects
A short run period is where producers can vary some factor inputs (variable factors) and leave other factors unchanged (fixed factors). Therefore in the short run the producers of commodity B shall increase the quantity of the variable factors such as raw materials, labor etc. in a bid to produce more quantity of commodity B whose price has now gone up. A variation in the amount of the variable factor input is shown by a movement along the original supply curve. Short run equilibrium in the market for commodity B is attained at the point of intersection of the new demand curve and the original supply curve (i.e. point e1). At this point, price (P1) is higher than that at the original level because of the increased demand but lower than the instantaneous level, this is because quantity supplied has now increased. Clearly, short run equilibrium quantity (Qe) is higher than the initial equilibrium level; this is due to the increased production arising from increase in the employment of the variable factor inputs.

Long run effects
Since commodity B is now profitable, producers will increase its production by increasing all factor inputs: both fixed and variable factors, so in the long run all factors are variable. When all factors are increased, production levels of B will certainly increase other factors constant. In addition if we assume perfect competition market conditions, availability of profits in the production of commodity B will attract new firms. But increase in the number of producers will lead to a change in supply. Therefore the long run supply curve of commodity B will shift out-wards to the right due to two forces: Increase in all factor inputs and increase in the number of producers. Long-run equilibrium shall be established at the point e2, where quantity supplied Q2 is greater than the short-run equilibrium quantity Q1. But long-run price P2 is, lower than short run equilibrium price P1 although higher than the original equilibrium price P0 as shown in figure 3.17 below.

Figure 3.17: Market for Commodity B
	D1

	Price of B	D0
	P0	e0
	S0
                              P1	e1	S1
                           P2
                               P0                                          e0            e2
	S0	D1
	S1	D0
	0
	Q0       Q1    Q2	Quantity of B

e0  =  Initial equilibrium point whose respective price and quantity are P0 and Q0
e1  =  The short-run equilibrium point whose respective price and quantity are P1 and Q1
e2  =  The Long-run equilibrium point whose respective price and quantity are P2 and Q2

We notice that the long-run equilibrium price P2 is higher than the original price P0. This is so because the long-run average cost of production (price of inputs) is greater than the initial average cost. This can be explained by looking at the analysis of the market for factor inputs in the production of commodity B shown in figure 3.18 below. 

Figure 3.18: Market for Facto Inputs for Commodity B

Df1
Cost of inputs/Cost	Df0
	P0	e0
	Sf0
                     C1=Pf1	e1	Sf1
                   C2=Pf2
                       C0=P0                                          e0            e2
	Sf0	Df1
	Sf1	Df0
	0
	Qf0       Qf1    Qf2	Quantity of inputs for B

The above diagram illustrates the market for factor inputs which are used in the production of commodity B. At the initial equilibrium point ‘e0’ the quantity and price of the factor inputs are Q0 and P0 respectively. The short-run equilibrium is given by point e where the demand for factors inputs is now higher at Df1 leading to higher factor price (average cost) C1=Pf1 and more inputs supplied Qf1. The long run equilibrium is given by point e2 where the new demand curve Df1 intersects the new supply Sf1. The cause of the shift in the supply curve arises from the fact that increase in the prices of these factor inputs makes them more profitable to their producers. In addition owners and producers of inputs used in the production of commodity A will now divert their resource to the production of inputs used in the production of B leading to an increase in the number of producers of these inputs. These two factors will lead to a shift in the supply curve of factor inputs outwards to Sf1, leading to the attainment of the long run equilibrium at point e2 where quantity Qf2 of factor inputs is demanded at factor price (average cost) C2 by the producers of commodity B. Since the long run average cost C2 is higher than the original average cost C0, the long run price of the commodity shall be higher than the original price as illustrated earlier in figure 3.17.

We now consider the market for commodity A and market for factor inputs used in the production of A. Since the consumers’ tastes have changed in disfavor of good A, other factors fixed the demand curve of commodity A will shift in wards to the left. Again three stages can be identified.

•	Instantaneous effect
Assuming that the market was originally in equilibrium with equilibrium quantity Qo sold at price P0, a downward shift in the demand curve leads to a fall in the commodity price. At the very instant, since quantity supplied cannot be changed price will fall but quantities will remain at the original level. At this new price level P0’ however, the market is not n equilibrium since demand does not equate to supply (see figure 3.19).

•	Short run effects
In the short run, since price of good A has fallen producers of commodity A will now reduce its output level by reducing the variable factor inputs used in the production of A. This is given by a movement along the same supply curve to the point of intersection of the new demand curve and the original supply curve giving rise to short run equilibrium point et. At this point, quantity supplied has fallen to Q1but price has risen slightly above the instantaneous level to P1 though lower than the original level Po.

•	Long run effects
Since commodity A is no longer profitable, in then long run producers of commodity A adjust both the fixed and variable factors downwards so as to produce for the now small market.  Since all factors inputs are reduced, quantity supplied also falls. In addition, some producers may close down and shift to the production of commodity B whose demand has increased leading to a reduction in the number of producers. These two factors lead to a shift in the supply curve of commodity A upwards to the left. Long run equilibrium is established at point e2 where the new demand curve D1 intersects the new supply curve S1. At this point, quantity Q2 has fallen below the short run equilibrium  level Q1 while price P2 has risen above the short-run equilibrium level P1 although it is lower than the initial level P0 (figure 3.19). This is so because the price of the factor inputs  (average cost) used in the production of good A is lower in the long-run than in initial period.

Figure 3.19: Market for Commodity A
	Price of A	D0
	S1	
	D1	S0
                              P0	e2
	P2                         e2
                            P0                                e1

	P0	S1	D0
	S0	D1

	0	Q2    Q1      Q0                Quantity of A

e0 = is the original equilibrium point whose respective price is Po and quantity is Q0
e1 = is the short run equilibrium point whose respective price and quantity are P1 and
Q1
e2 = the long run equilibrium point where price is P2 and quantity is Q2

Again, we note that in the long-run although quantity supplied has fallen leading to increase in price, long run equilibrium price P2 is lower than the original price P0. This can be explained by the analysis in the factor market given below.

Since demand for factor inputs is a derived demand (i.e. more inputs are demanded only if more of the commodity produced using the inputs is demanded), a reduction in demand fore commodity A leads to a reduction in factor inputs used in the production of good A. This is tantamount to a fall in the number of consumers of the factor inputs (producers of commodity A) leading to a shift in the demand curve of factor inputs I inwards to the left to Df1. In the short run the average cost of production (price of the factor inputs) falls below the initial equilibrium level, accordingly the short-run equilibrium price of the commodity C1 is lower than the original level C0 (see figure 3.20). In the long-run however, supply of factor inputs used in the production of good A is influenced by two factors; First, the producers of these inputs (resource owners) will allocate less of their resources (e.g land, fertilizers etc) to the production of these inputs since they are no longer profitable leading to less output. Second, some producers may quit the production of these inputs and may embark on production of inputs used to produce commodity B which is now more profitable; hence the number of producers of inputs for A falls. These two factors lead to a shift in the supply curve of factor inputs of good A upwards to the left to Sf1 as shown in the figure 3.20 below.

Figure 3.20: Market for factor inputs of goods A

	Price of A	Df0
	S1	
	Df1	S0
                      C0=Pf0	e0
	C2Pf2                         e2
                      C1=Pf0                                e1

		Sf1	Df0
	Sf0	Df1

	0	Qf2    Qf1      Qf0                Quantity of A

Ultimately the long run average cost of production C2 (price of factor input) is higher than the short run average cost C1 but lower than the original one C0. Accordingly, the long run equilibrium price of commodity A is higher than the short run equilibrium price but less than the original price level as illustrated earlier in figure 3.19.

Effect of Tax on Equilibrium Price and Quantity.
Imposition of a tax, distorts a market by changing the equilibrium price and quantity. Without a tax, at equilibrium, price paid by the consumer equals that received by the producer, but when a tax is imposed on a commodity; the new equilibrium is difficult to define since price paid by the consumer is different from that received by the producer (supplier) although the new equilibrium quantity demanded equals to that supplied. With existence of a tax, on a commodity; the price paid by the consumer equals that received by the producer plus the amount of tax.

There are two forms of tax that can be imposed on a commodity in a market. One type of tax is known as quantity tax and the second one is value tax also called ad-valorem tax. Quantity tax is paid or levied on every unit sold. On the other hand value tax is expressed in percentage form. For instance, if the value tax is 10 percent of the commodity which is valued at $100, then that commodity would now cost $110. We note here that the consumer pays $110 but the producer receives $100. Generally if the tax rate is ’t’, and the price paid by the consumer is ‘Pc’ while that received by the supplier is ‘Ps’ then under value-tax, Pc (1+t) Ps.
Ad-valorem tax is very common in developed countries because business people keep records and there are stringent tax rules and in addition there is less corruption and high level’ of social development. On the other hand, quantity-tax is common in less developed countries because it is easy to levy, and such countries are characterized by high levels of corruption, inconsistent tax rules, poor book keeping and low levels of social development. This book shall concentrate more on quantity-tax.

Generally, imposition of a tax leads to less quantity demanded or supplied and higher price paid by the consumer. Specifically, quantity-tax will lead to a shift in the supply curve upwards to the left or shift of the demand curve inwards by the amount of tax as shown below.
Figure 3.21: Effect of tax on Supply

	    Price	S1

	S0
	Pc
	t
	Pe 
	Ps

	0	D0
	Q1     Q0	Quantity 
Pe and Qe are the initial equilibrium price and quantity respectively, Price Pe is paid by the consumer and received by the producer. When quantity tax (per unit tax)’t’ is imposed, the supply curve shifts to the left from S0 to S1. Now with the existence of a tax price P is paid by the consumer but the producer receives only P5 per every unit sold. This means that out of the total per unit tax ’t’ imposed by government the consumer contributes (pays) amount PePc per every unit purchased, while the producer pays PsPe per unit sold. Q’ is the new quantity demanded by the consumer and supplied by the producer. As stated earlier it is difficult to describe the new equilibrium since price paid by the consumer is different from that received by the producer.

Alternatively we can illustrate the effect of a quantity tax on market equilibrium by looking at its impact on demand. The demand curve shifts inwards to the left by the amount of tax as shown in figure 3.22 below.
Figure 3.22: Effect of Tax on Demand

	    Price	

	S0
	Pc
	t
	Pe 
	Ps

	0	D1	D0
	Q1     Q0	Quantity 

The demand curve shifts inwards by the amount of tax‘t’. Pe and Qe are the initial equilibrium price and quantity respectively. After imposing tax, Q1 is the new quantity demanded that equals the new quantity supplied. P is the price paid by the consumer but the producer or seller receives P, the different Pc-Ps t: the per unit tax.

Let us now illustrate the effect of tax using a numerical example. Supposing that the demand and supply functions are as given below;
Qd  =  500 – 3P and 

Qs  =  100 + 5P

Where Qd and Qs are quantities demanded and supplied respectively while P is the price.

Equating the two equations, we get the equilibrium price and quantity as $50 and 350 units respectively.
Now supposing that a quantity tax (per unit tax) of $10 is imposed, we can use the two methods (i.e. effect of tax on supply curve or effect of tax on the demand curve) to find the new equilibrium quantity and the price paid by the consumer and that received by the producer.
First let us consider effect of tax on supply. Imposing a tax will shift the supply curve upwards to the left by the amount of tax, as we saw earlier.

Given that the supply function is,
Qs = 100 + 5P, it can be expressed as an inverse supply function by subjecting P as;

P  =  Qs – 20

Recalling that the supply curve will shift upwards to the left by the amount of tax, then new supply curve after tax will be;
P  =  Qs – (20 – 10) This gives us; 
Qs – 10 (Note that the slope is not affected but only the intercept). 

Or Qs = 5P + 50

Now equating the new supply function with the initial demand function, gives rise to new equilibrium quantity and new price paid by the consumer, i.e.
500 - 3P = 5F + 50

Collecting like terms together and solving for P, we get.
P = 56.25

This is the new price that the consumer shall pay for the good.
Substituting for F = $56.25 in either the new supply function or the demand function, we get the equilibrium quantity, which is,
Q = 331.25 units.
This is the quantity demanded by the consumer which is equal to that supplied by the producer.
Since the price now paid by the consumer is, F $56.25, yet the per unit tax is $10, it means that the price received by the producer is $46.25 i.e. $(56.25 -10), recall Pc = Ps + t. 

But out of the per unit tax of $10, the consumer pays, $(56.25 - 50) = $6.25, (i.e. price by the consumer after tax less the original equilibrium price), while the producer pays $(10 - 6.25) = $3.75, (i.e. tax imposed less that paid by the consumer).

Or $(50  - 46.25) = $3.75. (I.e. initial equilibrium price less that received by the producer after tax).

Finally, given that 331.25 units are demanded and sold, then the total amount of tax revenue received by government is $(1 Ox 331.25) $3312.5. Of this total tax revenue, the consumer contributes a total amount of $(6.25 x 331.25) = $2070.31, while the producer contributes a total of $(3.75 x 331.25) = $1242.19.

Similar results could be obtained if we considered the effect of tax on the demand curve. The demand curve would shift inwards to the left parallel to the original one by the amount of tax. That is given the original demand function as;

Qd = 500 - 3P

This can be rewritten as an inverse demand function, i.e.

P  =  

But since the demand curve shifts inwards by the amount of tax, the new demand curve after the imposition o a tax of $10 will be given by;

P  =   Or 

P  =   this can also be written as; 

Qd = 470 – 3P

Now solving for equilibrium quantity after tax using the initial supp function and the new demand function, i.e. equating;

Qs = 100 + 5P to Qd = 470 – 3P, we get, 

Q = 331.25 units. 

Substituting for Q =331.25

In either the original supply function or the new demand function, we get price received by the producer which is $46.25. Now adding the tax of $10 to the price received by the producer, we get the price paid by the consumer, i.e. $(10 + 46.25) = $56.25.

Effect of Tax on Consumer’s and Producer’s Surpluses
Imposition of a tax reduces both consumer’s surplus and producer’s surplus and creates revenue which is neither claimed by the producer nor the consumer nor government referred to as ‘dead weight loss’, as shown in figure 3.23 below.

Figure 2.23: Effect of Tax on Consumer’s Surplus and Producer’s Surplus

	    Price					    S1
	B
	S0
	Pc
	H	t
	Pe 	G
	Ps
	A

	0	D0
	Q1     Q0	Quantity 

Before tax is imposed, the equilibrium price and quantity are respectively; Pe and Qe and the consumer’s surplus before tax is given by area PeBC while the producer’s surplus is equal to area APeC. When tax per unit equal to’t’ is imposed, the supply curve shifts from So to S1. The new equilibrium is at point F where the equilibrium quantity is Q’ and price paid by the consumer is P while that received by the producer is P, such that
Pc – Ps = t.

Of the total per unit tax’ t’, the consumer pays Pc-Pe per every unit purchased while the producer pays Pe-Ps for every unit of commodity sold. We note here that the proportion paid by either the producer or the consumer depends on the steepness (elasticity) of both the demand and supply curves (see elasticity in chapter 4).

Since the after tax equilibrium is Q1, the total tax revenue received by government is PSPCFG (i.e. product of the new equilibrium quantity and tax rate), of which the consumer pays PePcFH and the rest is paid by the producer, i.e. PsPeHG.

The level of consumer’s surplus after tax is given by area PCBF, while that of producer’s surplus after tax is equal to area APSG. This means that part of the consumer’s surplus equal to area PePCFH and part of the producer’s surplus equal to PSPeHG are taken by government in form of tax revenue.

Some revenue, rather part of the combined surplus is however, lost such that neither the consumer nor the producer nor government gains it. The lost amount is equal to area GFC, This is known as the ‘dead weight loss’. Of this loss, the consumer losses FLFC, while the producer losses GHC. But these areas lost were originally part of their respective surpluses.

 Review Questions
1. 1) Briefly explain the following;
a)	A demand function,
b)	A demand schedule,
c)	A demand curve,
d)	The law of the demand.

2) Distinguish between;
a.	Change in quantity demanded and change in demand,
b.	Individual demand curve and market demand curve.

3) Briefly explain the factors that affect quantity demanded of a commodity.

4) Write briefly on the following; 
1.	A supply function,
2.	Supply schedule,
3.	Supply curve,
4.	The law of supply.
5) Distinguish between;
a)	a Change in quantity supplied and change in supply,
b)	Individual firm’s supply curve and market supply curve.

6) What are the factors that affect quantity supplied of a commodity?

7) 	(a) Distinguish between price ceiling and price floor,
(b)  What are the advantages and disadvantages of price ceiling and price floor?

8. Given the following sets of demand and supply functions, find the equilibrium price and quantity
a)	Qd = 500 – 3P
Qs = 100 + 5P

b)	Qd  =  500
Qs  =  100 + 2P

c)	P = 120 – 3Qd
P  =  5Qs

9) 	(a) What is market equilibrium?
(b) Distinguish between stable and unstable market equilibrium.

I 0), Given the following demand and supply functions;
	Qd  =  500 – 3P
	Qs  =  100 + 5P

Supposing that price is fixed $40. State whether it is price ceiling or price floor and determine the size of either the shortage of surplus.

11) Given the following demand and supply function;
 	Qd  =  500 – 3P and Qs  =  100 + 5P.
Determine the value of the consumer’s surplus and producer’s surplus.

12) Given that the demand and supply functions are; 
	Qd  =  500 – 3P and Qs = 100 + 5P

13)  Given the following demand schedules;

Price 	120	100	80	60	50	40	30	
Quantity 	0	2	6	11	18	28	40	

Supposing that the market price is $50, find the consumer’s surplus. 
Price 	20	40	60	80	100	120	150	200	
Quantity 	0	1	4	9	15	22	30	50	
If the market price is $120, find the producer’s surplus. 

Unite 3
Elasticity
3.1	Introduction
In the preceding chapter we discussed, among others; factors that affect the quantity demanded and supplied of a good, We saw that some of these factors are measurable such as; price of the commodity, consumer’s income, price of other goods, while some factors are not measurable such as; consumer’s tastes, religion of the consumer, cultural factors, seasons of the year and many others. A given change in any of these factors affect the responsiveness of quantity demanded or supplied of a commodity. It is this responsiveness that is referred to as elasticity in Economics. In other words, elasticity refers to the responsiveness to change of either quantity demanded or supplied. Basically therefore, there are two types of elasticity:

i)	Elasticity of demand and
ii)	Elasticity of supply.

3.2	Elasticity of Demand
This refers to responsiveness of quantity demanded due to a given percentage change in a facto that affect quantity demanded. Accordingly therefore, there ought to be as many types of elasticity of demand as there are factors of demand. ‘However, as noted earlier, quantity demanded is influenced by many factors some of which can not be quantified for instance tastes, religion etc. The study of elasticity therefore, concentrates on quantifiable factors such as; price of the commodity, price of related commodities and income of the consumer. This gives rise to three key types of elasticity of demand which are respectively;
i)	Price elasticity of demand,
ii)	Income elasticity of demand and
iii)	Cross elasticity of demand.

Price Elasticity of Demand (ep)
This refers to the responsiveness of quantity demanded due to a unit percentage change in the commodity price, that is;
ep	 = 	Percentage change in quantity demanded
Percentage change in price of the commodity

ep  =  

When simplified we get;

Where Q is quantity demanded and P is price.

From the above formula, the term is the gradient of the demand curve. But since a normal demand curve is downward sloped, this term is always negative. Therefore, negative one (-1) is pre-multiplied into the expression so as to turn the value positive, that is:

1.  ep  =  (-) 
This is the formula for price elasticity of demand.
 Point elasticity
Point elasticity of demand measures the price elasticity of demand at a point on a demand curve. It therefore measures the effect of small percentage changes in price. It is given by the formula:

2. ep  (-) 

4.1.1.2  Arc elasticity on the other hand, refers to the price elasticity of demand between two points (an arc) on a demand curve. It is given by the formula:

	ep  =  

	=	(-) 
Or simply as; 

3.  ep  =  (-) 

This therefore means that arc elasticity is simply the average elasticity of the point elasticity at the two points. 

Example 
Given the following demand schedule
Point 	Point (P)	Quantity (Q)	
A	30	10	
B	15	20	

Find 
i)	The price elasticity of demand at point A.
ii)	The price elasticity of demand at point B.
iii)	The price elasticity of demand between point A and B.
iv)	The price elasticity of demand between point B and A.

We note that (i) and (ii) are point elasticity and yield different solutions while (iii) and (iv) are arc elasticity so they yield the same value. We shall solve parts (i) and (iii) and the reader should solve (ii) and (iv). The student should find out that the value for parts (iii) and (iv) is the exact average of the values of parts (i) and (ii). In other words, arc elasticity is the exact average of point elasticity at the two given points.

(i)	 Point elasticity at point A
From the formula; 

	ep  =  (-) 

At point A, Price (P) = 30, quantity (Q) = 10, change in quantity Dq = (20 – 10) = 10 While change in price Dp = (15 – 30) = -15. 

S0  ep  =  (-)  -  = 1.5

(ii)	Price elasticity of demand between points A and B.
Using the formula

	ep  =  (-)  

Where, P1 and Q1 are price and quantity respectively at point A, while P2 and Q2 are the respective price and quantity at point B. Given; 

P1 = 30, P2 = 15, Q1 = 10, Q2 = 20, ΔQ = 10 and ΔP = -15, then by substation, we get

	ep  =  
Price Elasticity of Demand along a Linear Demand Curve
The following presentation shows that price elasticity of demand is not constant but instead varies along a demand curve. The knowledge of the value of price elasticity is of great importance particularly to a monopolistic producer when setting the price of her commodity as we shall see later in this chapter. 

Given a linear demand function:

4. Q = α – βP

Where Q is the quantity demanded, P is price, α and β are positive constant. Its slope is equal to; 

5.   =  -β

Then substituting for the slope in the formula for price elasticity of demand (point elasticity of demand), we get; 

6.  ep  =  β 

Since β is fixed, while price P and quantity Q vary, then the above expression (equation 6) shows that elasticity varies along a linear demand curve. Graphically, this is shown in figure 4.1 below. 

Figure 4.1:  A Linear Demand Curve 

	Price 	A

                               0   	B
	Quantity 
If we consider the above diagram together with the equation 6, and since the size β is fixed (slope of a linear curve is constant) we note that: At point A, quantity demanded (Q) is zero, substituting for Q = 0 in equation 6, we find that price elasticity is infinite. While at point B, price is zero implying that elasticity is zero by substitution.

Since points A and B are two extreme points on a demand curve, this therefore suggests the price elasticity of demand varies between zero and infinite i.e. 0 ≤ ep ≤ ∞  

Five different cases of elasticity can be identified. 

Case (i): Perfectly Inelastic Demand (ep = 0)
This is when price elasticity is zero. In this case therefore a change in price of the commodity does not affect its quantity demanded, implying that its demand curve is vertical.

Figure 4.2: Perfectly Inelastic Demand Curve

	Price 	  DD

	P2	        B
dP
                              P1                               A

	Q1	Quantity 

Case (ii): Inelastic Demand (ep < 1)
In this case, price elasticity lies between zero and one i.e. 0 < ep < 1. This means that a large percentage change in price lead to small percentage change in quantity demanded. The demand curve is therefore very steep. 

Figure 4.3: Inelastic Demand 

	Price	D

	P2	A

                                    dP

	P1	B
	
		   D
	0
	Q2        Q2	Quantity 

Case (iii): Unitary Elastic Demand (ep = 1)
In this case price elasticity is unit. This means that a given percentage change in price leads to equal percentage change in quantity demanded. 

Figure 4.4: Unitary Elastic Demand 
	Price 

	P2	B

	P1	          A
	DD
	0
	Q2           Q1          Quantity 

Cast (iv): Elastic Demand (ep > 1)
A commodity is price elastic if its elasticity exceeds unity. This would mean that, a small percentage change in price leads to a magnified percentage change in quantity demanded. Graphically, the curve is flatter.  

Figure 4.5: Elastic Demand 

	Price 
	A
	P1
	P2	B
	DD

                        0
	Q1                        Q1         Quantity 

Case (v): Perfectly Elastic Demand (p = ∞)
In this case, price elasticity is infinite meaning that quantity demanded changes with out a change in the price of a commodity. In other words infinite quantities are demanded at the same price. Graphically, the curve is horizontal.

Figure 4.6: Perfectly Elastic Demand
                    Price 

	P1	A                B	DD

	Q1               Q2   
	Quantity 

4.1.1.4: Factors that Affect the Coefficient of Price Elasticity of Demand
•	Number of substitutes
A commodity that has many close substitutes is likely to be price elastic. This is so because any slight increase in the price of the commodity, consumers will reduce the - consumption of the commodity significantly but increase the quantity demanded of the substitute commodities. Therefore the greater the number of close substitutes the higher the price elasticity of demand and vice versa.

•	Number of uses of the commodity
A commodity that has many uses tends to be more price inelastic than one with few uses. This is because the consumer will only reduce the number of uses when its price increases. For instance, consider electricity, this can be used for cooking, lighting, water heating, radio and TV sets etc. Suppose its price rises, the consumer may stop using it for cooking and water heating but continue using it for other purposes. Therefore the greater the number of uses, the more inelastic the commodity is likely to be and vice versa.

•	The consumer’s habits
When a consumer is addicted to a commodity, changes in its price may not affect much the quantity demanded of the commodity. For instance commodities such as beers (alcohols), cigarettes are price inelastic.

•	The proportion of income spent on the commodity
If a commodity takes a very small percentage of the consumer’s income, then changes in its price may not affect much its quantity demanded. Therefore the smaller the percentage of income spent on the commodity, the more inelastic the commodity is likely to be and vice versa. For instance commodities such as; matchbox, needle, aspirin- tabs are price inelastic.

•	The degree of necessity
The higher the degree of necessity of a commodity the more inelastic it is likely to be. This is because since the commodity is indispensable, increases in its price may not affect much the quantity demanded of the commodity. For instance commodities such as water, food, salt are price inelastic.

Solved Example
Given the following demand and supply functions. Find the price elasticity of demand at the equilibrium point.
Qd =36 - 4P and,
Qs = -12+12P

Solution
We need first to obtain the equilibrium price and quantity. From simple calculations (left to the students as an exercise), at the equilibrium point, price (F) is 3 and quantity (Q) is 24. Since we need to find price elasticity of demand, we now refer to the demand function from which we get the gradient i.e.

From Qd =36 -  4P, differentiating with respect to P we get the slope of the demand function, that is;

=  -4

Now using the formula for price elasticity of demand:

ep  =  =  0.5

This means that a unit percentage change in price leads to a 0.5 percentage change in quantity demanded. Since the value is less than unit, it means that the commodity has an inelastic demand.

4.1.2: Cross Elasticity
This refers to the responsiveness of quantity demanded of a commodity due to a given change in the price of another good, it therefore measures the percentage change in quantity of a good say Y arising from a given percentage change in the price of another good say X . That is;

	exy = Percentage change in quantity of good Y
         Percentage change in price of good X
	=  

Cross elasticity of demand takes on three possible values, that is; it can be negative, zero or positive.

Case (i): When Cross Elasticity is Negative
This would imply that an increase in price of commodity X leads to a fall in the quantity of good Y and vice versa. From the law of demand, increase in price of good X will lead to a fall in its quantity demanded. But since reduction in quantity of good X which is caused by an increase in price of good X is accompanied by a fall in quantity demanded of good Y, it would imply that goods X and Y are consumed together at the same time this would then mean that commodities X and Y are complements.

The magnitude of the value of cross elasticity determines the degree of complementarity. For instance consider two sets of goods A, B and X, Y if their corresponding cross elasticities are;

eAB  =  -0.4		and exy =  -1.6

Then commodities X and Y are stronger complements while A and B are weak complements.

Case (ii): When Cross Elasticity is Positive
If the value of cross elasticity of demand is positive, it would imply that an increase in the price of commodity X leads to an increase in quantity demanded of another good Y. But clearly from the law of demand, as price of good X rises less of it is demanded. But now that the consumer reduces the quantity of good X because its prise has risen and increases that of good Y yet its price has not fallen, it would mean that goods X and Y are Substitute goods. Generally therefore, when cross elasticity of demand is positive, it means that the two goods are substitute goods. However, the degree of substitutability depends on the size of the value of cross elasticity of demand. For instance consider two sets of goods A, B and X, Y. If their corresponding cross-elasticities are:
exy = 0.3 and eAB 1.4 then X and Y are weak substitutes while A and B are strong substitutes.

Case (iii): When Cross Elasticity is Zero
If however, the cross elasticity of demand is zero, it would mean that a change in the price of a good say X does not affect the quantity demanded of another good Y. In this case therefore commodities X and Y are said to be unrelated.

In summary therefore, if the value of the cross elasticity of demand of commodities X and Y is:

•	Negative, then X and Y are complements
•	Zero, then X and Y are not related
•	Positive, then X and Y are substitutes.
And the coefficient is determined by the degree of complentarity and the degree of substitutability. In other words, when goods are strong substitutes, then the cross elasticity of demand is positive and greater than unit or less than unit if they are weak substitutes. On the other hand if the goods are strong complements, then their cross elasticity is negative and greater than one in absolute terms or less than one (in absolute terms) if they are weak complements.

4.1.3: Income Elasticity of Demand
This refers to the responsiveness of quantity demanded of a commodity due to a given percentage change in the consumer’s income. It can also be defined as the percentage change in quantity demanded of a commodity divide by a given percentage change in the consumer’s income. That is,

	ey  =  
This can be simplified to give.

	ey  =  
Where; 

ey 	=	 income elasticity of demand
Y	 = 	income of the consumer
Q 	 = 	quantity demanded
dQ	 = 	change in quantity demanded,
dY 	= 	change in the consumer’s income.

Income elasticity of demand also takes on three possible values, i.e. it can be negative, zero or positive.

Case (i): When Income Elasticity of Demand is Negative
This would imply that an increase in the consumer’s income leads to less quantity demanded of the commodity. Such a commodity with negative income elasticity of demand is called an inferior good.

The size of the value of this income elasticity of demand determines the degree of inferiority of the good. For instance suppose the income elasticity of goods X and Y are (-0.48) and (-1.76) respectively, then commodity X is a weak inferior good and Y is a strong inferior good also known as a giffen good.

Case (ii): When Income Elasticity is Zero
This would imply that changes in the consumer’s income do not affect the quantity demanded of the commodity. A commodity with zero income elasticity of demand is called a necessity. This means that an increase or decrease in the consumer’s income does not affect the quantity demanded of a necessity of commodity.

Case (iii): Income Elasticity is Positive
This would imply that an increase in the consumer’s income leads to an increase in the quantity demanded of the commodity. Similarly a fall in the consumer’s income would lead to a fall in the quantity demanded of the commodity. A commodity with positive income elasticity of demand is called a normal good. The degree of normality of a good is determined by the size of the income elasticity of demand. For instance, suppose the respective income elasticity of goods X and Y are 0.3 and 1.8 then X is a weak normal good while Y is a stronger normal good also known as a luxury.

In summary therefore, if the value of income elasticity of demand of a good X is;
•	Negative, then X is an inferior good,
•	Zero then X is a necessity,
•	Positive then X is a normal good.

4.1.2.1: Factors that affect the Coefficient of Income Elasticity of Demand
Several factors affect the coefficient of income elasticity of demand and these include;
i)	The degree of necessity of the commodity: Certain commodities are indispensable to human life or to certain households, therefore for such commodities that a household can not do without, even if the household’s income fell greatly, it would continue purchasing the commodity although with a slight reduction. Such commodities have income elasticity of demand close to zero. Examples of such commodities include; salt, food, sugar to some households etc.

ii)	The initial income level of the household is also a key factor: Some commodities may be considered necessities by very rich households (e.g. Cars, Television sets etc), where as they are considered to be luxuries by poor households. On the other hand some commodities may be considered inferior goods such as ;second hand clothes, plastic cups, where as they are considered normal goods by poor households.

iii)	 Number of uses of the commodity: if a commodity has several uses, it tends to be a normal good. This is because at higher levels of income, more of the commodity is purchased so as to be used on other services, while at lower income; less shall be purchased because other services for which the commodity is used for may be left out. For example consider electricity, it can be used for lighting, ironing, cooking, water heating etc. At lower household income, uses such as cooking and water heating may be left out and use power for only lighting while at higher income levels, more and more uses are adopte1.

iv)	Proportion of income spent on the commodity is also a key factor. For instance if the commodity takes a very small percentage of the consumer’s income, changes in the consumer’s income may not affect much of its quantity demanded hence its income elasticity tends to zero.

v)	Fashion and design: This is another key factor of income elasticity of demand. In this case, the most recent fashion or design tends to be superior or luxury goods hence have income elasticity of demand that is positive and greater than one. But fashions that are of remote period tends to be inferior hence have income elasticity of demand which is negative and less than one.

3.3	 Uses of Price Elasticity of Demand
As we shall see shortly, there are many uses of elasticity in policy making. The policies include; setting of prices, taxation and international trade specifically devaluation. The knowledge of the value of price elasticity of demand can enable a producer to make the production decisions, that is, whether to expand production or reduce production, hence sales, whether to increase the price or reduce the price of the commodity and to government whether to impose a tax or subsidy or whether to devalue (depreciate) its currency or revalue (appreciate) its currency.

Setting price of a Commodity
With the knowledge of the value of the price elasticity of demand, producers can set the price of the commodity in such a way to increase the firms revenue ,hence profits. Specifically when a commodity has inelastic demand, to increase the firm’s revenue, the producer should increase the price of the commodity since a greater proportionate change in price will only lead to a proportionately less fall in the quantity demanded. On the other hand, if the producer of a commodity with an inelastic demand reduced its price, the firm’s revenue would fall, implying that the firm would lose profits.

But if the commodity has an elastic demand, to increase the firm’s revenue, the producer should reduce the price of the commodity since a small reduction in price would lead to a proportionately greater increase in quantity demanded, and with an increase in price of an elastic good, the firm’s revenue would fall.

On the other hand if a commodity has unitary elastic demand, changes in its price would leave the firm’s revenue unaffected.

This can be illustrated using figure 4.7 below. 

Figure 4.7: Effect of Price Elasticity of Demand on Revenue

	Revenue 

       R3
       R5

       R2
       R1

	
	TR

	Q1        Q2        Q3       Q4  Q5	Quantity 
         Price 

	A
	B
	C
	E   F
	DD

	Q1         Q2        Q3         Q4   Q5	Quantity 

	MR

As we saw earlier, price elasticity of demand varies along a linear demand curve. It is elastic towards the price (vertical axis) and inelastic towards the quantity (horizontal axis) i.e. to the left of point C on the demand curve, elasticity is greater than unit (elastic), while to the right of point C it is less than unit (inelastic). Now supposing that price is reduced from P1 to P2, quantity demanded would increase from Q1 to Q2 and revenue would also rise from R1 to R2, hence the firm would gain from a price reduction. In this same region (elastic) however, if the producer instead decided to increase price from P2 to P1, her revenue would instead fall from R2 to R1. This suggests that when the commodity is price elastic, to increase revenue, a producer should reduce price.

Next let us consider a region that is price inelastic (to the right of point C). For instance, if the firm reduced price from P4 to P5, quantity demanded would increase from Q4 to Q5 but revenue would fall from R4 to R5. This suggests that the firm would lose revenue from a price reduction of an inelastic good. But the firm would increase revenue if it increases price from say P5 to P4 since its revenue would now rise from R5 to R4.

Therefore, a producer whose commodity is price elastic, can increase revenue if she reduces its price, while that whose good is price inelastic can increase revenue if she increases its price.

Elasticity and Revenue, Mathematical Approach
Total revenue of a firm is defined as the product of price of the commodity and quantity sold i.e.

R = P.Q

Our interest is to see the effect of a change in price on total revenue. Remember that along a normal both price (P) and quantity (Q) change. Therefore to get the effect of change in price on total revenue we need to use the product rule of differentiation such that;

But from our earlier definition, price elasticity of demand is given by; 

	ep = (-) 

Rearranging gives; 

Next we substitute for and we get 

This can be simplified to give; 

We can now use the above expression to analyze the effects of a change in commodity price on its revenue. For instance supposing that the commodity is price elastic (elasticity is greater than unit), clearly the value in the brackets would be negative and since quantity can never be negative then the term must be negative.

Simply what this means is that increase in the price of an elastic good leads to a fall in its revenue because its demand would fall greatly. The reverse is true that is, a reduction in the price of an elastic commodity would lead to an increase in revenue since its demand would increase greatly.

Similarly from the equation above, if a commodity is price inelastic (elasticity is less than unit) then   would be positive (the reader should verify this by substituting any value of ep that lies between 0 and 1). Since  is positive, this would mean that increase in price (P) would lead to increase in revenue (R) or a reduction in price would lead to a reduction in revenue. In other words for a commodity whose demand is price inelastic, increase in its price would lead to an increase in revenue while a reduction in its price would lead to a reduction in its revenue.

What about a case when price elasticity is unit? Clearly if we substitute for ep = 1 in the above expression, collapses to zero. This would mean that if a commodity has unitary elasticity, then a change in its price (either increase or reduction) would leave revenue unchanged.

4.2.2: Elasticity and Tax
As we saw in the previous chapter, when a tax is imposed, both the consumer and producer are affected because both contribute towards the tax and less quantity is demanded and supplied. We however, need to note that the proportion of the tax incurred by either the consumer or the producer depends on the price elasticity of both the demand curve and supply curve. We next illustrate the impact of a tax on both the consumer and producer given different elasticity of demand and supply curves. For instance when the demand curve is perfectly inelastic, or the supply curve is perfectly elastic, all the tax is paid by the consumer in form of increased purchase price as shown in figure 4.8 below.

Figure 4.8: Effect of Tax when a Demand curve is Perfectly Inelastic
	Price 

	S1

	P1	S0
                                                                t
	P0

			0	Q0	Quantity 

When a demand curve is perfectly inelastic, the equilibrium quantity does not change even when a tax is imposed, but price changes. The initial equilibrium price paid by the consumer and received by the producer is P0. When tax‘t’ is imposed, the consumer now pays price P1 for the same quantity Q0 but the producer continues to receive the original price P0. Since tax ‘t’ is equivalent to the difference in prices P1-P0, implying that all the tax is borne by the consumer. Therefore when a demand curve is perfectly inelastic, all the tax is paid by the consumer and none by the producer. This is similar to a case when the supply curve is perfectly elastic as shown in figure 4.9.

Figure 4.9: Effects of Tax when the Supply curve is Perfectly Elastic 

	Price

	P1	S1
	t

	P0	S0
	D0
	0
	Q1	    Q0                   Quantity 

When a per-unit tax ‘t’ is imposed, the supply curve shifts upwards to S1 by the amount of tax. Equilibrium quantity falls and the price rises by the amount of tax. Although the consumer now purchases at price P1, the producer continues receiving price P0 for every unit sold, implying that all the tax is paid by the consumer.

Effect of Tax when the Demand Curve is 	Perfectly Elastic
Before the tax is imposed, Q0 is the equilibrium quantity and Po is the equilibrium price paid by the consumer and received by the seller (producer). When a per-unit tax ‘t’ is imposed, the supply curve shifts from S0 to S1 by the amount of tax ‘t’. At the new equilibrium, the consumer continues to pay price P0 but for less quantity Q1 and the producer receives only price P1. This means that the difference in price P0-P1 which is equivalent to the per unit tax ‘t’ is incurred by the producer alone: since she originally received price Po before tax but she now (after tax is imposed) receives price P1. as shown in figure 4.10.

Figure 4.10: Effect of Tax on a Perfectly Elastic Good

	Price	S1
	S0

	P0	D0
  t

                                 P1

	0
	                                                     Q1              Q0         Quantity 

Similar results can be obtained when the supply curve is perfectly inelastic. 

Figure 4.11: Effect of Tax on a good with a Perfectly Inelastic Supply Curve 

	Price	S0

	P0
	P1	t
	D0
	D1
	0
	Q0                   Quantity 

Before tax is imposed, Po is the equilibrium price and Q0 the equilibrium quantity. Since supply is fixed, quantity demanded supplied does not change even after tax is imposed instead it is the demand curve that shifts downwards to the left by the amount of tax from D0 to D1. The producer will now receive price P1 for the same quantity Q0 sold but the consumer will continue paying price P0. This implies that it is the producer who bares all the tax.

Let us now consider a normal demand and supply curves. If the demand curve is inelastic, more of the tax shall be paid by the consumer as shown in figure 4.12.

Figure 4.12: Effect of Tax on a Good with Inelastic Demand 

	Price
	S1
	S0

	Pe
	P0	t
	Ps

	D0

	0	Q1  Q0	Quantity 

At the original equilibrium, Q0 and P0 are the equilibrium quantity and price respectively. Price P0 is received by the producer and paid by the consumer. When a tax ‘t’ is imposed, the supply curve shifts upwards to the left to S1. The new equilibrium quantity is Q1 and is less than the original one. The consumer now pays Pc but the producer (seller) receives only price Ps. The difference Pc - Ps is the per-unit tax ‘t’ that was imposed. Of this tax t = Pc - Ps the greater Pc – P0 is paid by the consumer while the producer pays a smaller proportion P0 – Ps. This is so because the demand curve is inelastic.

However, if the demand curve is elastic, more of the tax is paid the producer (see figure
4.13).

Figure 4.13: Effect of Tax on a Good with Elastic Demand Curve

	Price 

	S1

	Pc	S0
	P0	t
	D
	Ps

	0
                                            Q1              Q0          Quantity 

The original equilibrium price and quantity are P0 and Q0 respectively. Price Po is paid by the consumer and received by the producer. After tax ‘t’ is imposed, the new equilibrium quantity is Q1 and the new price paid by the consumer is Pc but the producer receives only price Ps. Of the per unit tax t = Pc – Ps, a smaller proportion Pc – P0 is paid by the consumer, while the producer pays the greater proportion P0 - Ps. This means that when the demand curve is elastic, the consumer pays less proportionate tax than the producer.

The dividing line is when the demand curve is unitary elastic. In this case both the consumer and the producer pay equal proportion of the tax.

Figure 4.14: Effect of Tax on a Unitary Elastic Good

	Price 

	S1

	Pc	S0
	P0	t
	D
	Ps

	0
                                            Q1              Q0          Quantity 

In the case of a unitary elastic good, when a tax ‘t’ is imposed, both the consumer producer share it in equal proportions: Pc – P0 = P0 – Ps. That is, tax paid by consumer equals to that paid by the producer respectively.

In summary, the effect of an increase in tax on market equilibrium is that it shifts t supply curve upwards to the left. This is because effect of a tax is similar to a change cost of production. So increase in tax leads to increase in the cost of production leading to a shift in the supply curve upwards to the left. This will in turn lead to an increase the price of the commodity and a fall in the quantity demanded. If the demand curve is normal, the, tax is shared by both the producer and the consumer. However, the extent c. the tax burden depends on the elasticity of the demand curve. For instance if the demand] curve is inelastic, the greater portion of the tax is paid by the consumer and vice versa the demand curve is elastic. Similarly if the demand curve is perfectly inelastic, all + tax is paid by the consumer. And if it is perfectly elastic, all the tax is paid by the producer. Both the consumer and producer pay equal proportion of the tax when the demand curve is unitary elastic.

4.2.3: Elasticity and Devaluation
Devaluation refers to the legal reduction of the value of a country’s currency in terms of other currencies by the monetary authorities. It is an exchange rate policy which is only applied when a country runs a fixed exchange rate regime. A currency is said to be devalued if the official exchange rate is increased say from $1 = Shl000 to $1 Sh1500 implying that one now needs more shillings to purchase a dollar. The major objective of the devaluation policy is to increase revenue from a country’s exports and reduce expenditure on imports hence improving the trade balance position (exports less imports) of a country. Implicitly, devaluation is equivalent to a reduction in price of exports. But as we saw earlier in this chapter, this can only be successful if the country’s exports are price elastic both in demand and supply.

 Review Questions
1. 9 Clearly explain the effect of increase in tax on a good that is;
(i)	Price elastic,
(ii)	Price inelastic,
(iii)	Unitary price elastic,
(iv)	Perfectly price elastic,
(v)	Perfectly price inelastic.

10 Given the following demand function for good X;
 	Qdx = 50 – 0.4Px + 0.5Py – 0.25B

Where;
Px is the price of good X,
Py  = price of good Y,
B  = consumer’s income.

(a) Determine;
(i)	Price elasticity of demand,
(ii)	Cross elasticity of demand,
(iii)	Income elasticity of demand.

(b) Suppose P = 20, P,, =30 and B =52
Find the value of;
(i)	Price elasticity of demand,
(ii)	Cross elasticity of demand,
(iii)	Income elasticity of demand.
(c) From your answers in part (b) above,
(i)	How would you advice the producer if she is to increase revenue?
(i)	What is the relationship between goods X and Y and suppose the price of good X goes up, how would you advice the producer of good Y?
(ii)	What type of good is X? And suppose the income of the
(iii)	consumer went up, how would you advice the producer of good X?

11  Suppose Uganda’s major export is coffee, should Ugandan farmers celebrate when the Ugandan shilling depreciates (devalued)?

12 Supposing that you are an economic consultant and you find that the price elasticity of demand for Uganda’s coffee was under estimated, how will your findings be useful to;
(i)	rile coffee producers?
(ii)	To government?

13 Suppose you are a business consultant and your findings show that the price elasticity of a certain commodity X was over estimated. How might your fmdings be useful to the;
(i)	Producers of good X?
(ii)	Consumers of good X?
(iii)	To government?

Unite 4
Theory of Consumer Behaviour 
4.1	Introduction
In chapter three we discussed the concept of a market. We saw that a market comprises mainly the consumer and a producer. A consumer was represented by a demand curve while  a producer by a supply curve. In this chapter, we shall concentrate on a consumer by looking at the behavior of a consumer in exclusion from both other consumers and producers. 

We recall that a consumer is one who uses goods and services to satisfy her wants. She is assumed to be rational meaning that he aims at utility maximization; given her income and commodity prices. There are several theories that have been developed to try and explain the behavior of a consumer. However, they can be categorized into two distinct theories:

(i)	Cardinal utility theory which argues that a consumer has the capacity to measure the level of satisfaction that she derives from consumption of a given quantity of a commodity.

(ii)	Ordinal utility theory which argues that a consumer can not measure satisfaction numerically or subjectively. Instead she can rank the different baskets or bundles so as to choose the best basket.

4.2	Cardinal Utility Theory
The basic concept in this approach is utility;, which refers to the satisfying power that a good or service consumed possesses. In this approach it is assumed that a consumer assigns a cardinal measure which can be counted. This means that a consumer can tell exactly how much satisfaction she can derive from the consumption of a certain good. The theory assumes a cardinal measure in units called Utils i.e. that utility can be measured subjectively in units called Utils using an instrument called a Utilometer. However, some economists have suggested that utility can be measured in monetary units by the amount of money offered for a commodity.

Assumptions to the Cardinal Utility Theory
The Cardinal utility theory is based on the following assumptions;
•	Rationality: By the term rationality in consumption, we mean that a consumer aims at maximizing her utility given her income and the prices of the commodities purchased by her. The consumer will always exhaust the income if she is to maximize her satisfaction.
•	Utility is subjective: This means that the consumer is capable of measuring numerically and exactly the level of satisfaction that she gets from the consumption of a good. She is therefore able to know how much satisfaction he gets from the different bundles of goods consumed by her.
•	Total utility of a basket of goods depends on the different quantities of the individual commodities consumed by her i.e. U = U(Xi);i = 1,2...,n are the different quantities of the commodity. This means that the consumer derives satisfaction from all the different units of commodities consumed by her alone.
•	Consumer derives utility from the consumption of every commodity consumed by her. The consumer’s utility function is therefore independent of the utility functions of other consumers. This also means that, whether the consumer decides to buy or not, depends entirely on personal preference. So the consumer is assumed not be under influence of other consumers.
•	The theory assumes the consumption of only one commodity.
•	 All commodities available to the consumer are perfectly divisible into smaller units.
•	When more of a single commodity is consumed, total utility increases, reaches maximum then falls.
•	The theory assumes diminishing marginal (addition) satisfaction or utility as more of a single commodity is consumed. In other words, it is based on the law of diminishing marginal utility which states that, “As more and more of a single commodity is consumed, each additional unit consumed provides the consumer with less and less additional satisfaction than the preceding unit.”

4.3	Total Utility (TU)
This refers to total satisfaction derived by an individual from the consumption of a good or service. In other words, it refers to the sum of individual utilities derived from the different units of a particular commodity consumed. Graphically, the Total Utility curve rises from zero up to maximum point referred to as the point of satiety then it falls. The curve behaves in accordance with the law of diminishing marginal utility.
Figure 5.1: Total Utility Curve

	Utility 	             Point of Satiety

TU

	 0
	Xm                          Quantity of Good X

4.4	Marginal Utility (MU)
This refers to the additional utility derived from consumption of an extra unit of a commodity. It can therefore be defined as the change in total utility divided by change in quantity of a commodity consumed, that is;

	MU  =  .

In other words MU is the slope or gradient of the utility function. This implies that when the total utility function (TU) is rising, marginal utility (MU) is positive, and when TU reaches maximum MU is zero and when the TU function is falling MU is negative. We can illustrate this using figure 5.2 below. 

Figure 5.2: Marginal Utility Curve 

	Utility 	             Point of Satiety

TU

	 0
	Xm                          Quantity of Good X

Marginal 
	Utility 

	0
	Xm	Quantity of Good X

MU
The shape of the MU curve is in accordance with the law of diminishing marginal utility, which states that “as more and more of a given commodity is consumed, additional utility (MU) will keep on falling”. This law is illustrated using the following hypothetical table. 

A hypothetical Examples 
Quantity of X	Utility 	MU	
0	0		
1	12	12	
2	22	10	
3	30	8	
4	35	5	
5	35	0	
6	34	-1	
7	30	-4	
8	25	-5	

4.5	Equilibrium of a Consumer under the Cardinal Utility Approach
A consumer is said to be in equilibrium when she equates her marginal utility with the price of the commodity. This implies that the consumer can measure the satisfaction in money terms. If a consumer’s marginal utility exceeds the price of a commodity, the consumer  should purchase more units of the commodity. But as she consumes more of commodity, the marginal utility will start falling up to a point when the MU equals to the price of a commodity. At that point, the consumer shall be in equilibrium. On the other hand when the price of a commodity exceeds marginal utility, the consumer should  purchase less and less units of the commodity. As less and less units are consumed marginal utility will start rising up to the point when it is equal to the price of the commodity. Therefore at equilibrium, Mux = Px. 

However, it is not always the case that an individual will consume only one good, for simplicity, if we consider a situation where a consumer purchases two commodities, the consumer will be in equilibrium when she equates the marginal utility derived from each commodity to its respective price, that is;
ii.	Mux  =  Px
iii.	Muy  =  Py
Dividing equation (1) by equation (2) we get:
iv.	
The above expression states that a consumer is in equilibrium when she equates the of marginal utilities obtained from two commodities to the ratio of their respec prices. Rearranging the above expression we get;
v.	
Basing on the expression in equation (4), we can now write the general equilibrium condition of a consumer who consumes several commodities as;
vi.	 =  ……………… = 
The above expression means that the consumer is in equilibrium when she gets e additional satisfaction upon spending an extra unit of her income on any of commodities given the commodity prices.
Deriving a Demand Curve Using the Cardinal Utility Approach
The Cardinal utility approach provides a simple and clear approach to deriving demand curve of a normal good. It uses the concept of diminishing marginal utility the equilibrium condition where a consumer equates marginal utility to the price. Therefore as more and more units of a commodity are consumed, less and 1 additional (marginal) utility is derived thus the consumer shall be willing to pay less amount of money. The derivation shown in figure 5.3 below is based on following assumptions.
•	Utility is measured in money terms, hence at equilibrium; Mux = Px . marginal utility equals to price.
•	We assume the law of diminishing marginal utility, implying that if the marginal utility diminishes then the consumer should pay a lower price.
•	We assume that the consumer is rational (i.e. aims at utility maximization).
•	The consumer consumes one commodity.
•	The commodity is a normal good.
Figure 5.3: Deriving a Demand Curve using the Cardinal Utility Approach 

	Utility 	             Point of Satiety

	U2
TU

	U1

	 0
	X1   X2	Xm                          Quantity of Good X

Marginal 
	Utility 
                                                                                                P1 	                A
                                                                                            P2	                                   Demand 
	B	 Curve 

	0	C
	Xm                  Quantity of Good X  X1  X2      Xm
MU
From the above diagram we note that the Marginal utility curve falls continuously as the consumer consumes more units of X and this is due to the law of diminishing marginal utility. The consumer derives Total utility U1, from quantity X1 of commodity X and a higher Marginal utility: MU1 from that quantity. But since, at equilibrium the consumer equates marginal utility to price, i.e. MU1 = P1. Then she will be willing to pay a higher price P1 for quantity X1. This gives rise to point A on the demand curve. Similarly from quantity X2 units of the commodity the consumer derives total utility U2, and lower marginal utility MU2, but from the definition of consumer equilibrium, MU2 = P2. Therefore, she is willing to pay a lower price P2 for greater quantity X2 of commodity X. Accordingly, the consumer shall demaand quantity X2 at price P2 giving rise to point B on the demand curve. Quantity Xm of the commodity, gives the consumer the maximum total satisfaction, hence it yields zero marginal utility. Therefore by definition of consumer equilibrium the consumer shall be willing to pay a price of zero shillings for quantity X3 since MU3 = P3 = 0. Joining points A, B and C gives rise to a demand curve of commodity X.

We note that quantities of commodity X greater than X3 give rise to negative marginal utility, thus by definition of consumer equilibrium, the consumer should pay equivalently negative prices. But negative price have no meaningful economic implication. Accordingly we ignore the section of the demand curve beyond point C. Therefore the demand curve is equivalent to the positive section of the marginal utility curve.

4.6	Indifference Curve Approach (Ordinal Utility Theory)
The Ordinal utility theory of consumer behaviour is also commonly known as the indifference curve theory because its analysis is based on indifference curves. The major difference between the Ordinal theory and the Cardinal utility theory is that under the ordinal utility theory, the consumer cannot measure numerically the level of satisfaction derived from consumption of a good but can instead arrange or rank the different baskets of goods basing on the quantities contained in each and their satisfying power with the assumption that the goods are homogeneous. The consumer is assumed to have the ability to rank the different combinations in such a way that she chooses that combination with the great satisfying power.
The basic concept under this approach is the Indifference Curve: that, preferences are arranged in form of indifference curves. Indifference curves are psychological levels of satisfaction hence are more hypothetical than real.

Assumptions of Ordinal Utility Approach
The ordinal utility approach to consumer behaviour is built on the following assumptions;
•	Utility is Ordinal meaning that, a consumer can arrange her preferences according to the order of satisfaction that she derives from each basket. She does not need to know exactly the amount of satisfaction which she derives from each basket instead what is necessary is -to know the satisfying power of each basket. For instance a consumer can say precisely that basket A gives her more satisfaction than B without requiring her to measure numerically the amount of satisfaction.
•	A consumer is assumed to be rational this means that she aims at maximizing satisfaction given her income and the commodity prices and will always choose the basket that gives her the greatest level of satisfaction.
•	The theory assumes consumption of at least two commodities.
•	That total utility of a consumer depends on the different quantities consumed by her, that is U = U(X1, X2……… Xn) where 1, 2 …… n are the n commodities.
•	 It assumes diminishing Marginal Rate of Substitution. The slope of an indifference curve is known as Marginal Rate of Substitution (MRS) and it shows the rate at which the consumer is willing to substitute commodity say X for another good Y.
•	It assumes Consistency and Transitivity. By consistency we mean that if the consumer prefers combination A to B in one situation then she should not prefer B to A in another situation when A is still available otherwise she would be inconsistent in her choice. In other words, if A > B, = B > A. On the other hand, transitivity means that if the consumer prefers A to B and yet she prefers B to C then it would imply that she prefers A to C, i.e. if A > B and B > C = A > C.
 An Indifference Curve
An indifference curve is a locus of two commodity combinations that give rise to equal levels of satisfaction to a consumer. Therefore, along an indifference curve a consumer is indifferent between the commodity combinations. This means that faced with a set of different combinations, the consumer can choose any combination since each gives her equal satisfaction.

Consider figure 5.4, all points along the indifference curve (IC) such as A, B and C give the consumer the same level of utility U0 But of the three combinations, A contains the greatest amount of good-Y and the least amount of good-X, while C contains the greatest amount of good X and least amount of good-Y. Moving down the curve from A to C, the consumer reduces the quantity of good-Y so as to acquire more units of good-X, if she is to remain on the same indifference curve. Since along the same indifference curve, quantity of one good is reduced while that of another is increased, it means that an indifference curve has a negative slope. Also the reduction in good Y and increase in good X are not in equal proportions, instead down the curve, the successive reduction in the quantity of commodity Y declines progressively in exchange for an extra unit of good –X. This means that an indifference is convex to the origin, which implies that; 

•	It has a negative slope and 
•	Its slope decreases in absolute terms down the curve. 

Figure 5.1: An Indifference Curve 

	Good Y

	Y1	A

	Y2	B

                                 Y3	C	IC = U0

	 0
                                       X1 X2      X3                       Good X

4.7	An Indifference Map
An indifference map is a set of indifference curves that are parallel to each other since they represent different utility levels. Given an indifference map, the higher the indifference curve the greater the level of satisfaction and vice versa. Since a consumer is assumed to be rational, meaning that she prefers more to less, then she will prefer a commodity combination that lies on the highest possible indifference curve to one that lies on a lower indifference curve. 
Figure 5.3: An Indifference Map

	Good Y

	C
	A
	D	IC2 = U2
	B
	IC1 = U1
	0
	Good X

Combinations A and B lie on the same indifference curve IC1 hence give equal satisfaction to the consumer. Similarly, combinations C and D give the same level of satisfaction U2 to the consumer since they both lie on the same indifference curve IC2. But since indifference curve IC2 lies above IC1, it implies the level of satisfaction U2 is greater than U1, therefore the consumer will prefer any combination that lies on indifference curve IC2 to that that lies on IC1. However, although combinations along IC2 are preferred to those on IC1, the consumer has to choose only one combination on IC2 such as C or D. But the choice between C or D or any other point along IC2, depends on the level of the consumer’s income, preference for either good Y or good X and the price level of the two goods as we shall see later under the section of consumer’s equilibrium.

 Marginal Rate of Substitution (MRS)
Marginal rate of substitution of commodity X for Y denoted (MRSxy) refers to the slope or gradient of an indifference curve. It shows the number of units of commodity Y that a consumer should give up in order, to obtain an extra unit of another commodity X and maintain the same level of satisfaction.
Figure 5.6: Slope of an Indifference curve

	Good Y

	Y1	A

	Y2	B

                                 Y3		C	D	IC = U0
                              Y4
	 0
                                       X1 X2      X3          X4             Good X

Between points A and B, 
	MRSxy  =   

Between point C and D, 
	MRSxy  =  

Clearly given a convex indifference curve, we can easily see that, dy1 is greater than dy2 while dx1 is les than dx2. This implies that 

This means that along a convex indifference curve, the slope (MRS) diminishes in absolute terms. The economic implication is that, at the upper part of the indifference curve, i.e. the consumer is willing to forego more units of the abundant commodity Y in exchange for the scarce commodity X. but at the lower points of the indifference curve the consumer is willing it forego very little units of Y (because it is now scarce) for extra units of X, (since it is now abundant). 
Mathematical Approach to MRS
From the definition of an indifference curve, it implies that along the same indifference curve, there is a constant utility. In other words, along the indifference curve, the change in utility is zero. For simplicity, to explain this further, let us assume that a consumer derives satisfaction (utility) from consumption of two commodities X and Y i.e. her utility function can be expressed as U = U (X, Y). 

The above expression is just a general representation of an indifference curve function. Now to obtain its slope, we need to differentiate the utility function. But since total utility is constant along the same indifference curve, then it would mean that the slope is zero. That is, using total derivative we get; 

	dU  =   

=	

But as we noted earlier the term  refers to the change in total utility due to change in quantity of commodity X consumed. Therefore, it refers to marginal utility of commodity X. Similarly, is the marginal utility of commodity Y. Also (-)is the change in commodity Y due to change in commodity X, which is equal to the slope of an indifference curve also called Marginal rate of substitution (MRSXY). Therefore, 

dU = (-) 

Or simply 
From the last expression therefore we can conclude that the slope or gradient of an indifference curve (Utility function) is negative and is equal to the ratio of the marginal utilities of the two goods consumed.
 Properties of Indifference Curves
•	The different combinations of commodities that lie on the same indifference curve, give the consumer the same level of satisfaction.

•	An indifference curve which lies above the other shows higher level of satisfaction than the one below it. A rational consumer will always prefer an indifference curve which lies above to the one that is below.
•	An indifference curve is downward sloped, implying that its slope is negative. This means that if a consumer is to increase the quantity of commodity X she must reduce that of another commodity Y. 
•	An indifference curve is convex to the origin: This is deduced from the assumption of diminishing marginal rate of substitution.
•	Indifference curves do not intersect: This is deduced from the assumption of consistency and transitivity. If they intersected, then the point of intersection would imply two different levels of satisfaction thus inconsistence in, consumer choice which would contradict consumers preferences as illustrated in the figure5.7 below.
Figure 5.7: Intersection of Indifference Curves

	Good Y

	B	IC2
	A	IC1

	C
	Good X

From the above diagram, the consumer is indifferent between combinations A and B since they both lie on the same Indifference curve IC2. Similarly, she is indifferent between combinations A and C because they lie on the same indifference curve IC1. By consistency it would then imply that she is indifferent between combinations B and C. But since B lies on a higher indifference curve than C, then indeed combination B is preferred to C. Therefore the point of intersection would imply inconsistency.

We can use notation to elaborate further on the inconsistency of the point of intersection:
Using figure 5.7, we observe that point B lies on a higher indifference curve than point C. This implies that point B gives more satisfaction to the consumer than C, therefore B is preferred, i.e. B>C. On the other hand, points A and B lie on the same indifference curve IC2, implying that they both give equal utility to the consumer, i.e. A=B. Similarly, points A and B lie on the same indifference curve IC1, so they both contain equal satisfying power, i.e. AC. Then by the assumption of transitivity, it would imply that BC. But earlier w stated that B>C, hence a contradiction.
4.8	Implications of other slopes of indifference curves
(i) Vertical Indifference Curve
Suppose an Indifference curve was vertical, (see figure 5.8) this would mean that the consumer is satisfied with the same level of commodity say X but non-satiated with commodity Y. From the assumption of rationality where a consumer prefers more to less given her income, then combination B would be preferred to A since it has more units of Y but same units of X. But since there is preference for point B then points A and B can not be on the same indifference curve.
Figure 5.8: A Vertical Indifference Curve
	IC
	Good Y

	Y2	B

	Y1	A

	0	X1	Good X

(ii) Horizontal Indifference Curve 
On the other hand a horizontal indifference curve would mean that the consumer is equally satisfied with the same level of Y but different levels of X.

Figure 5.9: Horizontal Indifference curve

	Good Y

	A               B
	Y1	IC

	0
                                             X1                X2  		Good X

The consumer would prefer combination B to A since it contains more units of commodity X but same quantity of commodity Y. Again since there is preference of one point over another, points A and B can not be on the same indifference curve.

(iii) Linear Indifference
If the indifference curve is linear, then its slope or gradient (MRSxy) must be constant. This would mean that the consumer substitutes a given level of commodity X for a particular amount of units of commodity Y regardless of the quantity of each. But this can not be the case since the satisfaction derived by the consumer from different quantities of X and V varies at each particular point. In other words satisfaction derived from an extra unit of a commodity when it is scarce can never be equal to that obtained when the same commodity is abundant. Indeed satisfaction derived from a commodity obeys the law of diminishing marginal utility, therefore a linear indifference curve can not be possible.
Figure 5.10: A Linear Indifference Curve

	Good Y

	A
	Y1

	 Y2	B

	IC
	X1           X2			Good X

(iv)  Concave Indifference Curve
To understand more clearly the implication of a concave indifference curve, lets use the concept of marginal rate of substitution (the slope of an indifference curve), at different points along the curve. 

Figure 5.11: A Concave Indifference Curve
	Good Y

                             Y1	A  
                            Y2	dY1	            B
                            Y3	C

	dY2	Concave IC
	  Y4	D

	0
                                                                  X1 X2  X3 X4     Good X

Consider the slope of a concave indifference curve, between point A and B, and C and D, the slope or marginal rate of substitution (MRSxy) are respectively:

MRSXY1 between A and B is;   < 1 and 

MRSXY2 between C and D is; 	> 1

We note that X1X2 = X3X4 yet dY1<dY2, implying that the slope between A and B MRSxy1 is less than that between C and D, MRSxy2. This means that along a concave indifference curve the slope increases in absolute terms. The logical implication is that between A and B, the consumer is willing to forego very little of the abundant commodity Y in exchange for an extra unit of the scarce commodity X. But down the curve, that is between point C and D the consumer is willing to forego too much of the now scarce commodity Y for an extra unit of the now abundant commodity X which is however, unrealistic.

4.9	A Budget Line
As we saw earlier a consumer is faced with several bundles of commodities whose prices are assumed to be known to her and she has fixed income to spend on the goods and services. If the consumer wants to maximize her satisfaction then she must spend all her income on the goods and services. The fixed income can therefore be used to fetch different combinations of goods and services. These combinations can be plotted on a graph and a straight line be drawn to join them. For simplicity (so as to enable us plot on a graph), if we assume that there are only two commodities that the consumer consumes, then the line or locus of points of the two commodity combinations that exhaust the consumers income is known as the Budget line also called the Iso-expenditure.

For instance let us consider two commodities X and Y whose respective prices Px is $100 and Py is $200. And supposing that the consumer’s income B is $1000, we can construct a demand table as follows:
Given Px  =  100, Py  =  200 and B  = $1000, then, 

Quantity of X	Quantity of Y	
10	0	
8	1	
6	2	
4	3	
2	4	
0	5	

If we now plot the information in the above table on a graph, we get a budget line (see figure 5.12). 

Figure 5.12: A Budget line

     Good Y    5

	3

	                            Budget Line

	1
	 0	4	8	10	Good X

Mathematically, supposed the consumer’s budget or income is B and spends it on two commodities X and Y whose respective prices are Px and Py. Then the equation of the budget line can be expressed as;

	B =  PxX +  PyY
Or
	Y  =  X

From the above equation we can find the slope of the budget line by differentiation, which gives us; =  (-)
The negative sign of the slope means that the budget-line slopes downwards implying that since a consumer is assumed to have fixed income, for her to increase the quantity f commodity X, that of Y has to be reduced. The Y-intercept shows the point when the consumer purchases zero units of commodity X but only good Y, it is given by B/Py. Similarly, the X-intercept is given by B/Px and it shows the amount of good X purchased when the consumer purchases zero units of good Y, (see figure 5.13).
Figure 5.13: A Budget line:
	Good Y
	   B/PY

	Slope = dY/dX= (-)Px/Py
	dY
	dX
	                    Budget line

	0
                           B/PX	       Good X

5.2.2.1: A Shift in a Budget Line
From the equation of the budget line, we can identify two types of shifts in the budget line: Either a parallel shifts (same slope) or a tilt (change in slope). Also we note that these shifts will occur when the constants change (i.e. when consumer’s income or commodity prices change). For instance, the budget line will shift parallel to the original one when either the consumer’s income change or when there is equal proportionate change in the prices of the two commodities. But a change in the price of only one of the commodities will simply tilt budget line (change the slope).

Specifically, the budget line will shift outwards if either the consumer’s income increases or both prices fall proportionately. But it will shift inwards when there is either a fall in the consumer’s income or both prices rise in equal proportions. The different shifts are demonstrated below:

(i) Change in Income
Figure 5.14: A parallel shift in the Budget – line
	Good Y
                              B2
                              B0
                              B1

	0
	L1    L0    L2			Good X

Increase the consumer’s income shifts the budget – line outwards while a fall in the income shifts the line inwards. 
Figure 5.15: A Change in Price of Commodity X
                      Good Y
	B

	0
                                                                         L2            L0            L1	Good X

An increase in the price of commodity X will tilt the line in wards to BL2 while a fall in the price tilts the curve outwards to BL1 other factors constant, (i.e. fixed income and fixed price of good Y), In this case, the Y- axis remains invariant.

Figure 5.16: A Change in Price of Good Y
            Good Y	L1

	L0

	  L2

	B0	Good X

An increase in the price of good Y will tilt the budget line inwards to BL2 while a fall in the price of good Y tilts the line outwards to BL1 ceteris paribus. We note here that a change in the price of good Y keeps the X-axis invariant.

4.10	Consumer Equilibrium
A consumer is said to be in equilibrium when she chooses the most satisfying combination. That combination must be affordable by the consumer, meaning that it must be on the consumer’s budget line. The consumer will choose that combination which lies on the highest affordable indifference curve. Graphically, it is represented by the point of tangency of the highest possible indifference curve and the consumer’s budget line as shown in figure 5.17 below:

Figure 5.17: Consumer Equilibrium 
	Good Y

	B
	A	D	IC2
	E
	IC0

	C	IC1

	0
	Good X

Referring to the above diagram, the consumer would prefer indifference curve IC2, say by consuming combination D, because indifference curve IC2 gives the greatest level of satisfaction, however, she is constrained by her income given by the budget line BL. Combination D is desirable because it shows higher levels of satisfaction since it lies on the highest indifference curve, but it is unaffordable. On the other hand, combinations A, C & E are affordable by the consumer since they lie on or within the consumer’s budget constraint. Particularly combination A and C are affordable but undesirable because they lie on lower indifference curve. The consumer will therefore choose a combination which lies on the higher indifference curve and is also affordable. Point E describes such a combination that is both affordable and highest possible hence it shows the equilibrium point of a consumer. At point E, the slope of the indifference curve is equal to that of the budget line;

Recall that the slope of an indifference curve is given by;

MRSXY  = = Slope of indifference curve.

While that of a budget line is;  
Now equating the two slopes we get the equilibrium condition of the consumer, that is;

This equilibrium condition states that a consumer is in equilibrium when she equates the o of the marginal utility of the commodities consumed by her to the ratio of their Dective prices. If we now divide the left hand side by the right hand side, we obtain mother equivalent equilibrium condition as;

The above expression means that a consumer is in equilibrium when she derives equal additional utility after spending an extra unit of her income on either commodity X or commodity Y given their prices. This condition however, applies to only two goods X 3nd Y, yet in the real world, a consumer consumes more than two commodities. We can now therefore state the equilibrium condition for a consumer who consumes several commodities as;

Using a simple example, consider an individual with several options or commodities on which to spend her money income. For instance she may want to buy a dress, to go and watch soccer, watch a film, go clubbing, and make her hair. If at the end of the day, she feels that she has acquired the money- worth of all that she needed, then she is said to be in equilibrium.

 Income Consumption Curve (ICC)
An Income Consumption Curve (ICC) is a line that joins together the different equilibrium points of a consumer that arise from changes in the consumer’s income other factors constant. Consider an increase in consumer’s income; this would lead to an upward shift of the budget line such that the new equilibrium is established at the point of tangency of the new budget line and a higher indifference curve. A further increase in the income would lead to a further outward shift in the budget line leading to another equilibrium point further on a higher indifference curve. The income consumption curve can be traced out as shown in the figure 5.18 below.

Figure 5.18: An Income Consumption Curve 
	Good Y
	
	  B2

	   B1
	                                         Income Consumption Curve
	B0	e2
	e1
	e0	         IC2
IC1
	IC0
	0
	L0              L1            L2                  Good X

The consumer is initially in equilibrium at point e0 on budget line B0 L0 and indifference curve IC0. An increase in the consumer’s income would lead to a shift in the budget line outwards to B1L1. She would therefore attain equilibrium at point el on a higher indifference curve IC1. Any further increase in the income will shift the budget line further outwards to B2L2 and she would attain equilibrium at point e2 on a higher indifference curve IC2. Joining points such as e0, e1, e2 gives rise to an Income Consumption Curve.
The shape of an income consumption curve reflects the type of the commodity. For instance, in figure 5.18 when the consumer’s income rises, more quantities of both X and Y are purchased, this means that both X and Y are normal goods.

But in figure.5.19 below when he consumer’s income rises, less quantities of X is purchased and more of Y is purchased, implying that X is an inferior good while Y is a normal good.

Figure 5.19: Income Consumption of an Inferior Good X

Good Y
	B2
	ICC for 	Inferior Good X
                 B1	IC2

                  B0	IC1
                      
	         IC0

                   0	X2  X1  X0 L0       L1         L2        Good X

But figure 5.20 shows that commodity Y is inferior while good X is normal because less quantity of good Y and more quantities of X are purchased at higher income. 

Figure 5.20: Income Consumption curve of an inferior good Y
	Good Y
                  B2
                  B1
                  B0

                   Y0
                   Y1
                    Y2		IC0	                                    ICC for Inferior Good Y
		IC1	IC2
                     0 		L0       L1    L2                 Good X

4.11	 Engel Curve
An Engel curve is derived from an Income Consumption Curve (ICC). Recall that along an ICC, there are different levels of income of the consumer and indeed points on the ICC define different equilibrium points of a consumer arising from income changes Consider figure 5.21 below;

Figure 5.21: Deriving an Engel Curve.

	Good Y
                  B2

	  B1
	e2         ICC
	B0	e1	I2
	e0	I1
	I0

	X0     X1 L0   X2           L1         L2	Good X

Income

	             Engel curve
	B2	c
                   B1	b
                  B0	a

	X0     X1    X2	Good X

When the consumer’s income is B0, she is in equilibrium at point e0 the point of tangency of the budget line B0L0 and indifference curve Io. Therefore at income level B0, the consumer consumes quantity Xo of good X, this gives rise to point ‘a’ in the lower diagram. When the consumer’s income rises to B1, she attains equilibrium at point e1 on budget line B1L1 and indifference curve Ii. Hence at income level B1, she demands quantity X1 of good X giving rise to point ‘b’. A further increase in the income to B2 leads to equilibrium point e2 which corresponds to point ‘c’ in the lower diagram where quantity X2 is demanded. Joining points a, b, and c gives rise to an Engel’s curve. An Engel’s curve therefore defines the relationship between the income of the consumer and the quantity demanded of a commodity. Specifically an Engel curve is the locus of points (curve) that show different quantities of a good consumed at the different income levels.

An Engel curve of a normal good is upward sloped because at higher income levels, more quantities of a normal good is demanded. But for an inferior good, the Engel curve is negatively sloped.

4.12	 Price Consumption Curve (PPC)
This is a curve that joins the various equilibrium points of a consumer that arise from changes in the price of one of the commodities other factors remaining constant. As the price of commodity say X increases the consumer moves along the price consumption curve towards the origin. On the other hand, if the price of X falls the consumer would move outwards along the Price consumption curve. Referring to figure 5:22, supposing that the consumer is initially in equilibrium at point e0, on the budget line BL0 and on indifference curve IC0, consider a fall in price of commodity X, other factors constant, the budget line would shift outwards to BL1 and the consumer would be in equilibrium at point e1 on a higher indifference curve IC1. If however, the price of X increases, then the budget line would shift inwards to BL2 and the consumer would be in equilibrium at point e2 on a lower indifference curve IC2 joining point e0, e1, and e2 would gives rise to a Price Consumption Curve (PCC).

Figure 5.22: The Price Consumption Curve
                      Good Y
	B
	PCC

	IC1
	e2 e0    e1	IC0
	IC2

	0
                                                                        L2            L0            L1

	Good X
The Shape of the PPC
The shape of the PPC determines the relationship between the two commodities X and Y (i.e. whether complements or substitutes). For instance the PPC in figure 5.22 above shows that commodities X and Y are complements, because increase in quantity of X is accompanied by an increase in that of Y and vice versa. 
On the other hand the PCC in figure 5.23 below shows that X and Y are substitute commodities, since an increase in quantity of X demanded is accompanied by a fall in that of Y.

Figure 5.23: The PPC of Substitute Goods X and Y
                      Good Y
	B
	
IC1
	
		IC0
	IC2
	PCC for Substitute
	0	Goods X and Y
                                                                         L2            L0            L1	Good X

From the diagram, when the price of good X rises, the budget line tilts inwards from BL0 to BL2. The consumer now reduces the quantity of good X demanded but instead increases that of good Y. But with a price fall of good X, her budget line tilts outwards and she acquires equilibrium at point el on indifference curve IC1 where she demands more quantity of good X and reduces that of good Y whose price has not changed. This implies that since whenever the consumer increases good X she reduces the quantity of good Y, and vice versa, then goods X and Y must be substitutes.

4.13	 Price Effect, Substitution Effect and Income Effect
Usually a change in the price of a commodity results in a change in its quantity demanded specifically a fall in price of a commodity results in an increase in its quantity demanded. Since quantity of the commodity is changing as a result of a change in its price, the overall effect on demand is referred to as Price Effect also known as Total Price effect. Price effect can be splint into two separate effects; Substitution Effect and Income Effects.

To illustrate these two effects, we shall assume a fall in the price of a commodity: When the price of a commodity falls, other factors kept constant, a consumer ill reduce the quantities of other substitute goods whose prices now appear relatively high and increase the quantity of the commodity whose price has fallen. It is this increase in the quantity of the substitute good that is referred to as Substitution Effect.

Also when the price of a good falls, the consumer’s purchasing power increases such that she is now in position to either purchase more of the good whose price has fallen and the same quantity of the other good whose price has not changed or more of both goods. The increase in the purchasing p9wer arising from a price fall is equivalent to an increase in the consumer’s income hence it is referred to as Income Effect of a price change.

To illustrate graphically these three effects we shall use the following assumptions;
•	Two commodities X and Y where good Y (composite good) represents other commodities;
•	The price of commodity X falls;
•	Price of commodity Y remains constant;
•	Consumer’s income remains constant.

A fall in the price of commodity X will lead to a right-ward tilt of the budget line to the right to BL1. The new equilibrium position will be set at e1 on a high indifference curves IC1 where more quantity of good X, X1 is now demanded.

Now with a fall in the price of good X, the consumer moves from a lower indifference j curve IC0 to a higher indifference curve IC1. To stop the consumer from attaining a higher indifference curve at the reduced prices, some money income should be removed from her income. This would lead to a shift in the budget line inwards parallel to the new one: Another budget line is drawn parallel to the budget line BL1 and tangent to the original Indifference Curve IC0 at point e2. This new budget line B2L2 is known as the Compensating Variation budget line or hypothetical budget line and it assumes that the consumer’s real income is the same as before the price reduction since both points eo and e2 lie on the same indifference curve IC0. Since the consumer is assumed to stay on the same Indifference curve even after a price fall, it enables us to find how much of commodity Y has been substituted by commodity X.

Budget line B2L2 is referred to as hypothetical because in the real world no employer can reduce an employee’s income simply because the market price of a commodity consumed by the employee has fallen. This means that the consumer shall not remain at equilibrium point e2 because it actually does not exist but will instead move to a higher Indifference curve IC1 and consume at point e2 since the price of the commodity has fallen. The hypothetical budget line simply enables us to separate substitution effect from Income effect., A movement from point e to point e1 (i.e.. from a lower indifference curve to a higher indifference curve) is referred to as Price Effect (P.E). And a movement from point e0 to point e2 (i.e. along the same indifference curve) is known as the Substitution Effect. While a movement from point e2 to point e1 (i.e. from a lower income level or budget line to a higher one), is known as Income Effect of a price change.

Figure 5.24: Price Effect, Substitution Effect and Income Effect 
	Good Y

	B

	B2

	e0	e1
	IC1
	e2
	IC0

	0	X0       X1   L0 X1        L2            L1         Good X

Therefore, Total price effect (P.E) equals to the sum of Substitution effect (S.E) and Income effect (I.E), i.e. FE = SE + IE Or e0e1 = e0e2 + e2e1.
In terms of quantities of good X, substitution effect is shown by the difference of quantity demanded between Xo and X2 and income effect is shown by the difference of quantity demanded between X2 and X1 while total price effect is shown by the difference between Xo and X1. That is, X0X1 = X0X2 + X2X1.

The relationship between P.E, S.E and I.E is given by the Slutsky equation (Derivation of the Slutsky equation is advanced for this book).

Before we proceed, a student should note the following about figure 5.24:
•	The price of commodity Y (other goods) has been assumed to be fixed throughout the analysis.
•	Price of good X at point e0 is higher than that at point e1.
•	The consumer’s income at point e0 is equal to that at point e1.
•	Price of good X at point e2 is equal to that at point e1
•	Income level at point e2 is less than that at e0.
•	The amount of income that should be subtracted from the consumer’s income so as take him to the original indifference curve is known as Compensating Variation (CV), it is equal to the difference in the income level BB2.
•	But if we wanted to take the consumer from a lower indifference curve IC0 to a higher in difference curve IC1, without reducing the price of good X, the alternative method would have been to increase her income. This would lead to a shift in the budget line upwards parallel to line BL0 and tangent to indifference curve IC1 (not shown in the diagram and is left as an exercise to the student to demonstrate). The increment in the income level is known as Equivalent Variation (EV).

From figure 5.24, we have shown that X1 is greater than X0 or rather that point e1 lies to the right of e0 implying that price effect is negative (i.e. a fall in price leads to more quantity purchased). Also we have shown that X1 is greater than X2 or rather that point e1 lies to the right of e2 also implying that income effect of a price change is always negative. This is however, not always the case. Where as Substitution effect is always negative (i.e. a fall in price of a good leads to more of that good demanded and less of the substitute good demanded other factors constant), income effect can either be negative, positive or zero depending on the type of the good. And since price effect is the sum of substitution effect and income effect, then price effect can also be either negative, zero or positive depending on the sign and magnitude of income effect. In other words, the final location of the point ‘e1’ can either be to the right, directly above or to the left of the original point e0 and on the higher indifference curve.

We should note that Income effect per se of a normal good is always positive (i.e. increase in the consumer’s income leads to increase in quantity demanded of a normal good). But income effect of a price change is always negative for a normal good, zero for a necessity and positive for an inferior good. That is, for a normal good, a fall in price (-) leads to an increase in consumer’s real income (+) which in turn leads to an increase (+) in quantity demanded: i.e. (-) x (+) x (+) = (-) . But if a good is a necessity income effect of a price charge will be zero (i.e. a fall in price (-) leads to an increase in real income (+) but quantity demanded remains uncharged (0). That is, (-) x (+) x (0) = (0).
And if a good is inferior, income effect of a price change will be positive (i.e. a fall in its price (-) leads to an increase in the consumer’s real income (+) but instead she demands less quantity of the inferior good (-): i.e. (-) x (+) x (-) = (+).

Therefore total price effect is influenced by the size (magnitude) of the income effect: It can either be negative or positive. Generally if a good is a giffen good (extreme inferior good), Total price effect is positive because a fall in price leads to a fall in quantity demanded , in other word, the demand curve of a giffen good is negatively sloped . But if a good is non-giffen (i.e. either luxury, simple normal, necessity or simple  inferior), then total price effect is negative implying that a fall in its price leads to more the good demanded, i.e.  that is the demand curve of a non-giffen good is negatively sloped.

We now summarize the relationship between Price Effect (PE), Substitution Effect (SE) and Income Effect (IE) for the different types of goods as follows. When a good is;
•	Luxury good (extreme normal), PE (-) = SE (-) + IE (-), i.e. PE is negative since both SE and IE are negative.
•	Simple Normal good, PE (-) SE (-) + IE (-), i.e. also PE is negative because both SE and IE are negative, however, IE of a price change for a luxury good is more negative than for an ordinary normal good.
•	 Necessity, PE (-) = SE (-) + IE (0), i.e. since IE is zero and yet SE is negative, then the sum which is PE must be negative. I.e. since I.E is zero and yet S.E (-) then T.P.E is negative since it is the sum of the two
•	 Simple Inferior good, PE (-) = SE (-) + 1E (+), i.e. Although IE is positive its magnitude is less than that of the negative SE so it can not counter the SE hence PE is negative.
•	Giffen good (extreme inferior), PE (+) = SE (-) + IE (+); i.e. In this special case IE is a positive and great so its magnitude exceeds that of the negative SE such that the resultant (sum), PE is positive.

We can now illustrate the above summary using a diagram and we shall observe that although the final location of the equilibrium point of the consumer (i.e. point e1) lies at the point of tangency of a higher indifference curve and the higher budget line, its location in relation to the original equilibrium point e0 depends on the type of the good, s shown in figure 5.25.
Figure 5.25: PE, SE and IE of different types of Goods 

Good Y

	B1	e Giffen 

	B2	e Inferior 
	e0	e Necessity
	IC1
	e2	e Normal
	IC0	e Luxury 

	0
                                               X0       X2          L0               L2                   L1	              Good X

From the diagram;
e0 is the initial equilibrium point on budget line BL0 and indifferent curve IC0, and the final equilibrium point is on budget line BL1 and indifference curve IC1. But the specific location of the final equilibrium point depends on the type as indicated in the diagram.

The above analysis shall be vital in deriving the demand curve of a good using the indifference curve approach which is our next concern in the section that follows hereunder. We can however, foretell that since its only under the case of a giffen good where PE is positive, (i.e.  0) its demand curve will therefore be positively sloped. But the demand curves of all other goods are negatively sloped (though vary in slopes) since PE is negative (i.e. 
 Deriving a Demand Curve using the Indifference Curve Approach
Under the indifference curve approach, the demand curve is derived from a Price Consumption Curve (PCC). Recall that a PCC traces out the equilibrium points of a consumer arising from changes in price of one good other factors constant while a demand curve shows the different quantities demanded at the different prices. From our previous analysis, a PCC is obtained by joining the initial equilibrium point of the consumer (e0) with the final point (e1). Recall also that we are still assuming that the price of good X falls other factors remaining constant such that price at the original point (e0) is greater than price at the final point (e1). From figure 5:25 apart from the point (e0) therefore the demand curve of all these goods must be downward sloped. We shall illustrate the remaining cases i.e. inferior, necessity and luxury and should show that their demand curves are down-ward sloped but only vary in steepness. 
Figure 5.26: Deriving a Demand Curve of a Normal Good 
  Good Y

	 B

	PCC

	e1  e2          IC2
	e0	IC1
	IC0

	0
	X0    X1 L0  X2            L1                L2	Good X

Price of X

	P0	a
	P1	b
            P2	c

                                       Demand Curve of Normal Good X

	0	 X0      X1  X2	Good X

Referring to figure 5:26, at higher price P0. the consumer is in equilibrium at point e0 on indifference curve IC0 and budget line BL0. When the price of X falls to P1 the budget line tilts to BL1, the consumer now attains equilibrium point e1 which is a point of a tangency of the higher indifference curve IC1 and budget line BL1. A further fall in price f good X to P2 leads to equilibrium point e2. Joining points; e0, e1 and e2, we get a price consumption curve (PCC). It is from the PCC that we derive a demand curve. For instance along the PCC, at point e0, the price of X is P0 and the consumer demands 4uantity X0 of good X. This gives rise to point a in the lower diagram. And at point e1 the price of good X is lower at P, and the consumer aw ne quantity of good X which gives rise to point b in the lower diagram. At point C3, the price of good X is further lower at P2 and at that price the consumer demands quantity X2 of good X, giving rise to point c in the lower diagram. Joining points a, b and c, will give rise to the demand curve of a normal good X.

Demand Curve of a giffen good
From our earlier analysis (Figure 5:25) we showed that the final location of a giffen good lies to the left of the initial equilibrium point; also as shown in the figure 5.27 below.
Figure 5.27: Deriving a Demand Curve of  Giffen Good
  Good Y

	 B

	e2	IC2	
	  e1
	     IC1    

                                                e0  IC0
	0
	                 L0              L1                L2	Good X

Price of X

	P0		  Demand Curve of Giffen Good X
	P1	g    f
            P2	h	

	0                 X2  X1  X0	Good X

The initial equilibrium of the consumer is at point e0. At this point, the price of good X is P0. When price now falls to P1, the budget line tilts to BL1 and the consumer attains equilibrium at point e1 which is however, to the left of the original point. A further fall in price to P2 leads to equilibrium point e2. Joining points; e0, e1 and e2 gives rise to the PCC of a giffen good which is upward sloping. Now using the PCC, at the initial equilibrium point e0 the price of X is P0 and the consumer demands quantity Xo of a good X, giving rise to point in the lower diagram. When the price of X falls to P1 the consumer attains equilibrium at point el, but demands less quantity Xi of good X giving rise to point g. A further fall in price to P2 leads to equilibrium point e2 where the consumer demands far less quantity of good X, i.e. X2 giving rise to point h in the lower diagram. Joining points; f, g and h, we get the demand curve of a Giffen good X. We note that the demand curve of a giffen good is upward sloping because the total price effect is positive.

 Review Questions
1. 1.	(a) What are the assumptions of the cardinal utility theory?
(b) Distinguish between the terms; total utility and marginal utility and show how they related.
2	a) Explain the concept of consumer equilibrium under the cardinal utility theory.
(b) Explain how a demand curve is derived under the cardinal utility theory.

3 Although water is essential to human life, it is cheaper than Silver. Explain the paradox.

4.	What are the assumptions of the cardinal utility theory?

5	(a) What is an indifference curve?
(b) Why is the indifference curve convex to the origin?

7.	(a)What is a budget line?
(b) Comment on the causes of shifts of a budget line.

8	(a)  What is the marginal rate of substitution?
(b)  Show that an indifference curve has a negative slope (hint; use 	calculus).
(c) Show that a budget line has a negative slope (hint; use calculus).

9.	State and explain the equilibrium condition of a consumer.

10.	What are the properties of an indifference curve?

11.	What would be the economic interpretation of the point of tangency of a budget line with;
i)	A convex indifference curve?
ii)	A concave indifference curve?

13	(a)What is an Engel’s curve?
(b) Sketch an Engel curve for a;
i)	Normal good X,
ii)	Inferior good X,
iii)	Giffen good X,
iv)	A necessity good X.
14	(a) What is a price consumption curve?
(b)  Sketch a price consumption curve of;
i)	Complementary goods X and Y,
ii)	Substitute goods X and Y,
iii)	A normal good X,
iv)	A necessity good X,
v)	A giffen good X.
15	Using a well- labelled diagram, explain the concepts ; Price effect, Substitution effect and Income effect of a fall in price of
i)	A normal good X,
ii)	A necessity good X,
iii)	Inferior good X,
iv)	A giffen good X.

Unit 5
Production Theory
5.1	Introduction
As discussed earlier, a market comprises among other partners a consumer and a producer. In the previous chapter, we discussed the behavior of a consumer. Two consumer theories were identified and discussed. In both theories we noted that the major aim of a consumer is utility maximization.

In this chapter we shall now turn to the other partner in a market: the producer who on the other hand aims at profit maximization. We shall look at production decisions of a producer over a period i.e. in the short run period and the long run period. In this chapter we shall specifically look at a production function, causes of shifts of a production function, concepts such as total product, average product and marginal product, the law of diminishing marginal productivity and the stages of a production function and the long-run production decisions of a firm.

 5.2	The Theory of a Firm
A firm is a technical unit in which commodities are produced. It hires the services of the factors of production to produce goods and services. The primary factors of production are land, labour, entrepreneur and capital. The concept of a firm ranges from a sole proprietor to a big enterprise. An input is anything a firm uses in the production process while an output is anything that a firm produces for sale or consumption. The management of production decisions can be grouped into four categories.

•	How much shall be spent on the purchase of inputs?
•	How shall the inputs be divided among the various types of inputs?
•	How much of each type of input shall be allocated to each type of output? This is relevant to a firm producing different types of commodities?
•	How much of each final product shall the firm produce?

Production theory seeks to analyze the input and out-put relations and answer the following questions.

•	If all the inputs are simultaneously increased or decreased at a certain rate WI output increase or decrease in the same proportion?
•	Supposing, that there is more than one process of producing a commodity, how will the output change in response to changes in factor proportions?
•	How can the least cost combination of the inputs be achieved? This is a very vital question because the main objective of the firm is to maximize profits by minimizing costs.

Assumptions in Production Theory
i)	A firm sells all its output;
ii)	Sales revenue is equal to the value of goods;
iii)	The firm produces each output as cheaply as possible given the techno1o used;
iv)	 All units of each factor of production are equally efficient;
v)	The price of each factor of production is given, i.e. it is fixed in the market for factor inputs.

5.3	Basic Concepts in Production Theory
•	The Production Function
A production function describes the technological relationship between inputs and output in physical terms. It shows the relationship between the quantities of various inputs used per period of time and the maximum quantity of output that can be produced in that time period. It represents the ability of the firm to convert inputs into output given the technology; A production function can be described in different ways such as:

i)	It may take the form of a table

Capital 	Labour 	Quantity 	
1	10	30	
1	20	70	
1	30	100	
1	40	90	

(iii)	It may be in a form of an equation 
Q = Q(L, K)……………………………(i)
Q = a + Bl……………………………..(ii)
Q = A Lα Kβ ………………………… (iii)

Where Q = Output, K = Capital and L is Labour. The first equation is an implicit function that shows that output produced depends on labour and capital inputs. The second equation is a linear function and shows that output depends only on labour input (a and b are constants). The third equation is a Cobb-Douglas production function and shows that output depends on both labour and capital. 

(iv)	It may also take the form of a curve or a graph.

Figure 6.1: A Production Function 

               Output

Total Product 

	0	Factor Input 

The standard economic assumption which affets the shape of the production function is the law of diminishing marginal returns, which states that “as more and more of a variable input X is employed on a fixed factor, total output increases first at an increasing rate and later at a decreasing rate until a point is reached where additional quantities of input X will yield diminishing marginal returns assuming all other factors are kept constant”.

•	Average Product (AP)
This is simply defined as total output divided by total units of the variable factor. Generally, as more of the variable factor are used average product first rises and then later on falls. The point where the AP reaches maximum is called a point of diminishing average productivity. Assuming that labour is the variable factor, then Average Product of labour is the total output level divided by total labour input that is

		APL = 
•	Marginal Product (MP)
This refers to a change in total product resulting from the use of one more unit of a variable factor. The marginal product curve also first rises, reaches maximum then falls. The level of output where the MP reaches maximum is called the point of diminishing marginal returns. If labour is the variable factor then marginal product of labour (MPL) is the change in the output level due to a unit change in the labour input level, i.e.

	MPL  =  

Since to get marginal product is obtained by differentiating the total product function, it means that marginal product is the slope of the total product function.

Relationship between a Production Function, Marginal Product and Average Product Curves
The relationship between these concepts can be explained using by the hypothetical table below.

Table 6.1:Total Product, Marginal Product and Average product
Capital (K)	Labour (L)	Output (X)	MPL = 	APL = 	
1	0	0	-	-	
1	10	30	3	3	
1	20	70	4	3.5	
1	30	100	3	3.33	
1	40	100	0	2.5	
1	50	90	-1	1.8	
1	60	75	-1.5	1.25	
1	70	55	-2	0.8	

A graphical relationship of the three curves is given by figure 6.2. From table 6.1 together with figure 6.2 we can note the following:
•	Total product curve rise first at an increasing rate (increasing marginal product), then at decreasing rate (decreasing marginal product) reaches maximum (when MP = 0) and then it falls (when marginal product is negative).
•	When the Total product curve is rising, Marginal product is positive. When Total product is at maximum, MP = 0 and when Total product is falling, Marginal product is negative (recall, marginal product is the slope of the Total product function).
•	Marginal product rises, reaches maximum then it falls (when average product is still rising) to zero and into negative.
•	Average product rises reaches maximum (when MP = AP) and then it falls but will never be zero nor negative because output is never zero at positive input factor employment.
•	The point when MPAP is referred to as the intensive margin and it marks the boundary between the first region and second region of production.
•	The point when Total product is maximum (i.e. when MP = 0) is referred to as the extensive margin and it marks the boundary between the second region and the third region of production.

From the definition of average product, i.e. APL = , APL will only be zero if and only if Q = zero. But since output can never be zero at positive variable factor L, then APL can also never be zero. Similarly, APL, can never be negative because Q can never be negative. We also need to show that at maximum average product AP = MP. Recall that at maximum APL (point of diminishing average productivity) the slope of the AP curve is zero. i.e.

	  =  0

But 	APL  =  , by substitution; 

	APL  =  

Since we are differentiating a quotient with two variables Q and L, we use the quotient rule of differentiation which gives us; 

	  =  0

Or 	L  = Q

This gives ,

But  = MPL and = APL

Therefore by substitution we get; 

	MPL  =  APL

This means that at maximum average productivity, MPL = APL.  

Figure 6.2: Total Product Marginal Product and Average Product 
	Q
               Output

                      Total Product 

	0	Input (Labour) 

                Output 	I	II	III

	APL
	0
	Input (Labour)

MPL

6.2.5: Regions of a Production Function
A typical production function can be divided into three regions: The first region begins from zero output up to the point where marginal product equals to the average product (intensive margin). The second region starts from the point where Average Product is at maximum up to the point where Marginal, Product is zero (Extensive margin). The extensive margin shows the level at which all the fixed resource is fully utilized.

In the first region, total product, marginal product and average product are all positive. In this region the variable factor (e.g. land) is not fully utilized implying that Average Product is still rising. So it benefits the producer when more units of the variables factor are employed since increase in the variable factor leads to increase in total product. Therefore it would be irrational for a producer to operate in this region.

The second region of production function is also referred to as the economic region of production or the optimal region. In this region Total Product (TP), Marginal Product (MP) and Average Product (AP) are still positive although MP and AP are declining. In this region, there is efficient utilization of the fixed factor by the variable factor; therefore production should take place in this region. However, to determine the exact point of optimal production, we need more information about the price of the factor inputs and the price of the output (we shall cover this in the last chapter: Factor pricing.)

The third region of the production-function is characterized by declining TP, AP and MP. Indeed in this region, MP is negative. This implies that employment of an extra unit of a variable factor would instead lead to a decline in total output. The explanation for the decline in total output is due to over utilization of the fixed factor input by the variable factor. Several examples can be given for this case. One of them is found in Resource/Environmental Economics known as the “tragedy of the commons”. For instance if fishing in a lake is not regulated (existence of free-fishing or open fishing such that a lake is a common good), every fisherman will try to maximize his output such that at the end of the day there will be over fishing. Alternatively if we consider harvesting a forest, if it is not regulated there will be over cutting such that ultimately less timber will be harvested. Another good example of the tragedy of the commons is grazing in an open ground (common Pasture). Each herdsman will try to maximize his output by increasing the number of heads of cattle (variable factor) so as to increase the output (meat &milk). But as each herdsman increases the number of cattle on the fixed input (fixed land/pasture), there will reach a point when the land is overgrazed and ultimately the amount of output (meat/milk) will fall since the cattle shall then be thin or under fed.

Several other examples are found in agriculture and in manufacturing. For instance consider the use of fertilizers on fixed amount of land: Other factors constant, output will increase with increase in fertilizer use, but there will come a point which is such that use of fertilizer in excess of some level instead leads to less output. Another example is use of labour as the variable factor with fixed capital and land. This applies to both agriculture and manufacturing: If labour is employed beyond some level, total output falls. This is because too much labour in excess of other factor inputs leads to inefficiency which arises from disguised unemployment that manifests itself inform of shirking. It is this disguised unemployment that forms the economic basis for retrenchment policy. The underlying objective of retrenchment is to increase labour efficiency hence increase total output.

Generally however, it is irrational to operate in the third region of production since employment of an extra unit of the variable factor leads to less of total output generated. This region is therefore referred to as the uneconomic region of production.

In summary, a variable factor (e.g. Labour) should not be employed in the third region of production even if it were For free. Therefore production should not take place in this region in economic terms.

 5.4	Production Decision of a Firm
In our preceding analysis, we concentrated on a situation where the production decision of a firm (producer) is based on a single factor in put. However, production of any output usually involves use of more than one variable factor input. In this case, therefore the producer (firm) attempts to provide answers to the second question in the management of production decisions that we outlined at the beginning of this chapter. That is, how shall the inputs be divided among the various types of inputs so as to produce a given quantity of output? The following examples can provide a hint to understanding of this production problem

•	A farmer intends to produce 100 tones of maize. He asks himself the following question “How many factors; acres of land, laborers, tones of fertilizers, tones of seeds etc should be employed?
•	A builder intends to construct three-bed roomed house of a given size and asks himself; How many tones of cement, bricks, tones of sand, tones of aggregates, laborers, iron sheets should be used?
•	A poultry farmer intends to produce 100 trays of eggs daily. So he asks himself; how many birds, tones of feed, laborers etc should be employed?

Such production decisions and many others do exist in the real world and through Economics solution can be obtained.

For simplicity however, we shall limit ourselves to only two factor inputs; capital (K) and labour (L) in our analysis. This will enable us demonstrate the problem and solution graphically (since a simple graph has two axes). Graphically, the above proc problem is demonstrated by an Isoquant.

1: Isoquant
An isoquant is a curve that shows combinations of two factor inputs say capita (K) and labour (L) required by a firm to produce a given level of output. It is a form of production function. Its shape and slope depends on the rate at which one factor can be substituted for another to produce the same level of output. This rate of substitution is called the Marginal Rate of Technical Substitution. A typical isoquant, is convex to the origin as shown in figure 6.3 below.

Figure 6.3: An Isoquant
	K

	Isoquant 
	0
	L

Properties of Isoquants
An Isoquant has similar properties as those of indifference curve, for instance
(i)	It is down- ward sloping,
(ii)	An isoquant that lies above another shows a higher level of output,
(iii)	It is convex to the origin,
(iv)	It does not touch any of the axes. Other wise it would lead to a corner solution where a particular level of out put can be produced using a single variable factor which might be unrealistic, and
(v)	They do not intersect.

2: The Slope of an Isoquant
The slope of an isoquant is also referred to as the Marginal Rate of Technical Substitution, (MRTS). It shows the number of units of one factor in put say capital that must be substituted by an extra unit of another factor input say labour but leave the level of output unaffected. Clearly the slope is negative since addition of another factor precludes reduction of another factor input. Mathematically; since along an Isoquant, the level of output is fixed, then it implies that change in output along a given Isoquant zero that is, dQ = O.

Cnsider an Isoquant given as follows; Q0 = Q(L,K). Which means that production of a given level of output Q0, depends on the amount of labour and capital inputs employed. Using calculus, we obtain the slope of the production function by finding the tal derivative and equating it to zero since along an isoquant, output does not change. That is;

	Dq0  =  Dk  =  0

Or 	Dk

Dividing both sides by dL and  we get; 

	(-) 
But = MPL and 

= MPK. Therefore, 

 =  MRTSL,K

The above equation states that; the slope of an Isoquant  is negative and is equal to the ratio of the marginal product of labour to marginal product of capital and it is referred to as the Marginal Rate of Technical Substitution of labour for capital.

 Isocost line
As we stated earlier, a firm hires the services of factor inputs in order to produce output. But in most cases firms (producers) have a limited amount of money (are constrained) to use in the purchase of these factor in puts. In this case, the firm attempts to answer the question: How much money shall be spent on the purchase of factor inputs. This is however, influenced by two factors; the cost or the price of the factor inputs and the level of output the firm intends to produce.

With a fixed amount of money (cost outlay) available to the producer and given the factor input prices, there are several combinations of factor inputs that can be purchased by the firm. In order for the firm to maximize its output, it needs to purchase as much inputs as possible, accordingly, it needs to spend as much as possible and perhaps to exhaust the cost outlay. The maximum level of expenditure is given by an Isocost line also known as an Iso-Expenditure, which has similar characteristics as a budget line. Therefore for simplicity, we assume that the producer has a fixed cost outlay equal to C and uses it to purchase two factor inputs; labour L and capital K whose respective prices are FL and PK.

We define an Isocost line as a locus of factor input combinations that exhaust a firm’s cost outlay. Mathematically we can represent it as,

C = PLL +P KK

Where, 
PLL is the amount of money spent on the purchase of labour input while PKK is amount of money spent on the purchase of capital inputs, while C is the total co outlay.

Supposing that we now re-arrange the above equation to make K the subject (sin? conventionally we always put K on the Y-axis) we get;

	K  =  L

This is an equation of the Isocost line and it is easy to see that it is a straight line (linear). 

If we now differentiate K with respect to L we obtain the slope of the Isocost, i.e.

The negative sign shows that an Isocost line is down ward sloped (negatively sloped). This implies that, if a producer (firm) has a fixed cost out-lay, for it to increase the amount of one factor input, it has to reduce that of another, ceteris paribus.

5.5	Equilibrium in Production
Since the traditional goal of a firm is profit maximization, then it will opt for that point that maximizes profits and minimizes costs. Such a point occurs at the tangency between the highest possible Isoquant and the Isocost line, as shown in figure 6.4 below. In that figure, point E defines the equilibrium point of production. An isoquant that lies above the given isoquant IQ0 would be preferred since it shows higher output level (1Q2), but it is not attainable due to the firm’s constrained cost outlay (CC). On the other hand, an Isoquant that lies below IQ0 such as IQ1 is attainable although undesirable (e.g.) since it shows lower output level. So point E shows the optimal combination of labour and capital by a firm.

Figure 6.4: Equilibrium in production 

	Capital 
	C

	E	IQ2
	K0
	IQ0
	    IQ1

	0
	L0	C	Labour 

At the equilibrium point E since the Isoquant is tangent tot eh Isocost, then the slope of the Isoquant must be equal to that of the Isocost. But the slope of an Isoquant is the marginal rate of technical substitution (MRTS) and is equal to the ratio of the marginal productivities i.e. 

		MRTSL,K  =  

And the slope of an isocost line is equal to the ratio of the input prices i.e.

Now if we equate the two expressions we get; 

	MRTSLK  =  , so that; 

The above is the equilibrium condition in production and it states that; at equilibrium, the ratio of the marginal productivities of the factors should be equal to that of their respective prices.

The above equation can be re-arranged to obtain

This is also an equilibrium condition in production and it means that at equilibrium, the addition to output arising from the use of an extra unit of labour should be equal to that arising from the use of an extra unit of capital given the factor input prices.

 Production in the Long - run
Under short-run production, output (production) depends on a single variable factor therefore the shape of the production function is influenced by the law of diminishing returns also known as the law of variable factor proportion. Accordingly output increases, reaches maximum then it falls when marginal returns are negative. Indeed in the short run, the time period is short enough to enable the firm vary some other factors of production such as land, machinery, buildings vehicles etc that may be kept fixed.

In the long run however, the time period is long enough to enable the firm vary all its factor inputs. Therefore there are no fixed factors in the long run. Instead all factor inputs are variable. In this case variation in output is explained by the law of Returns to Scale which states that “when all factor inputs are increased in the same proportion, output may increase either by the same proportion, greater proportion or less proportion than the factor inputs.” To put it in another way: supposing that all inputs are doubled, the law of returns to scale would imply that output may also either double, more than double or less than double.

If output increases by the same proportion as factor inputs, we say that the production function exhibits constant returns to scale. But if output increases by greater proportion than the increase in factor input then we refer to this as increasing returns to scale. And if output increases by a less proportion than the factor inputs, we call this, decreasing returns of scale.

Mathematically, supposing that the original production function is a Cobb-Douglas function and is expressed as; 

		Q0  =  ALαKβ
	Where A, α and β are positive constants. 

Consider an increase in the two factor inputs: Labour (L) and Capital (K) say by a constant y, (where y > 1)

Then the resulting production function or output level shall be given as, 

	Q1  =  yα+β ALαKβ

Removing the brackets we get; Q1 AyαLαyβKβ
Factorizing out y, we get; 
	Q1  =  yα+βALαKβ
This can also be expressed as; 

	Q1  =  yα+β (Q0).

Since the resulting production function can be expressed in terms of the constant raised to a power and in terms of the initial production function, then original production function is said to be homogeneous. The power to which the constant is raised is known as the degree of homogeneity and it is a measure of returns to scale. 

From the above example we can state the following conditions; if, 

	α + β = 1 :	We have constant returns to scale. 
	α + β > 1 :	We have increasing returns to scale.
	α + β < 1 :	We have decreasing returns to scale. 

Returns to scale are a type of economies of scale which on the other hand refers to the advantages that accrue to a firm due to large scale production. As we shall see later in our next chapter (specifically under long-run cost curves), there are several types of economies of scale such as, technical, managerial, transport, marketing economies of scale among others. But returns to scale are classified under technical economies of scale.

Expansion Path
As we stated earlier, a firm hires factor inputs in order to produce output. And the major objective of a firm is to maximize profits which can be obtained by increasing output producing on a higher Isoquant) so as to increase revenue and minimizing costs. However, firms are constrained by their cost outlays which are represented by Isocost tines. If a firm wants to move to a higher Isoquant, then it must hire more of both factor inputs but this can only be achieved if it raises its cost outlay. Increase in the cost outlay Es reflected by a shift in the Isocost outwards parallel to the original one. An outward 5hift in the Isocost line will in turn enable the firm to produce on a higher Isoquant; ieading to a new equilibrium point of a firm. Therefore as the firm’s cost outlay icreases more and more, its Isocost line will continue shifting outwards. And the firm will progressively shift to a higher Isoquant (produce greater output level). Hence its equilibrium point will occur to the right of the original one. If these different equilibrium points are joined together; we obtain a curve known as an Expansion Path.

3v definition therefore, an expansion path is a curve that traces out the different equilibrium points of a producer that arise from increase in the cost outlay. An expansion path can exist both in the short-run and in the long-run. A short run expansion path arises when increase in the firm’s cost outlay is spent on only one variable factor. On the other hand a long run expansion path is obtained when increase r the cost outlay is spent on all the variable factors. The two curves are shown in the figure 6.5 below. 

Figure 6.5: Short-run and Long-run Expansion Paths 
           Capital 

	C2
	B 
	C1	                                         Long-run Expansion Path

	C0
	Q2
	K0	A		Q1	D  Short-run Expansion Path 
	Q0

	0	L0 L1 L2L3 C1   L4 C2

AB is the firm’s long-run expansion path along which the firm expands both its labour and capital inputs. While AD is the firm’s short run expansion path along which it varies only one factor input labour and keeps the capital input factor fixed at K0.

To produce output level Q0, the firm hires K0 and L0 inputs of capital and labour respectively. If the firm increases, its cost outlay to C1C1 and hires more of both capital and labour it will need less labour L1 to produce output level Q1 than when it hires only labour input, in which case it would need more labour L3. Similarly if its cost outlay increased further to C2C2, it would need less labour L2 if it hired more of both labour and capital so as to produce output level Q2 than if it increased only labour in which case it would hire L4. The short-run expansion path is therefore horizontal and parallel to the labour axis showing that capital input is kept fixed but only labour is varied while the long-run expansion path is upward sloping showing that both inputs are increased so as to increase output.

Expansion Path and Returns to Scale
As noted above, a firm’s long run expansion path is obtained when a firm increases its total cost outlay such that it employs more of all factor inputs. Supposing that the firm increase all its input factors in the same proportion, then we can use the shape of the expansion path to define the type of returns to scale. Again as we saw earlier, there are three types of returns to scale.

Constant Returns to Scale (CRS)
In this case the expansion is such that the distance between the successive multiple isoquant is equal: as shown in figure 6.6.

Figure 6.6: Expansion Path of Constant Returns to Scale
	Capital 
                             C2

	C1	Expansion Path for CRS

                             3K                                     C	2Q0
                             C0 		B
	2K	2Q0
	K	A
                                                                     Q0
	0
	L      2L     3L     C1             C2	Labour

The above diagram demonstrates that when factor inputs are for instance doubled, output also exactly doubles. Therefore the distance between the successive multiple Isoquant is the same that is; AB = BC. 

Increased Returns to Scale (IRS)
In the case of increasing returns to scale, the distance between the successive multiple Isoquant on the expansion path decreases as shown in figure 6.7. 

Figure 6.7: Increasing Returns to Scale 
	Capital 
	C2

	C1
	                                         Expansion Path for IRS
	   Q2
	3K	C
	K2	3Q0
	2K	B	2Q0
	K1   K	A
	Q0

	L     L1    L2 3L  C1               C2	Labour 
	2L

The above diagram demonstrates that if factor inputs are for instance doubled, the output level generated (Q1) is more than double the original one (i.e. Q1 > 2Q0). Similarly to produce out level 3Q0 (i.e. three times the original one), the firm need less than triple its inputs, since by tripling its inputs to 3L and 3K, the output generated, (i.e. Q2) is such that Q2 > 3Q0. In other words this would mean that for a firm to double output, it would need to less than double the factor inputs. So the distance between the successive multiple Isoquant, (i.e. 2Q0 and 3Q0), decreases, that is; AB > BC.  

Decreasing Returns to Scale (DRS)
However, for the case of decreasing returns to scale, the distance between the successive multiple Isoquant on the expansion path increase as shown in figure 6.8 below. 

Figure 6.8: Decreasing Returns to Scale 
	Capital 
	C2

	K1
	                                         Expansion Path for IRS
	   Q2
	3K	C
	K2	3Q0
	2K	B	2Q0
	K1   K	A
	Q0

	L     2L    L1 3L  L1               C2	Labour 
	C0

Figure 6.8 demonstrates that if the factor inputs are for instance doubled, the output level generated Q1 will be less than double the original Q0 (i.e. Q1 < 2Q0). Similarly output level Q2 which is obtained by tripling factor inputs to 3L and 3K is far less than triple the original level (i.e. Q2 < 3Q0). This also would imply that for a firm to double its output it would need to more than double its factor inputs. Therefore, the distance between the successive multiple Isoquants, (Q0, 2Q0 and 2Q0), increases; that is, AB < BC.  

 Review Questions
1. 1 (a) What is a production function?
(b) Distinguish between a short run production function and a long run production function.
(c) What factors can lead to a shift of production function?

2 Distinguish between Total product, Average product and Marginal product.

3 Using a clear diagram, explain the relationship between Total product, Average product and Marginal product.

4 Distinguish between the different regions of a production function.

5 Distinguish between the law of diminishing marginal productivity and law of returns to scale

6 	(a) What is an Isoquant?
(b) Briefly explain the properties of an Isoquant.

7 Given the following information;

Labour input 	0	1	2	3	4	5	6	7	8	9	10	
Output 	0	2	5	9	14	14	17	19	20	19	17	
v)	Obtain the Marginal product schedule,
vi)	Obtain the Average product schedule,
vii)	At what labour input level does diminishing marginal productivity sets in?
viii)	At what labour input level does diminishing average productivity set in?
ix)	What is the intensive margin labour input level?
x)	What is the extensive margin labour input level?
xi)	What is the optimal labour input level?
xii)	What is the economic region of labour input level?

8. Clearly explain the concept of equilibrium in production.

9. 	(a) What is an expansion path?
(b) Distinguish between short-run and long-run expansion path?

10 	(a) What are returns to scale?
(b) Using a well labelled diagiam, explain the following;
(i)	Increasing returns to scale,
(ii)	Decreasing returns to scale,
(iii)	Constant returns to scale.

Unit 6
Theory of Costs
6.1	Introduction
In the previous chapter, we talked about a producer, we saw that a producer varies a single factor input in the short run and varies all inputs in the long run. We stated that a producer hires factors of production to produce goods and services. Factors of production include among other; land, labor, capital, raw materials and building. The producer needs to pay (reward) for the hired factors of production. For instance the payment for land is rent, that for labour is wages, capital is interest, for an entrepreneur is profits etc. It is the payment to these factors of production that is generally known as cost. As noted earlier, there are two production periods, the short run (where some factor inputs are varied while others are fixed) and the long run (where all factor inputs are varied). Accordingly there are two types of costs: fixed costs and variable costs.
In this chapter we shall define the different types of costs, discuss their shapes and relationships.

6.2	Types of Costs
Costs are expenses of a firm and are derived from a production function. Costs to a firm are the rewards by a firm to the different factors of production that are employed by the firm. Therefore, economic costs on any input factor are the payment required to keep that factor in its present employment. Cost curves show the minimum costs of producing the various levels of output. Costs are subdivided into; implicit and explicit costs.

Implicit Costs
These are basically social costs. They are those kinds of costs that cannot be included in the computation of the firm’s profits. This is so because; such costs cannot be easily monetized. Examples of such costs include; noise, opportunity costs, time wasted etc.

Explicit Cost
This refers to the actual expenditure of a firm that is incurred when purchasing the input factors. These include costs on; raw materials, labour, energy, transport, land, building and others. Explicit costs include both fixed costs and Variable costs. A general cost function can be expressed as:
	C = a + bQn
Where;
C	 = 	Total cost;
Q 	= 	Total output;
a , b and n are positive constants.

In the above expression a represents Fixed cost while bQn represents Variable costs and n is a positive constant that can either be unit, in which case the cost function would be linear or is greater than unit giving rise to a non-linear cost function. Indeed if output Q is zero, total cost C would be equal to fixed cost, but if output is nonzero, then total cost is the sum of both fixed costs and variable costs. Clearly as output increases, variable costs also increase but fixed costs do not change regardless of output levels.

Fixed Costs (FC)
Traditional economic theory distinguishes between the short run and long run periods. Short run period is a period during which some factors are fixed while others are variable. In the long run however, all factors become variable.

Fixed costs are those costs incurred regardless of the level of output. Fixed costs are at times referred to as supplementary or indirect cost. Such costs include: land rent, house rent, and depreciation, salary of top managers, insurance premium and interest. The fixed cost curve is therefore horizontal as shown in figure 7.1

Figure 7.1: Fixed Cost 
            Cost (C)

	a 0	  FC

0

Output (Q)

From the diagram, we note that at all levels of output, cost is fixed at A0

Variable Cost (VC)
These are costs that vary with the level of output. Accordingly, at zero output level, there are no variable costs that are incurred. Variable costs are sometimes referred to as direct, prime or operating costs. A Total Variable Cost curve (TVC) takes the following shape. 

Figure 7.2:  Variable Cost Curve 

	          Cost (C)	TVC

0	Output 

The TVC curve has an inverse S-shape which reflects the law of variable factor proportion. 

Total Cost (TC)
This is the total sum of Total Fixed Cost (TFC) and Total Variable Cost (TVC), i.e. TC = TFC + TVC. Graphically, a TC curve is derived by summing up vertically the TFC and TVC curves. 

Figure 7.3: Total Cost, Total Variable Cost and Total Fixed Cost Curves

	Cost (C)	TVC
	  TC

	TFC

	0	Output (Q)

It is worth noting that the Total Cost Curve (TC) starts at a point above the origin (at the TFC curve), assumes a shape similar to that of TVC, hence is parallel to the TVC curve. This is so because TC = TFC + TVC. When output is zero, TVC = 0 implying that TC will be equal to TFC. Also since FC is constant, it implies that the shape of the TC curve will resemble that of the TC curve since TC varies from TVC by a constant equal to FC. Fixed Cost is therefore a shifting factor of the TC curve. In other words when FC increases by a given constant, the TC curve would also shift by the same constant. 
6.3	Variation of Costs in the Short run 
As stated earlier, in the short run some costs are variable while others are fixed while in the long run, all costs are variable because time is long enough to allow the firm to adjust or vary all its input factors. The shapes of the short run costs are explained by the law of diminishing marginal returns also known as the law of variable proportions and are expressed in terms of averages. 

Average Fixed Costs (AFC)
This is defined as Total Fixed Cost divide by total output. 
	AFC  =   

The AFC curve takes the following shapes.

Figure 7.4:  Average Fixed Cost Curve 

	Cost

	AFC

	0
	Output

The AFC curve takes a shape of a rectangular hyperbola (i.e. it is asymptotic to both axes). The curve does not cross the cost axis because at zero output, AFC is undefined. Similarly, the curve does not cross the quantity or output axis because if it did, then AFC would be zero in which case TFC would be zero, which cannot be the case because output Q is never zero. The curve will however, diminish downwards because TFC is constant yet output is increasing, therefore the average will continuously keep falling. 

Average Variable Costs (AVC)
This is defined as a Total Variable Cost divided by total output. 

		AVC  =  
AVC refers to the per unit variable cost incurred when producing each unit of output. The curve is U-Shaped due to the law of diminishing marginal returns: That is, initially when more output is produced, the per-unit variable cost diminishes since the fixed factors are under utilized by the variable factor. But as more and more output is produced, eventually the per unit variable cost will start increasing when the fixed factors are now over utilized. 

Figure 7.5:  Average Variable Cost Curve

	Cost

	AVC

	0	Output 

The AVC curve is derived from the TVC curve. Geometrically, AVC at any output level is obtained by drawing a line from the origin to a point on the TVC curve then finding the slope of the line segment, as shown in figure 7.6 below. 

Figure 7.6: Deriving the AVC curve 

	B	TVC
  Cost 

	0	Q1   Q2   Q3	Output 

    Cost 

	AVC

	0
	Q1  Q2    Q3 	Quantity 

From the diagram above, AVC at output level Q1 is equal to AQ1/OQ1 and AVC at output level Q2 is CQ2/0Q2. Similarly AVC at output level Q2 is equal to BQ3/OQ3. Mathematically it is equal to the tangent of the angle made by a line segment to any point of the origin. 

Average Total Cost (ATC)   
This is also referred to as Average Cost (AC). It is defined as Total Cost divided by Total output, i.e.
ATC  =   

But since TC = FC + VC,
Substituting for TC we get;
	
	ATC  =  
Or   	
But 	 AVC
Therefore 	ATC  =  AFC  +  AVC

Graphically, the ATC curve is a vertical summation of the AFC and AVC curves (see figure 7.8). Alternatively, it can also be derived from the TC curve; the AC at any output level is got by drawing a line from the origin to that point on the TC curve then getting the slope of the line segment, just s we demonstrated for AVC.

The Short run AC curve is U-shaped due to the law of diminishing marginal returns, while the long-run average cost curve is U-shaped due to economies and diseconomies of scale. Considering the short-run AC curve, in the initial stages of production particularly the first region of production, the fixed factors are under utilized by the variable factors, so it pays the producer to increase the amount of variable factor input such that the average cost of production falls. However, as more output is produced, hence more variable factor employed, a point will be reached when the Fixed-Variable factor combination will be efficient hence leading to optimal output. This point is reflected by the minimum point of the AC curve. Beyond this optimal point further variable factor employment will instead lead to over utilization of the fixed factors hence leading to diminishing returns. This is shown by the upward rising section of the AC curve.

Marginal Cost (MC)
This refers to the change in the firm’s Total Cost when one additional or less unit of output is produced. it can therefore be defined as a change in total cost divide by a unit change in output. MC at any output level is therefore equal to the slope of the TC curve at that point. MC is entirely determined by variable cost, in other words, fixed costs do not contribute to MC. Accordingly, MC can also be defined as the slope of the TVC curve; i.e.

	MC  =   =  

A simple proof of the above is as follows:

From the expression; 

	TC  =  TC + TVC

Differentiating both sides with respect to quantity we get; 

Expanding we get;

That is; the slope of the TC curve equals to the sum of the slope of the TFC curve and the TVC curve. 

But since Fixed Costs do not change with change in output, then it implies that; 

		 (TFC) = 0

Therefore, 

	MC  =  

This means that the MC curve is equivalent to the slope of either the TC curve or the TVC curve. 

Graphically, the Marginal cost curve is U-shaped as shown below. 

Figure 7.7: Marginal Cost Curve

	Cost

	MC

	0	Output 

The MC curve is also U-shaped due to the law of diminishing marginal returns. 

Relationship between the Short run Cost Curves
We can now summarize the above discussion of short run cost curves using a single diagram and see how the cost curves are related. 

Figure 7.8: Relation between MC, AC, AVC and AFC
	AC
	Cost 	MC
	AVC

	AFC

	0
	Output 

The relationship between the cost curves reveals certain fundamental principles which can be summarised as follows; 
•	The AC, AVC and MC curves are all U-shaped. 
•	The MC curve meets the AVC and AC curves at their minimum points. 
•	The MC curve meets the AVC before it meets AC curve. 
•	The AFC curve falls continuously with increase in output. 
•	The AVC curve moves closer rather asymptotic to the AC curve but does not meet it. In other words, at higher output levels the AC tends to approximate the AVC because the AFC becomes smaller but since AFC can never be equal to zero in the short run, the AC curve can never meet the AVC curve (recall AC = AFC + AVC).

From the statement that the MC curve meets the AVC and AC at their minimum, it is imperative to prove that at minimum AC, MC = AC. Similarly we also need to prove that at minimum AVC, MC = AVC. We proceed to the proofs as follows; 

Once the above relationships is shown in the figure 7.9 below, (i.e. the MC curve cuts the AC curve at its minimum point). 

Figure 7.9: Relation between MC and AC
	AC
	Cos	    MC

	0
	Quantity 

The MC curves cuts the AC curve at its minimum point. But we recall that a minimum point just like a maximum point is known as a turning point. Mathematically, the slope of a curve at a turning point is always equal to zero. This implies that, at the minimum point of the AC curve its slope or gradient must be zero. But since AC is defined as Total Cost divided by Total output, the slope of the AC curve can also be defined as the derivative of  with respect to output. 

And since TC and Q are both variables, then we use either the product rule or quotient rule of differentiation as discussed below.

At minimum AC, the slope of the AC curve is zero since it is a turning point. That is; 

		(AC)  =  0

But AC is defined as;   AC  =  

Then by substitution we get; 

	 =  0

Now using the quotient rule of differentiation we get;

	 =  0

Or   
Simplifying we get; 

	 =  MC  and  =  AC

Therefore at minimum AC, MC = AC. 

Similarly at minimum AVC, the sloe of the AVC curve is zero, i.e. 
	
	 =  0
But AVC  =  

Then by substitution we get; 

	 =  0

Now using the quotient rule we get, 

	 =  0

= 

Simplifying we get; 

But since by definition, marginal cost (MC) is given by the slope of the TC or TVC curve, i.e. 

	MC  =  

And also AVC  =  , then by substitution we get, 

MC  =  AVC, at minimum AVC as required. 

Example

Consider the following total cost function:

	C  =  3Q2  +  10, 
We can derive the following cost curves; 
(i)	Total Fixed Costs (TFC)  =  10
(ii)	Total Variable Cost (TVC)  =  3q2
(iii)	Average Fixed Cost (AFC)  =  10/q
(iv)	Average Variable Cost (AVC)  =  3  =  3Q
(v)	Average Total Cost (C/Q) = AFC + AVC = 3Q + 10/Q
(vi)	Marginal Cost (MC)  =   =  6Q.

Variation of Costs in the Long-Run 
Introduction 
We recall that a long-run is a period that is long enough to enable a firm to expand its output or production by varying all its factors of production. As stated earlier, in the long run, there are no fixed costs; in other words all costs are variable. The variation of costs in the long run is explained by economies of scale. The average cost of production can either decrease due to economies of scale or increase due to diseconomies of scale.

Deriving the Long run Average Cost Curve (LAC)
The Lon-run Average Cost curve (LAC) is derived from Short-run Average Cost curves (SAC). The tangent to all the SAC curves representing thei minimum points gives rise to the LAC curve. SAC curves can represent the alternative plant sizes that the firm could build in the long-run. For simplicity, supposing that we assume three plant sizes shown by three SAC curves, that is:

		SAC1:  represents a small plant; 	
		SAC2:  shows a medium plant; 
		SAC3:  represents a large plant, as shown below. 

Figure 7.10: Deriving the Long-run Average Cost curve

	Cost 	SAC2
	SAC1
	 C1	SAC3
	C2	LAC
	C1
	 C2	A
	B

	0	Q1QA    Q2                QB	Output 

Plant sizes may represent production capacities say per-day. For instance, a small plant can represent say 100 units of output per day, while a medium plant can define 500 units a day and a large plant can define 1000 units a day.

From the diagram, output Q1 can be produced at less cost C1 using the small plant than a higher cost C1’ using a medium plant. Also output Q2 can be produced cheaply at an average cost C2 when using a medium plant than at a higher cost C2’ when using a small plant. The question however is; when should a firm install a larger plant? The points of intersection of the SAC curves such as points A and B are crucial for a firm when deciding whether to install a bigger plant or not. For instance for output level less than QA, the firm should use a small plant. To produce output QA the firm can use either the small plant or the medium plant since it would incur the same cost. But beyond output level QA, the firm should install a medium plant since it would be cheaper. Similarly for output level greater than QA but less than QB the firm should use the medium plant. Output level QB can be produced at the same cost when the firm uses either the medium plant or larger plant. But beyond output level QB, the firm should use a large plant. Also the decision to expand the plant size may depend on the firm’s forecast about its demand. In other words, if the firm expects the demand to grow, then it should expand the size of the plant. 

Now when we relax the assumption of three plant sizes and instead assume that there is infinite number of plant sizes then we can draw a smooth curve that is tangent to all the SAC curves (envelopes all the SAC curves) and that curve is known as the Long-run Cost curve (LAC) or the envelope curve. 

Figure 7.11:  Long run Average Cost Curve (Envelope Curve)

Cost 
	SAC1	SACB
	LAC
	SAC2

	Output 

Indeed a LAC curve is an envelope curve, for it envelopes all the SAC curves. A LAC curve is U-shaped and this is due to economies and diseconomies of scale which refer to advantages and disadvantages of large scale production respectively.

The LAC curve can be divided into three parts. 

Figure 7.12: Regions of a LAC Curve 

	Cost 

	III    LAC
	I	II

	0
	Output 

In the first region, average cost is falling as the firm expands its output. This is due to economies of scale. In this region, the firm experiences increasing returns to scale. In the second region, the average cost is not changing yet output is increasing. Here the firm experiences constant returns to scale. In the third region, output is increasing at increasing g average cost. This is due to diseconomies of scale therefore in this region the experiences diminishing returns to scale.

6.4	Economies and Diseconomies of Scale
As a firm expands in size, many changes accompany the expansion. For instance it hires better trained personnel, it trains its own personnel, purchases specialised machines and computers, constructs special buildings e.g. ware houses, cold rooms, purchases specialized vehicles, develops new marketing techniques, acquires confidence from its suppliers and customers etc. In addition it may participate in research to develop new brands spends more in advertising, widens its market share and a lot more. This expansion comes along with benefits or advantages that lead to reduced average cost of Production. It is these advantages that are referred to as Economies of Scales. Economies of scale lead to the falling part of the Long- run average cost curve and are divided into two categories; Pecuniary economies and Real economies of scale.

Pecuniary economies are enjoyed by a firm when it pays less for the factor inputs because of purchasing in large quantities. For instance a large firm is likely to pay a lower price per unit input (raw material) when it purchases in large quantities. Also large firms enjoy discounts when it hires transport companies to transport its output, or discounts in increased advertising etc.
On the other hand, real economies of scale are realized out of efficiency that is associated with large scale production which leads to reduced physical quantities of factor inputs leading to lower average cost. Examples of real economies include;
i)	Technical also known as production economies;
ii)	Selling or marketing economies;
iii)	Transport or storage economics and
iv)	Managerial economies

For instance the average cost of storage or transport falls with large production. Consider a firm that hires a warehouse or truck to store or to transport its goods respectively. The total costs of hiring to store or transport one tonne of the commodity is the same as that for five tonnes provided the five tonnes can fit in the store or truck. However, the average cost of storing or transporting one tonne is higher than that of storing or transporting five tonnes. As regards to managerial economies, when a firm expands it tends to employ all specialized workers such that efficiency is increased.

On the other hand over expansion of a firm may lead to disadvantages that lead to increased cost of production. These disadvantages are referred to as Diseconomies of scale. The rising part of the long run average costs curve is due to diseconomies of scale. When a firm over expands, it may experience several problems that can either be managerial due to failure to monitor all workers well such that some workers may shirk. Also when a firm over expands, it might experience transport and storage problems and perhaps production problems, arising from over utilization of the machines leading to constant breakdowns.

 Review Questions
2.	1. Distinguish between implicit costs and explicit costs and give examples.
3.	Distinguish between total cost, fixed cost and variable cost and provide examples where necessary.
4.	Define Average total cost, Average variable cost, Average fixed cost and marginal cost. And clearly show the relationship between these costs.
5.	Justify the shapes of ATC, AVC, AFC and MC.
6.	Show that (hint; use calculus);
(i)	At minimum ATC, MC ATC,
(ii)	At minimum AVC, MC =AVC,
(iii)	Slope of TC = slope of TVC,
(iv)	ATC =AFC+AVC.
7.	Explain why MC curve meets the AVC curve before meeting the ATC curve.
8.	Given the following information;
Output (Q)	0	1	2	3	4	5	6	7	8	9	10	
Variable Cost (VC)	0	10	18	24	39	33	38	44	53	62		

Supposing that fixed cost is 30, Construct; TC, FC, AFC, AVC, ATC and MC schedules.

9.	 Show that at the point of intersection of the MC and AVC, MC and ATC, the AVC and ATC curves are at their minimum points.
10.	Given the following total cost function;
c  =   - 3Q2  +  10Q  +  20
a) Find;
i)	FC
ii)	VC
iii)	MC
iv)	AFC
v)	AVC
vi)	ATC
(c)	Show that MC equals to the slope of TVC or the slope of IC
(d)	Suppose output varies from 1 to 10 using the given cost functions, find the values of; TC, FC, VC, AFC, AVC, ATC and MC schedule.
(e)	Find the break-even and shut-down output levels.

(5)	Explain hov the Long-run average cost curve (LAC) is derived.
(6)	What is the relationship between returns to scale and economies of scale?
(7)	With relevant examples, distinguish between economies and diseconomies of scale.
(8)	Explain the relationship between an expansion path and long run average cost curve.
(9)	The shape of the Long-run average cost curve (LAC) is due to economies and diseconomies of scale, elaborate.

Unit 7
Profit Maximization

 7.1	Introduction
There are several objectives as to why firms operate there businesses and stay in the markets. These objects depend on the size of the firm and ownership visa-avis management. Indeed small firms (sole proprietorship) have objectives different from those of large firms. And also firms run by owners also have objectives different from those run by employed managers.

Traditional microeconomics however focuses on the profit motive; that the major objectives of firms, small or large, own- managed or employee- managed is to maximize profits.

Recent models have argued that there are other objectives of firms, particularly large firms run by employee- managers such as;
•	Sales-revenue maximization, 
•	Larger market share and
•	Long run survival among others.

In the long run however, such firms will revert to profit maximization.
A large firm may decide to reduce the price of its commodities (price undercutting) when it senses that a competitor intends to join the market to discourage the competitor since it would fear making losses, but soon after the competitor withdraws from joining the market, the incumbent firm raises the prices in order to maximize profits.

Also firms that claim to acquire large market share by selling at lower prices initially to persuade the customers, after establishing themselves in the market and acquiring loyalty and consumer confidence, they start raising prices so as to maximize profits since they by then command a large market share, besides the consumers are loyal to it.
All in all profit maximization remains the major goal of the firm especially in the long run.
We now need to establish the condition for profit maximization, but first we need to understand the following concepts:

 7.2 	Total Revenue (TR)
This is defined as the product of price and output, i.e.
		R  =  P.Q
Total revenue is the gross income of a firm. The shape of the Total Revenue function (R) depends on the type of the market structure (as we shall see in our next chapter). For instance when price is fixed and only output varies (for example under perfect competition), then clearly the total revenue function is a linear function passing through the origin and its slope is equal to price. On the other hand, when both price and output vary (for example under monopoly), the total revenue function rises from the origin (i.e. when Q = 0) to a maximum then falls. In this case the slope of the total revenue curve is not equal to price but instead less than price, as demonstrated in the following section.
Figure 7.1:  Total revenue functions 

	Revenue 	                                  TR Curve of a Monopolist 
	TR Curve of a Perfect Competitor 

	0
	Quantity 

7.3	 Marginal Revenue (MR)
The word marginal refers to rate of change. Therefore marginal revenue is the rate of change of total revenue due to charge in output, Simply MR refers to the additional revenue generated due to a sale of an additional unit of output. In other words, MR is the slope of the TR function, that is;
	MR  =  
The shape of the MR curve depends on the type of market structure. For instance under perfect competition when price is constant the MR curve is a straight horizontal line parallel to the horizontal axis and it is equal to price or the demand curve of the firm.
This can be shown below using differential calculus, that is; 
		MR  =   
But R = P.Q, then by substitution we get; 

		MR = 
But since under perfect competition, price P is fixed then we have, 
		MR = P = P
Graphically, this is shown in figure 8.2 below. 

Figure 7.2: The Marginal Revenue curve of a Perfect Competitor 

	   Price 

Marginal Revenue 
	MR = P

			0
	Output 

Now let us consider the case when price output vary (i.e. the Monopoly situation). 

	MR  =  
But since both price and output vary, we shall now use the product rule of differential which gives us; 
	MR  =  P.
	Or		MR =  P + Q 

You should easily recall that the term refers to the slope of a demand curve which is always negative. And since output Q can never be negative then it implies that the term Q  is always negative. 

This then, clearly means that marginal revenue must always be less than price under monopoly at any output level. (Recall the demand curve is also the price curve, i.e. D = P) as shown below. 

Figure 7.3: The Marginal Revenue Curve of a Monopolist

                 Price MR

                            P1 

	D = P
	MR1

	0
	Quantity 
          MR

7.4	 Relationship between Total Revenue and Marginal Revenue 
The relationship between TR and MR can be illustrated using the following diagram; 
Figure 7.4: Total Revenue, Marginal Revenue and Demand curve 

	Revenue

TR

	Output 

Marginal 
          Revenue

	D = P

		               MR	Output 

From the diagram we can note the following;
•	When output is zero, price is at its highest and is equal to MR, and TR is zero (i.e. R = P.Q, but Q = 0). 
•	When TR is rising, MR is positive but declining. 
•	When TR is at maximum (turning point) MR is zero.
•	When TR is falling, MR is negative. 

7.5	 Profit (п)
The simplest definition of profit that we shall use in this book is: The difference between Total Revenue and Total Cost that is;

	п  =  TR – TC or simply        п = R – C

In the following diagram, we illustrate the profit function and use it to establish the condition for profit maximization. 

Figure 7.5: The Profit Curve 
	TC
Revenue Cost	E
Profit 	B
	TR

	A

	0
	AA        QП          QB	Output

	П

We recall that the Total cost curve (C) starts from the origin due to a fixed cost and takes a shape similar to that of the Total Variable cost curve. And we also recall that profit (п) is the difference between Revenue (R) and cost (C). From figure 8.5 we need to describe three points; 
•	Before point A,
•	Between point A and B,
•	Beyond point B. 

Before point A, the Total Cost curve (C) lies above the Total Revenue curve (R). In other words, the Total cost is greater than the Revenue. This implies that the firm makes negative profits (loss); therefore the profit function (п) lies in the negative sections (i.e. below the horizontal axis). 

At point A (output level QA), Total cost (C) equals to Total Revenue (R) and since п = R-C and yet R = C at this point, then profit (п) must be equal to zero. 

Between points A and B, Total Revenue exceeds Total Cost, therefore profit (п) is positive. The profit function will however rise, reach a maximum at some output level Qп (or point e on the revenue function) beyond which the difference between R and C will decline though positive such that the profit curve will start falling.

At point B (output level QB) the revenue curve and the cost curve meet. In other words R = C, implying that п = 0. But beyond point B, the cost curve now lies entirely above the Revenue curve meaning that Total Cost exceeds Total Revenue; accordingly the firm makes negative profits (loss). So the profit curve is again in the negative section (that is, below the horizontal axis).

Condition for Profit Maximization
Again if we refer to figure 8.5, maximum profits occur at output level Qп. Indeed at this point the profit curve (п) is at its maximum (turning point). But from calculus at a maximum point, the slope of a curve is zero. Recall that the slope or gradient of a curve is obtained by differentiation, therefore;
		 =  0
But by definition п = R – C. This implies that, 
		  =  0
Or 		 =  0

Recall that,  = MR: The slope of the Total Revenue function and 

 =  MC  =  The slope of the TC function. Then by substitution we get; 
MR = MC: This is the condition for profit maximization which simply states that: at maximum profits Marginal Revenue equals to Marginal Cost or rather that the addition to Total revenue should be equal to the addition to Total cost.

The above conditions (i.e. MR = MC) is just a necessary condition for profit maximization, implying that it might not be unique. For instance consider the case of a perfect competition market structure. As we had earlier established, the MC curve is U- shaped, while the MR curve of a perfect competition is horizontal as shown in the figure below.

Figure 7.6: Condition of Profit maximization under Perfect competition 

	     MC
Marginal Cost
Marginal Revenue

	F	        G	MR

	0	QF	     QO	Output 

From figure 8.6 above, points F and G satisfy the condition for profit maximization (i.e. MR = MC). Therefore it would imply that output levels QF and QG are profit maximizing levels, which is not the case. Because when we critically look at points F and G, we observe that at point F, the MC curve is falling while at point G the MC curve is rising. In addition output level at point F (i.e. QF) is less than that at point G (i.e. QG).

The task before us is to identify which of the two points F and G is indeed the profit maximizing one. We shall divide our diagram (Figure 8.6) into three regions; before point F, between points F and G and beyond point G.

Consider output level less than QF. At that level, MC exceeds MR. This means that if a firm produces any output level less than QF, additional (increment) to Total cost exceeds the increment to Total revenue, but the addition to total cost (MC) falls as out put approaches QF. In other words it benefits the firm if it produces more and more output closer to QF: Now between points F and G, MR is greater than MC. This means that for output level greater than QF, the addition to the firm’s Total Revenue exceeds the addition to its Total cost. For that matter, the firm should produce more and more since it benefits. Finally let us consider output level beyond QG. As the firm produces more and more output greater than QG, instead the addition to its Total cost exceeds that to its Total revenue.

Indeed the gap widens as it moves away to the right of output level QG (Point G). But on the other hand, if it moves from the right towards point G (decreases its output towards QG) instead the firm benefits since the addition to costs falls. From this simple analysis we can conclude that point G is the converging point of the firm. That is, to the left of point G, the firm should increase its output level from Q = 0 up to Q = QG. But to the right of point G, the firm should decrease its output level until Q = QG. We can therefore conclude that point G (with greater output level QG) is the profit maximizing point. But at point G the MC curve is rising so we can now state the sufficient condition for profit maximization as: At the point of profit maximization (MR =MC) the MC curve must be rising.

The sufficient condition can be stated mathematically as: The slope of the MC curve must be positive at the point of profit maximization. Below we provide a simple proof;

Recall that slope refers to rate of change which is obtained by differentiation: So,

		 > 0

But as we known that MC  =  , then by substitution we get; 

		 > 0

Or 		 > 0

The last statement refers to the second derivative of the cost function and it states that: The sufficient condition for profit maximization requires that the second derivative of the cost function be positive. 

In summary, the two conditions for profit maximization are; 
1.	The necessary condition, which states that MR = MC
2.	The sufficient condition, which states that at the point where MR = MC, the MC curve must be rising. 

 Review Questions
1.	Explain the relationship between Total revenue curve, Average revenue curve, and Marginal revenue curve;
(i)	Under monopoly market structure, 
(ii)	Under perfect competition market structure.
2.	Show that a demand curve of a firm is also its Marginal revenue and Average revenue curve under perfect competition.
3.	Derive the relationship between a demand curve and the marginal revenue curve under monopoly market structure.
4.	Derive and explain the relationship between marginal revenue, price and price elasticity of demand under monopoly.
5.	Derive the condition for profit maximization and clearly state both the necessary and sufficient conditions.
6.	Using a well- labeled diagram, explain the relationship between Total Revenue, Total Cost, Profit and Marginal profit.

Unit 8
Market Structures

8.1	 Introduction
In this chapter we shall look at a group of firms that tend to behave alike. As we shall see, under a market structure, firms of the same industry (market) tend to produce closely related or similar commodities; they have similar pricing, advertising and other sales promotion mechanisms. We shall therefore look at the characteristics of these markets and give examples of the different market structures. Thereafter we shall look at the individual market structures, discuss the assumptions underlying each market structure, look at its demand curve, marginal revenue curve, total revenue curve and short run and long run equilibrium situations.

Recall that we defined a market as a place where goods and services are exchanged between producers and consumers. It is also a situation whereby transactions take place between consumers and producers with or without the use of money. When defining a market, economists do not reserve the term to denote only the organized exchange operating in a well-defined physical location. But it can also refer to a group of8sellers and buyers whose activities affect price at which a particular commodity is sold.

Basically, there are four groupings of markets, also known as market structures, which are:
•	Perfect competition,
•	Monopoly,
•	Monopolistic competition and
•	Oligopoly.

There are a number of criteria that are used to classify a market and these are;
•	Number of firms in a market: If there are numerous firms, then either the market is perfect competition or monopolistic competition and if there are few, then it is oligopoly. A special case of oligopoly is when there are two firms; this case is referred to as duopoly. But if there is a single firm in the market then it is monopoly.
•	Nature of the product: If the goods are hornogenous then it is perfect competition, if differentiated it is monopolistic competition or oligopoly.
•	Ease of entry and exit: This can be as a result of cost of production or natural or artificial blockage: If entry and exist is easy then it is either perfect competition or monopolistic competition. But if entry and exist is difficult due to high costs of production then it is oligopoly. If entry and exist is blocked then it is monopoly.
•	According to the level of advertisement: If the level of advertising is high and persuasive, then it is either monopolistic competition or oligopoly. And if advertising is only informative, it is monopoly. If there is no advertising then it is perfect competition.
•	Availability of information: If information is available and costless then we have perfect competition.
•	The degree of collusion: This is normally under oligopoly and at times under monopolistic competition. It simply refers to a situation when a group of firms producing similar goods come together to decide on price and output in the market such that they behave like a monopolist.

On the buyers’ side, if there is only one buyer then we have what is called monopsony but if there are a few buyers its called oligopsony, while if there are many buyers then we have perfect competition.

8.2	Perfect Competition

Assumptions and Characteristics
It is a market structure characterized by complete absence of rivalry among the individual firm. It is a market based on the following assumptions or characteristics.
•	There are a large number of sellers and buyers such that each individual firm however large it may be supply only a small quantity to the market. The buyers are also many such that no buyer can influence the market prices. So both sellers and buyers are considered to be price takers.
•	Product homogeneity: There is no product differentiation of any form. This assumption together with the assumption of large number of sellers implies that there is only one price in the market structure therefore the demand curve is perfectly elastic.
•	Free entry and exit: There are no barriers to entry and exit. When firms earn abnormal profits other firms are free to join the industry but if there are losses firms are free to leave the industry.
•	Profit Maximization: The major goal of firms in the industry is to maximize profits.
•	Government intervention: There are no government interventions in the market of any form, for instance subsides, rationing etc.

The above assumptions are fulfilled in the market structure called pure competition. It is different from perfect competition which in addition to the above assumptions requires the fulfillment of the following two assumptions.
•	Perfect mobility of factors of production: It is assumed that factors of production for example labour, land, capital and entrepreneurship are mobile. Factors are free to move from one firm to another, one industry to another and from one economy to another. There exists external mobility and internal mobility of labour. Also this assumption assumes that labour can move between different jobs and that raw materials are not monopolized by one firm.

•	Perfect knowledge of market conditions: It assumes that all buyers and sellers have perfect knowledge about the conditions of the market. The knowledge should be on both current and future market conditions. In other words knowledge is free, so both consumers and producers know about the price and output levels in the market. There is no market-uncertainty about developments in the market since information is free and costless.

Demand Curve, Average Revenue Curve and Marginal Revenue Curve of a Firm under Perfect Competition.
Figure 9.1 (a) shows the demand and supply curves of a market while, figure (b) shows the demand curve of a firm. Price P is determined by market using forces of demand and supply. So each firm has to sell at the set price P any amount of output.

Figure 8.1: The Demand Curve of a Firm under Perfect Competition

  Price 	Price
	SM

	  P                                                                     P                                                     DF

    DM

				        Quantity 					                                Quantity 
(a)	 Market 							(b) Firm 

The demand curve is perfectly elastic due to the existence of perfect substitutes (i.e. commodities are homogeneous). Also no firm has an influence over the market, since the market determines the price and the firm is just a price taker. In addition there is perfect information in the market meaning that consumers are assumed to know all the producers and the price at which the commodity is charged.

Total Revenue curve (TR)
Just as we saw earlier in chapter eight, Total Revenue is defined as the product of price and output (i.e. R= P.Q). But since price charged by a perfectly competitive firm is determined by the market, hence it is fixed, then it means that it is only output that varies. Accordingly the Total Revenue curve is a linear function (straight line) and it passes through the origin (since Q = 0, also R = 0). 

	Revenue

	TR

	0
	Quantity 

Average Revenue (AR)
Average Revenue is defined as Total revenue divided by total output, i.e.

		AR  =  

Bust since R = P.Q then, 
		AR  =   = P
This means that the RA curve is also equivalent to the price or demand curve. 

Marginal Revenue (MR)
Marginal revenue is defined as the change in total revenue due to the sale of an extra unit of output. In other words MR is the slope of the TR function. But since under perfect competition, TR is linear then its slope must be constant. Therefore the MR curve is a straight line parallel to the output axis and is equal to the demand curve as shown below. 

		MR  =  

But R  =   P.Q, then by substitution we get; 

	MR  =  

And since price is fixed under perfect competition, then, 

	MR  =  P  =  p

This means that the MR curve is also equivalent to the demand curve. Therefore under perfect competition; P = AR = MR, just as shown in figure 9.3 below.

Figure 8.3 Marginal Revenue curve of a Perfectly Competitive Firm

	Price 

	AR = MR = D = P

	0
	Quantity 

Equilibrium of a Firm under Perfect Competition 
•	Short-run Analysis 
As we saw earlier in the previous chapter, a firm is in equilibrium when it maximizes its profits. Profit is maximized when Marginal Cost equals to Marginal Revenue (MC=MR). In the short run a perfectly competitive firm can be in equilibrium when making either profits or losses.

a)	A Firm making Profits
This occurs when a firm sells at a price higher than its average cost of production. 

Figure 8.4: A Firm making Profits.
   Price / Cost 	MC
                                                                SAC

	Pe	e	AR = MR = DD

                   C
	D

	  0	Qe	Quantity 

	SAC  =  Short run Average Cost curve 
	SMC =  Short run Marginal Cost curve 

Point e is the profit maximizing point (i.e. at equilibrium MC = MR). Output Qe is produced at average cost C and sold at price Pe. Therefore the total cost of the firm is given by area OCDQe while its total revenue is equal to area OPeeQe. This implies that the difference which is area CPeeD is the firm’s profits. Output Q is the profit maximizing one because beyond Qe. MC exceeds MR implying that the increase in cost will exceed increase in revenue.

Recall that the equality MC = MR as a condition for profit maximization is just a necessary one but not sufficient. The sufficient condition requires that at the point of equilibrium the slope of the MC curve be positive i.e. MC should cut MR curve from below. The implication of the sufficient condition is that at output level when MC is less than MR, it pays the producer when she produces more, since more output would add more to revenue than to cost. On the other hand at output level when MC is greater than MR, more output would add more to cost than to revenue, so it pays more to a producer when she reduces production. It is only at the point when MC equals MR that addition to cost equals to addition to revenue. 

b)	A Firm making Losses 
This occurs when price charged is less than average cost of production as shown below. 

Figure 8.5:  A Loss making Firm	SMC	SAC
   Price / Cost 	
        Revenue                                                       
	F

	C		

                  Pe	                                                             AR = MR = DD
	e

	  0	Qe	Quantity 

Recall that MC cuts the SAC curve at its minimum’ point. From figure 9.5, the firm is in equilibrium at point e where MC = MR. Output Qe is produced at an average cost C which is however, higher than the price Pe at which it is sold. Therefore Total cost will exceed Total revenue by area (PeCFe) which will then be the firm’s loss.

Long-run Equilibrium Analysis
Due of the free entry and exit, in the long run other firms are attracted to the industry when there are abnormal profits and some firms leave the industry whenever there are losses. As a result, total output will increase (if firms enter the industry) leading to a fall in the market price hence fall in profits of the firm. The process will continue until all firms earn super normal profits. In case of losses, some firms will leave the industry such that total output decreases leading to increase in prices which in turn reduces the loss. This process will also continue until all firms in the industry earn normal profits.

Figure 8.6: Long run Equilibrium of a Firm 

	Revenue	LMC         LAC

	e
	C = Pe	AR = MR = DD

	0	Qe			Quantity

LAC= Long-run Average Cost curve 
LMC= Long-ran Average Cost curve

In the long run profits are maximized at the point where LMC LAC This point is at the lowest point of the LAC curve. So the profit maximizing condition of the firm in the long run is LMC MR LAC = P. This is the long run equilibrium condition of a firm under perfect competition. In the long run output Qe is produced at average cost C and sold at price Pe. But since price equals to average cost, then total revenue is also equal to total cost (i.e. since Pe = AR then TR = TC). This implies that the firm earns only normal profits or zero economic or zero abnormal profits.

Processes to Long- run Equilibrium
We earlier saw that a perfectly competitive firm can make either profits or losses in the short inn. And that profits (losses) will attract (discourage) some other firms from the industry. The process to long run equilibrium therefore depends on the initial conditions of the firms in the industry (i.e. whether making profits or making losses in the short run). For instance if in the short run the existing firms are earning super normal profits, other firms get attracted to the industry. o increase in the number of firms leads to increase in the output in the market. This leads to a shift in the market supply curve outwards to the right leading to a lower price in the market. A reduction in the market price leads to a downward shift of a firm’s demand curve (since a firm is a price taker, P = AR = MR). This in turn will lead to a reduction in the firm’s profit. The process continues until the firm’s supernormal profit is at zero meaning that the firm makes only normal profits. This is partly illustrated in figure 9.7.

Figure 8.7: Effect of an Increase in Number of Firms on a Firm’s Demand Curve 

Price 	S1	               Price 
	S2

          P1	P1                                    AR1=MR1=D1

         P2	P2                                     AR2=MR2=D2

	  D

	Q1           Q2     Quantity 					Quantity 

The above is an analysis in the commodity market. But in the factor market, increase in the number of firms leads to increase in the demand for the factors of production. This will in turn lead to an outward shift in the demand curve for the factors of production thus leading to increase in the price of the factor hence cost of production.

Figure 8.8: Effect of increase in Number of Firms on Factor Input Price 

Price 		               Price 
	S		       of output 

          PF1	AC2 = PF1                                    

         PF2	AC1=PF2                                     

	  D2
	D1	0	DF
	0	      Quantity of inputs				                  QF1    QF2    Quantity 
                                                                                                                           of input
(b)	 Market 					(b)  Firm

If we assume that the market for factor inputs is perfectly competitive and that inputs are homogenous, then the price of the inputs (which is part of average cost to a firm shall be determined by the inputs market and so the firm will be a price taker. Figure 9.8(a) represents the market while (b) shows the firm. An increase in the number of firms in the market will lead to increased demand for factor inputs leading to a shift in the market input demand curve outwards to the right from D1 to D2. A new factor input price PF2 shall now be set. But since input price’ is equivalent to average cost of the firm, it implies that the firm’s average cost rises from C1 to C2. In other words, with entry of new firms in the market (industry) the average cost of production increases hence shifting the AC curve upwards. But increase in AC will further reduce the profits of the firm.

Therefore, the level of profits is eroded by two forces; one arising from price reduction in the goods market and the other due to increase in the cost of production. The process will continue until the firm earns only normal profits.

Figure 8.9: Long -run Profit Adjustment under Perfect Competition
	AV2   AC1
	Price 	MC
	AC
	MC	e1
                       P1                                                                                                    D1=AR1=MR1
	e2
           AC2=P2                                                                                                        D2=AR2=MR2
                  AC1
	B

	0
	                   Q2    Q1	Quantity 

Point el is the short-run equilibrium point of a firm (i.e. MC=MR). At this point the firm produces output level Q1 at average cost AC1 and sells it at price P1, hence making profit equal to area AC1P1e1B. When new firms enter the market to share the profits, the market output level increases but since the market demand has not changed, price in the market falls. This leads to a shift in the firm’s demand curve downwards fromD1to D2. Similarly, increase in number of firms raises the competition for factor inputs hence raising their prices (Average cost). This leads to an upward shift in the Average Cost curve from AC1 to AC2. 

Long-run equilibrium of the firm is established at point e2 where the average cost curve tangent to the demand or marginal revenue curve. At this point the firm produces output Q2 which is less than the original level, at average cost C2 which is higher than the initial level and sells it at price P which is less than the original price P1. But since price now equals to average cost (P2 = AC2), then Total revenue must be equal to Total cost in the long-run. Therefore, the firm makes just normal profit in the long-run and more firms will join the industry.

We however, note that in the long-run, the firm;

•	Produces at optimal (minimum average cost);
•	Charges a lower price (i.e. P2<P1) than in the short-run: This is because market output has increased with increase in the number of firms yet demand has not changed;
•	The firm incurs a higher average cost (C2>C1): This is due to increased demand for factor inputs arising from increased number of firms;
•	Supplies less to the market (i.e. firm’s market share falls; Q2<Q1) this is because, increased number of firms leads to increased production but since the market demand is assumed to be fixed, each firm’s share will fall.
•	Earns zero supernormal / abnormal / economic profits in other words, it earns just normal profits (since AC=P).

On the other hand if firms were making losses in the short-run, then a reverse process would occur. That is, some firms would quit the industry due to freedom of exit. This would to a shift a shift in the market supply curve upwards to the left leading to a fall in output and an increase in market price. But since firms are price takers, increase in market price means a shift in the demand curve upwards. So the remaining firms would now charge a higher price which reduces the amount of loss.

In the factor market when some firms quit the industry, the demand for factor inputs fall. So the market demand curve for factor inputs shifts inwards to the left, which in-turn leads to a fall in the factor input price hence a fall in the Average Cost (AC). But a fall in the AC leads to a downward shift of the AC curve which then reduces the los further.

The process continues, that is, the upward shift of the firm’s demand curve (hence increase in the commodity price) and a downward shift of the AC curve (reduction in the average cost of production) until the AC curve is tangent to the demand or Marginal revenue curve, leading to the long-run equilibrium of the firm. At the long-run equilibrium point, price charged by the firm will be equal to the average cost hence the firm will make just normal profits and no more firms will exit the industry (the diagrammatical illustration is left to the student as an exercise).

The Supply Curve of a Firm under Perfect Competition
In our earlier discussion on revenue and profits, we established that the profit maximizing point occurs at the point where MR MC, and at that point, the marginal cost curve must be upward sloping. So given that the MC of the firm is upward sloping and that price changes in the industry and also that the firm is a profit-maximizer (i.e. produces at a point where MC = MR), then the next equilibrium point of a firm will occur on the right of the initial one in case of a price increase. This is because an increase in the market price will lead to an upward shift of the firm’s demand curve (AR = MR =  DD) such that it will intersect the marginal cost curve to the right of the initial equilibrium as shown in figure 9.10 below.

Figure 8.10: A supply curve of a firm
    Price	AV	Price 
	MC	AVC
	c	SS
	P3                                                 AR3=MR3	P3	c

	P2	b	AR3=MR2                  P2	b

	P1	a	AR1=MR1                 P1	 a

             0		0
	Q1   Q2              Q3             Quantity                          Q1       Q2        Q3   Quantity 

Suppose point a is the initial equilibrium point (i.e. MC = MR). At this point the firm produces quantity Q1 and sells it at price P1 giving rise to point a on the supply curve (ss). If the market price increases to P2, the firm’s demand curve shifts up to P2 = AR2 = MR1. The new equilibrium shall be established at point b where MC = MR2 and this new equilibrium occurs to the right of the original one (right of point a). At a higher price P2, the firm supplies more quantity Q2, giving rise to point b on the supply curve. A higher increase in the market price to P3 leads to a further upward shift in the demand curve to P3 = AR3 = MR3 and the new equilibrium is established at point c which occurs to the right of b. At price P3 the firm supplies quantity Q3 giving rise to point c on the supply curve. Joining points; a, b and c, we get the supply curve of the firm. We note that a supply curve of a perfectly competitive firm is similar to the rising section of the firm’s Marginal Cost curve over and above its Average Variable Cost curve.

We have now established that the firm’s supply curve is equivalent to its rising portion of its MC curve over and above the AVC curve, we next provide a mathematical derivation of the supply curve of a perfectly competitive firm and also distinguish between the short-run and long-run supply curve.
We recall that profit is the difference between Revenue and Costs, i.e.
П  =  R – C

But revenue is the product of price and quantity, i.e. R=P.Q. Then by substitution we get;
П = PQ – C

Maximizing profits will therefore be equivalent to maximizing the difference between revenue and cost, i.e.
MaxQ>0.PQ – C

Using calculus and bearing in mind that price under perfect competition is fixed, then 
(P.Q) - C  =  0

So, P  =  , But 

This then gives us;
P  =  MC

This means that optimal output level occurs when price equals cost. This also means that the supply curve of the firm is equivalent to the marginal cost curve.

Short-run Supply Curve of a Perfectly Competitive Firm
Recall that total cost of a firm in the short run is made up of Fixed Costs (FC) and Variable Costs (VC). If a firm produces zero output, its total revenue will be zero (i.e. since R = P.Q, if Q = 0) and its total cost will be equal to Fixed costs. Therefore, its profit level will be given by; 

П  =  R – C
= 0 – FC
= -FC
The point where the firm produces nothing is termed as the shut down point. The firm will shut down only if the profit obtained after producing some level of output is less than that obtained after producing nothing. That is; 
П  =  R – C
But C = FC + VC
By substitution, shut down occurs when; 
R – (FC + VC) < - FC
But since R = P.Q then by substitution we get; 
PQ < VC
Dividing through by Q we get; 
P  <   =  AVC

The above statement means that the firm will not supply anything (shut down) if price is less than Average Variable Cost. Therefore the shut down point occurs at the point where P = AVC. But as noted earlier, the supply curve of a firm is equivalent to the rising part of the Marginal Cost curve; we can now affirm that the short-run supply curve of a perfectly competitive firm is equivalent to the rising portion of the MC curve over and above the AVC curve. 

The Long-run Supply Curve of a Perfectly Competitive Firm
We recall that in the long run, there are no fixed costs instead all costs are variable. Also in the long run the firm is in equilibrium when it makes zero supernormal profits. The firm will therefore decide whether to stay out of business and can zero profits or remain in business at the equilibrium point since it would earn the same level of profits (zero supernormal profits). Therefore the firm will decide to stay in operation in the long run if its realized level of profits is at least equal to zero; i.e. 
R – C ≥ 0

But since R = P.Q then we have; 
P.Q – C ≥ C
Or P.Q ≥ C

Dividing through by Q we get; 
P  ≥  =  AC

This means that the firm will not supply any output in the long run at any price level less than its Average Cost. In other words, the long run supply curve of a perfectly competitive firm is equivalent to the rising part of its Marginal Cost curve over and above its Average Cost curve. 

The Supply Curve in an Industry
Since an industry is a combination of several firms producing the same commodity the supply curve of an industry is the horizontal summation of individual firm’s supply curves. 

Figure 8.11: The Market or Industry Supply Curve 

Price 	Price 	Price 
	     SS
	SA	SM
	P2	 P2
     P2

  P1	P1	P1

       0	0	0
	A1      A2     Quantity                    B1     B2            Quantity           Q1                Q2    Qty

Assuming that there are two firms in a market; A and B, at price P1 firm A supplies quantity A1, firm B supplies quantity B1, so the total supply in the industry at price P1 is Q = A1 + B1. Similarly at price P2, firm A supplies A2 while B supplies B2, implying that the total quantity supplied in the market is Q2  = A2 + B2. Since the industry supply curve is obtained by summing up all the individual firm’s supply curves, then it is more elastic than any individual supply curves.

Equilibrium of an Industry
Equilibrium refers to the state of stability i.e. when there is no tendency to change. A firm is in equilibrium when it maximizes its profits (i.e. the point where MC = MR). At such a point, a profit maximizing firm has no tendency to change its output. If it increases its output beyond that point (MC = MR) then MC will exceed MR hence making losses. On the other hand if it produces below the point the profits will be less because less output is produced.

The conditions for profit maximization; MC = MR at the highest level of output applies to all firms. An industry on the other hand is in equilibrium when there is no tendency for total market output to change. At this point neither new firms enter the industry nor do old firms leave the industry. Also at that point all firms in the industry earn normal profits therefore, LAC=LMC = MR = P.

8.3	Monopoly
In this part, we shall now look at another market structure called monopoly, which is a market structure where there is a single producer hence all decisions are taken by the firm. Under monopoly, the firm is at the same time the industry. We shall look at the demand curve and marginal revenue curve; thereafter we shall look at the short run and long run equilibrium conditions of the firm.

Characteristics of a Monopoly Market Structure
Monopoly is a market structure characterized by the following;
1)	One producer or seller of the commodity.
2)	Production of a commodity or good with no close substitutes.
3)	Blocked entry due to monopoly power.
4)	It advertises informatively so as to make consumers aware of the product.
5)	A monopolist sets the price and consumers are price takers.
6)	Its objective is to maximize profits.

Sources of Monopoly Power
1.	Allocation or distribution: A certain commodity can be produced only in a single or specified place say due to natural existence for instance mineral ore, hydroelectric power etc.
2.	Patent rights: For instance publishers or manufacturers.
3.	Ownership of strategic raw material especially those under government control.
4.	Exclusive methods of production because there are some specific unique techniques of production required to produce the commodity.
5.	Protectionism: This involves the imposition of foreign trade barriers on the product to exclude foreign competition.
6.	May arise if it is only possible to produce a good in a complex factory or after installation of large amount of equipment such that it would be uneconomical to have more than one firm supplying the same commodity.

The Demand Curve of a Monopolist
Since a monopolist is both a firm and at the same time the industry, then it is a price setter and consumers are price takers. Its demand curve therefore is down ward sloping. The monopolist can either determine the price to be charged or the quantity to sale but not both. For instance from figure 9.12 below; if it sets price at P1 quantity Q1 shall be demanded. On the other hand if it supplies quantity Q2 then it must sell it at price P2. For that matter, the monopolist can not set price P1 and sell quantity Q2 nor supply quantity Q2 at price P1.

Figure 9.12: A Demand curve of a Monopolist
	Price 	D

	P1

	P2

	    D
	 0	Q1     Q2	Quantity 

If the monopolist fixes a high price, quantity demanded will be low and vice versa. A monopolist is said to be a price maker and the consumers are price takers. This is because the monopolist can influence the prices in the market by changing the quantity produced. The demand curve is also its average revenue (AR) curve as shown below;

	AR  =    =  P

The Marginal Revenue Curve of a Monopolist
The marginal revenue curve of a monopolist slopes downwards because when more commodities are offered for sale price falls therefore the extra revenue received from additional output decreases. 

Figure 9.13: The Marginal Revenue Curve of a Monopolist
	Price
	P

               DD = AR

	0	Quantity 
 MR

If the demand curve is linear, then the MR curve of a monopolist is also linear, and it starts at the same point on a vertical axis as the demand curve falls at twice the rate of that of the demand curve. In other words, MR curve is twice as steep as the demand curve (see proof below).

For the methodical proof about the relationship between the MR curve and the demand curve of a monopolist, let us consider for simplicity a linear demand function given as;

(1)	 Q = α – Βp

We next obtain an inverse demand curve (i.e. make price P the subject):

(2)	P  =  
If we let α =  and b = then by substitution we get:

(3)	P  =  α – bQ

Equations (2) or (3) are referred to as inverse demand functions; where a, is the price intercept and –b the gradient of the demand curve. 

We recall that revenue R = P.Q, so multiplying through equation (3) by output Q we get; 

(4)	R = PQ = (a – bQ)Q

But by definition, marginal revenue (MR) is the slope of the total revenue function, then differentiating equation (4) with respect to quantity we get; 

(5)	 =  MR = a – b2Q

Equation (5) shows the Marginal Revenue function, clearly its slope is -2b and its intercept is a. If we now compare equations (3) and (5) we note that both the demand curve and marginal revenue curve begin from the same point (have same intercept) a, but MR falls at a rate twice that of the demand curve. 

Relation between MR and Price Elasticity of Demand
The Marginal revenue (MR) of a monopolist at any level of output is related to the price and to the price elasticity of demand at that level of output through the following expression. 

	MR  =  P 
Where 
	MR	=	Marginal Revenue 
	P	=	Price 
	e	=	Price Elasticity of demand 

Proof:
Recall that R = PQ
(6)	MR  =  

But under monopoly, both price and quantity vary, so to solve equation (6) we use the product rule of differentiation i.e.
(7)	MR  =  P
Or 
(8)	 MR  =  P + Q

We need to interpret equation (8). First we note that the term  is always negative because it is the slope of the inverse curve and since Q is always non-negative, then it means that under monopoly MR is always less than price. (The student should be able to see this). 

But price elasticity of demand is defined as:
(9)	e  =  (-) 

Taking the reciprocal and rearranging we get; 
(10)	

Now substituting equation (10) into equation (8) we get; 
(11)	MR  =  P = Q , which when simplified gives; 
(12)	MR = P., as required. 

From equation (12), it is clear that the extent to which a firm must change its price so as to increase its revenue depends on the price elasticity of demand of the good, specially:

(i)	When e > 1, MR > 0 implying that the total revenue curve is rising. Therefore for the firm to increase revenue, it should reduce its price. Reduction in price will lead to increased expenditure on the commodity hence will benefit the producer. 

(ii)	When e = 11, MR = 0, and TR is maximum. In this case a small change in price (increase or decrease) may not affect the TR.
(iii)	When e < 1, MR < 0 implying that TR is falling. In this case revenue will increase when price is increased. Therefore increase in price of an inelastic commodity leads to increase in expenditure on the good hence benefits the producer. 

8.4	Equilibrium of  Monopolist 
We shall loot at both short-run and long-run equilibrium of the firm. Also since a monopolist is the only firm in the market, the firm’s demand curve and supply curve is equivalent to the market (industry) demand and supply curve, similarly the firm’s short run and long-run equilibrium is equivalent to the market equilibrium. 

Short-run Analysis 
Like any other firm, a monopolist maximizes profits at a point where MC = MR. Unlike a perfect competitor however, a monopolist in most cases makes supernormal profits in the short run, (Figure 9.14). A monopolist may not stay in production if she makes losses in the short run.

Figure 9.14: Short run equilibrium of a monopolist 
	AC
	P	MC

	A

                        P1
	B
	C1	D = AR

	e

	0
	Qe	Quantity 
	MR

The firm maximizes supernormal profits at point e where MC – MR. Output Qe is produced at an average cost C1 (given by the cost curve) and sold at price P1 (given by the demand curve). Therefore the firm’s profit is given by area C1P1AB.

Long run Equilibrium Analysis of a Monopolist 
In the long run other firms would wish to enter the market to share supernormal profits but unlike the case of perfect competition where there is freedom of entry, there is blocked entry arising from monopoly power that stops other firms from joining the industry. So the monopolist remains the sole firm both in the short run and in the long run. This enables her to make supernormal profits both in the short run and in the long run. The monopolist may however, increase the level of output, depending on the market demand or future expectations. Three different situations are likely to happen; 
(i)	The monopolist may anticipate a small market size such that it produces at less than optimal or excess capacity as shown in figure 9.15. 

Figure 9.15: Less than Optimum 
	Price / Costs 	LAC
		LMC

	A
                        P1
	
	C1	D = AR

	e

	0
	   Qe   Q2	Quantity 
	MR

Q1  Profit maximization output 
Q2  Cost maximizing output 

In this case the monopolist shall produce at the falling part of the Long-run Average Cost curve (LAC); the firm shall produce output level Q1 at the point where MC = MR, but this level is less than that, that minimizes costs (i.e. output level Q2). This is one key feature that characterizes monopoly firms: they are ineffective unlike perfect competition. 

(ii)	The monopolist may anticipate the market to grow beyond optimum as shown by figure 9.16.

Figure 9.16: Beyond optimum 
   Price / Costs 

	LMC
	P1	LAC

	D = AR

	C1

	0	Q
	Q1    Q2
	MR

		Q1  Cost minimizing output 
		Q2  Profit maximization output 
If the market size is very large, the monopolist shall expand production and produce at the rising part of the LAC curve (beyond optimum). Output Q2 that the monopolist shall produce is greater than Q1 that minimizes costs. 

(iii)	Alternatively, the market size may expand up to optimal, in which case the monopolist may now behave like a perfect competitor as shown by figure 9.17.

Figure 9.17: At Optimum 
Price / Costs Revenue

	LMC
	P	LAC

	C	D = AR

 	0	Q1	Q
         MR

A monopolist does not produce output that minimizes average cost unless by coincidence. In this case, the monopoly shall be efficient because production takes place at the minimum point of AC curve. Output level Q1 is both the cost minimizing and profit maximizing output so it is the efficient (optimal) output level. Generally however, the monopolist will either produce at less than optimal (excess capacity) or at more than optimal in most cases.

8.5	Income Distribution under Monopoly

The existence of a single firm in the market, gives it a leeway such that it can decide on what price to charge and what quantity to produce. Due to monopoly power monopolists can charge different prices to different consumers a practice known as price discrimination whose major purpose is to maximize profits. We shall look at the conditions necessary for successful price discrimination and the different forms of price-discrimination. We shall there after compare a firm without price discrimination and one that discriminates. And finally we shall compare a monopolistic firm with a perfectly competitive one.
Income Distribution and Consumers Surplus under Monopoly
A monopolist can influence income distribution in his own favour by using his monopoly power to obtain positive super-normal profits in the long run. So the monopolist gains while consumers lose unlike under perfect competition. (See figure. 9.18)
Figure 9.18: Income Distribution under Monopoly

	A	MC  AC

                           P1                                      B
                             P2	E	E

	D = AR
e
	C1	F

	0	                 Q1              Q1      MR 	  Quantity 

If a monopolist produced output Q2 where AC = AR (like in the case of perfect competition in the long run), super-normal profits would be zero. But the monopolist will instead produce at a point where MC = MR a point where profit is maximize. Accordingly, the monopolist will be in equilibrium at point e where it produces output Q1 at average cost C1 and charge price P1 such that;
•	The monopolist produces less output level Q1 compared with that produced by a perfect competitor which is Q2
•	The monopolist charges a higher price P1 compared with that charged by a perfect competitor which is P2.
•	The monopolist incurs lower average cost of production, C1 (due to monoposony power), while a perfect competitor incurs higher average cost, C2 = P2, (because there are many firms so they compete for the resources).
•	The monopolist derives greater supernormal profits given by C1P1BF while the perfect competitor obtains just normal profits.
•	The monopolist allows less consumer’s surplus which is given by area P1AB while a perfect competitor allows greater consumer’s surplus equal to area P2AE.

8.6	Monopolist and Consumer Sovereignty
Under perfect competition consumers are sovereign in the sense that output levels respond to the change in demand and firms gain no long run benefits from one’s change of tastes. Firms will join industries whose goods have a higher demand and leave those industries whose demand has fallen. The process will continue until there are no supernormal profits in the long run. This is however, different under monopoly market system; when the demand of a good produced by a monopolist increases, his demand curve will shift outwards. This will increase both Total Revenue (TR) and Marginal revenue (MR) at any output level, as shown in figure 9.19 below.

Figure 9.19: Monopoly and Consumer Sovereignty

	P3
	P2	MC
                  P1	G              AV
	B

	D2
D1

	C2	
                  C1	   MR2

	0	Q1  Q2	MR1

The MR curve will shift from MR1 to MR2 and the profit maximizing output will increase from Q1 to Q2 (i.e. where the new MR curve meets the MC curve) The selling price will increase from P1 to P2, average cost will change from C1 to C2. The firm will make more super-normal profits. Firm’s super-normal profits will increase, because;

1.	If a firm sold output Q1 at a higher price P3 given by the new demand curve D2, it would make more profits, since price is now higher but average cost is the same.
2.	The maximum profit after the increase in demand and output exceeds the initial profit level. Clearly from the diagram, the initial level of profits is equal to area C1P1BE, but the new level of profits obtained from output level Q2 sold at price P2 is C2P2GH which is indeed greater than the original one.

Therefore a monopolist can limit the extent to which output increases so as to restrict consumers’ sovereignty and increase the price of the good to acquire more profits, for instance from the diagram it can limit output to Q1 and sell at higher price P3 which will exceed original price P1.

8.7	Price Discrimination
The firm discriminates between customers if it sells the same commodity at different Prices to different customers even though the cost of production is the same.

Figure 9.20: Price Discrimination under Monopoly

	MC        AC
	G
P2	B
	P1

	D = AR 
	e
	 C1	F

	0
	Q2   Q1	MR	Quantity 

Consider figure 9.20 above; a monopolist will produce output Q1 at point e, which is the profit maximizing output (i.e. it is where MC = MR). She can however; sell quantity Q2 at price P2 and the remaining quantity Q2 Q1 at price P1. Her total revenue is then given by OP2GQ2 + Q2KBQ1. The corresponding profit levels will be C1P2GH + HKBF. This however, exceeds the maximum profits C1P1BF that he would get if he does not discriminate between customers. The gain in profits due to price discrimination is P1P2GK. But this additional profit was originally part of the consumer’s surplus. The consumer’s surplus is therefore reduced by P1P2GK. That is; an increase in the amount paid by consumers if they are to consume total output Q1 at different prices. Under price discrimination therefore, the monopolist’s profits increase while the consumer’s surplus reduces by the same amount.

Forms of Price Discrimination
•	Discrimination according to Income: Where low prices are charged to the poor and high prices to the rich for the same services, for instance in hospitals, football stadiums, cinema halls etc.
•	Discrimination according to sex for instance charging a low price to female than male e.g. in discotheque.
•	Geographical discrimination (i.e. dumping) where commodities are sold at different prices specifically at low prices in a foreign country than in a domestic country. This is done because of different reasons which may include; disposing of surplus and discouraging production of the same commodity in the foreign country.
•	According to time: e.g. Cinema-shows. Where a lower fee is charged in morning hours and on working days and a higher fee in the evening and on weekends.
•	Nature of the commodity: publishers of books tend to charge a higher price for books with hard cover than for those with soft covers although both have similar contents.

Conditions for Price Discrimination
1.	Different markets should have different elasticity of demand. A higher price should be charged in the market where the elasticity is low (inelastic) and a lower price should be charged in a market where the elasticity is high (elastic).
2.	The two markets should be separated from each other to avoid recycling of goods from a cheaper market to an expensive one.

3.	It should be impossible for buyers to transfer the commodity from where the price is low to where price is high.

Advantages of price Discrimination
1.	It enables the poor to get essential commodities and services at relatively low prices.
2.	To the producer it increases his total revenue hence profits.
3.	It is a form of redistribution of income that is; the poor are subsidized while the rich are charged highly.
4.	It enables producers to dispose of surplus products.

Disadvantage
The major disadvantage is that price discrimination reduces consumer’s surplus.

8.8	Monopolistic Competition

In the previous two subsections we saw two extreme cases: A case where there are numerous producers such that an individual producer has no influence in the market which we called perfect competition and a case where there is a single producer who has maximum influence on the market which is called monopoly. We now turn to another market structure which is mid way between perfect competition and monopoly which is called Monopolistic Competition. We shall look at the demand and marginal revenue curve of a monopolistically competitive firm. We shall also look at the short run and long run equilibrium situations of the firm.

Characteristics of a Monopolistically Competitive Firm
Monopolistic Competition is a market structure characterized by the following:
•	There are many producers in the market.
•	There is free entry and exist of firms: When firms make losses they are free to quit and when they make profits others are free to enter.
•	The goal of the firm is profit maximization, both in the short run and in the long run.
•	The firm is assumed to behave as if it knows its demand and cost curves with certainty.
•	The long run consists of a number of identical short run periods which are assumed to be independent of each other in the sense that decisions in one period do not affect future periods and are not affected by past decisions.
•	The products or commodities are differentiated though with close substitutes and the differentiation may be in form of packaging, design, quality, taste, branding, etc.
•	Because of product differentiation there is need for persuasive advertising.

Examples of such firms include those that produce soap, detergent, cigarette etc.

Demand Curve of a Monopolistic Competitor.
The demand curve is more elastic than that of a monopolist (figure 9.21). This is because of the presence of close substitutes.

Figure 9.21: A Demand Curve of a Monopolistic Competitor 

	Price 
	D

	D

	0
	Quantity 

The demand curve is down ward sloping because each firm has monopoly power over its product and is not a price taker.

It is assumed that each firm makes its own pricing and output decision with the assumption that other firms will not change their prices. Each firm has an Assumed Demand curve (Al)) whose elasticity depends on the consumer’s loyalty i.e. if the consumers are very loyal to the producer, even the price of the good rose, the fail in quantity demanded will be relatively less so they would not buy much of the substitute goods, giving rise to an inelastic demand curve.
However, all firms are likely to behave in similar way in case of changes in the market demand or in conditions of supply say due to changes in input prices. So each firm is faced with two demand curves as shown in figure 9.22;

1.	The Assumed Demand curve (AD): if one firm changes price, other firms do not change.
2.	The True Demand curve (TI): Arising from similar behaviour by other firms. If many firms change their prices then;
•	The gain in sales from price reduction is less than what the firm expects.
•	The loss of sales from a price increase is less than what the firm expects.

Figure 9.22: The demand curves of a Monopolistic Competitor 

	P2
                          Pe	e

	P1	AD

         TD

	Q1  Q4 Qe     Q2                   Q1	        Q	uantity

From the above diagram, we note the following; 
QeQ1	=	Expected gain in sales,
QeQ2	=	Real gain in sales, 
QeQ3	=	Expected loss in sales,
QeQ4	=	Real loss in sales.  

The behaviour of each individual producer is influenced by its Assumed Demand curve (AD). When the firm reduces its prices to P1 it expects to sell quantity Q1, but ends up selling Q2 given by the True Demand (TD) curve. So the gain in sales QeQ2, is less than the expected gain Qe Q1. 

On the other hand, when the firm increases is price to P2 it expects to sell out put Q3 given by the Assumed Demand Curve (AD) but it ends up selling quantity Q4 given by the True Demand curve TD. So the loss in sales due to price increase QeQ4 is less than the expected los in sales QeQ3.
Short run Equilibrium of a Monopolist Competitor 
Under monopolistic competition, firms choose their output decisions basing on their assumed demand curves. This assumed demand curve gives rise to an assumed total revenue curve hence assumed marginal revenue curve. Like any other market structure, equilibrium occurs at a point where MR = MC. Two situations may however, occur in the short-run: Either the firm experiences a shortage or a surplus as shown below. 
A Shortage in the Short-run
The firm will produce at point e where MC = MR and it will assume that it can sell output Q1 at price P1 but at price P1 the true demand of the firm is Q2. So there will be a shortage of its products  given by Q1Q2. Therefore the firm will increase its output in the next period. 

Figure 9.23: A Monopolistic Competitor Experiencing a Shortage in the Short-run
	Shortage 
	Price 	MC
	P1

	e
	AD

	TD

	0
	Q1          Q2	Quantity 
	MR

A Surplus in the Short-run
Alternatively, the firm produces output Q3 (where MC = MR) and it assumed that at price P2 other firms do not change their prices such that it can sell output Q3. But at price P2 instead all other firms make similar decisions such that the firm’s actual demand at price P2 is Q4 (i.e. given by the true demand curve), so the firm has unsold goods (surplus) therefore its not in equilibrium and it will have to reduce is output in the next period.   

Figure 9.24: A Surplus in Short-run Analysis of Monopolistic Competitor 
	Price 
	Surplus
	      MC
	 P2

	AD

	TD
e
         MR
	0	Q4        Q3	Quantity 

The changes in output continues until the firm is in short run equilibrium where its actual or True Demand equal its Assumed Demand curve such that there is neither a surplus nor a shortage as shown in figure 9.25.

Figure 9.25: Short run equilibrium of a Monopolistic Competitor 
	Price 
	SMC
		A	SAC
	Pe
	C1	B
	  B
	AD

 						TD
	0
	Qe	Quantity 
	MR

The firm’s profit maximizing output occurs at a point where MC = MR. In addition the Assumed Demand curve should equal the True Demand. The firm will therefore produce output Qe which it sells at price Pe yet produced at average cost C1 such that it earns supernormal profits given by C1PeAB as shown in figure 9.25. 

Long run Equilibrium of a Firm under Monopolistic Competition
From the preceding section, a monopolistic competitor makes supernormal profits in the short run. But since there is free entry of new firms in the industry, other firms will be attracted by the profits to join the industry and also the existing firms will expand their production. These two factors will lead to an increase in out in the whole industry. The firm’s long run equilibrium situation is shown by figure 9.26.

The entry of new firms affects the revenue and costs of the existing firm as follows:
i)	Each firm sells less output at each price as new firms are introduced such that average revenue falls.
ii)	The new firms add to the demand of factors of production so that average cost of production increases. Supernormal profits are therefore reduced and the fall in profits continue until supernormal profits are completely eliminated implying that in the long run all firms earn normal profits.

Therefore, long run equilibrium will be established when;
i)	Each firm maximizes its profits on the basis of its Assumed Demand curve and assumed MR curves.
ii)	The Assumed Demand equals the True Demand curves.
iii)	Each firm’s profits are at normal level.

Figure 9.26: Long-run Equilibrium of Monopolistically Competitive firm.
	Price Cost	LMC     LAC

               Ce=P0

	AD

	TD

	0	Qe	Quantity 
    MR

From the diagram, the profit maximizing output is at point e (where MC MR), so the firm produces quantity Qe at average cost C and sells it at price Pe. At that output, assumed demand (AD) equais to true demand (ID). Since price equals to average cost, (i.e. Pe Ce), it follows that total revenue (TR) equals to total cost (TC) implying that the firm earns only normal profits.

Summary:
In this section, we have looked at a monopolistically competitive market structure. We saw that in this market structure, there are several firms that produce closely related commodities. And since there is some level of differentiation among commodities, a firm has some monopoly power. This gives rise to a downward sloping demand curve. This therefore means that decisions about price and quantities can be taken by the firm. There is however market uncertainty which may lead to either a surplus or shortage in the short run. At equilibrium the firm’s assumed demand curve must equate to the true demand curve. Also die to competition, the firm makes normal profits in the long run. n the nest lecture, we shall look at yet another market structure; Oligopoly which is closely related to monopolistic competition.

8.9	Oligopoly

Under perfect competition each firm knows that it can sell all that it can produce at the given market price and it can acquire all its inputs at a given price hence there are no market uncertainties in this market structure. Similarly monopolistic firms know the demand curve for their goods; the firms demand curve is the same as the industry’s demand curve, because there is only one firm in the industry. Therefore each firm can determine its corresponding marginal revenue curve with certainty. Also it is assumed that a monopolist knows the costs of its input factors, since it is the only buyer (monopsony); it can make the profit maximizing decisions. A monopolistic competitor on the other hand acts as if it knows its demand curve therefore it can also make profit maximizing decisions basing on the assumed demand and assumed MR curves.

In this section, we shall look at our last market structure: Oligopoly market. We shall discuss the characteristics of an Oligopoly market; the key one being market uncertainty. Among the several Oligopoly models, we shall discuss the kinked demand curve model developed by Paul Sweezy which is a result of market uncertainty.

Characteristics of Oligopoly market structure
o	Firms are uncertain of the pricing and output decisions that their rivals would take whenever there is an action by one firm, hence no firm knows how much it can sell at each price and its demand and MR curves are unknown.
o	There are a few unequal competing firms and each firm is large enough such that its actions have a significant effect on its rival’s sales and profits.
o	There is heavy and extensive advertising and quality changes for instance if one firm reduces its price others may follow or they may change the design or quality or packaging or may involve in extensive advertising. On the other hand if one firm increases the price simply because of profit motive others may not follow the price increase.
o	Each firm is concerned with the actions of other firms.
o	There is product differentiation and goods are close substitutes to each other. Examples include beer producers, soft drinks and petroleum products.

The Demand and Marginal Revenue Curves of an Oligopoly Firm:
Several models have been developed to try and explain the Oligopoly market situation; among them includes duopoly models by Cournot and Bertrand, collusive models (where firms form cartels) and non- collusive models. In this book however, we shall look at the Kinked demand curve model 1eveloped by Paul Sweezy which is a non-collusive model. 

Figure 9.27: The Kinked Demand Curve 

         Price Cost
	E	MC2
	A	MC1	    MC3

	Pe	B
                            MR1	F
	C
	    D
	J
	0	Qe	Quantity
	MR2

The diagram illustrates the equilibrium position of an Oligopoly market structure. Point B is the equilibrium point where Pe is the equilibrium price in the market and Qe is the corresponding equilibrium quantity. All firms in the market are supposed to sell at price Pe. If a firm increases its price above Pe it would follow the elastic demand curve ABC hence it would lose its market share because other firms do not follow the price increase.

Thereafter the firm would think that its demand curve is the elastic one, i.e. ABC. The firm now knows that by reducing price, it will benefit since its demand curve is elastic. Therefore by reducing its price below Pe it expects to increase its market share basing on the wrong assumption that other firms would not follow. But instead other firms follow the price reduction hence leaving the market share unchanged. Consequently the firm now follows the inelastic demand curve BD. This shows that the demand curve has a kink at point B hence a Kinked demand curve ABD.

We note that above price Pe the firm follows the elastic portion BA of the kinked demand curve and below price Pe the firm follows the inelastic portion Bi) of the kinked demand curve.

Since there are two demand curves, the corresponding Marginal Revenue (MR) curves are also two (i.e. MR1 (AF) and MR2 (GH). The two MR curves are separated by a gap G. MR1 (AF) is the MR curve that corresponds to the elastic portion AB of the kinked demand curve and MR2 (Gil) is the MR curve that corresponds to the inelastic portion BD of the kinked demand curve.

Equilibrium in this market structure is attained at a point where MC = MR and MC meets the MR curve in the discontinuous portion FG thus giving rise to equilibrium quantity Qe and Price Pe. Slight changes in costs do not change or affect the equilibrium position of the firm in this market structure. This is because of the discontinuity or the gap in the MR curve such that MC can fluctuate between the gap FG (i.e. MC can shift from MC1 to MC3) without affecting the equilibrium point. Therefore quantity Qe is produced and sold at price Pe at equilibrium. This explains why prices are stable under Oligopoly market structures.

Collusive Oligopoly Models (Cartels)
In order to avoid competition, or rivalry underlying each firm e.g. in form of price war and other market uncertainties, oligopoly firms may come together or reach an agreement and form a cartel, where they fix output quotas or prices of their products. This is known as cl1usion and one good existing example is OPEC (Organization of Petroleum Exporting Countries).

The prices may be set by either a low- cost firm (i.e. a firm that produces at least cost) or a dominant firm (i.e. a firm with majority market share). Collussion makes oligopoly firms to behave like monopolists and by so doing they block entry of new firms. Unfortunately, many cartels are unstable because some firms tend to cheat on one another particularly the lowest producers tend to charge a lower price.

Summary
In this chapter we have looked at the different market structures. We discussed the major characteristics that underlie each market structure and also discussed their equilibrium situations. We saw that under perfect competition each firm knows that it can sell all that it can produce at the given market price and it can acquire all its inputs at a gi.ren price hence there is no market uncertainty in this market structure. Similarly monopolistic firms know the demand curve for their goods; the firms demand curve is the same as the industry’s demand curve, because there is only one firm in the industry. Therefore each firm can determine its corresponding marginal revenue curve with certainty. Also it is assumed that a monopolist knows the costs of its input factors, since it is the only buyer (monopsony); it can therefore make the profit maximizing decisions. A monopolistic competitor on the other hand acts as if it knows its demand curve therefore it can also make profit maximizing decisions basing on the assumed demand and assumed MR curves. Finally we looked at Oligopoly market and we saw that there are several firms producing closely related but differentiated commodities. Oligopoly firms advertise heavily and persuasively. Another key characteristics of Oligopoly firms is market uncertainty which makes firm fail to know its true demand curve hence fail to set profit maximizing price and out put levels. We also saw that, unlike under other market structures, Oligopoly firms may not change their equilibrium price and out put levels when costs change slightly.

 Review Questions
1.	1. Explain the underlying assumptions of a perfectly competitive market structure.
2.	
(a)	Briefly explain why a demand curve of a perfectly competitive firm is perfectly elastic.
(b)	Show that the demand curve of a perfectly competitive firm is also its Marginal revenue curve and also its Average revenue curve.

3.	In the short-run, a perfectly competitive firm can make either profits or losses, elaborate.

4.	Explain how firms under perfect competition attain long-run equilibrium when initially;
(i)	They are making profits.
(ii)	They are making losses.
5.	Using a clear diagram, explain how the supply curve of a firm is derived. (b).Justify your answer in (a) above using a mathematical derivation.
6.	Mathematically derive the;
a)	Short-run supply curve of a perfectly competitive firm,
b)	Long-run supply curve of a perfectly competitive firm.
7.	Clearly explain the short-run and long-run equilibrium situations of a perfectly competitive firm.
8.	Using clear diagrams explain the process to long-run equilibrium of a perfectly-competitive firm that makes losses in the short-run.
9.	The process to long-run equilibrium for a perfectly competitive firm is influenced by the short-run equilibrium situation. Elaborate.
10.	
1.	What are the underlying assumptions of the monopoly market structure?
2.	Briefly explain the sources of the monopoly power.
11.	Explain why the demand curve of a monopolist is downward sloped.
12.	Clearly explain the relationship between the demand curve and marginal revenue curve of a monopoly firm. (Hint; use calculus).
13.	 Derive and comment on the relationship between Marginal revenue, price and price elasticity of demand under monopoly.
14.	Describe the short-run equilibrium of a monopolist.
15.	In the short-run, a monopolist may not necessarily produce at optimal, elaborate.
16.	A monopolist allows less consumer’s surplus than a perfect competitor elaborate.
17.	Consumers are more sovereign under perfect competition than under monopoly, elaborate.
18.	In the long-run, consumers are better off when dealing with a perfect competitor than when dealing with a monopolist.
19.	
a.	What is price discrimination and what are the different forms?
b.	State the conditions necessary for price discrimination.
c.	What are the advantages and disadvantages of price discrimination?
20.	Using a single diagram, compare and contrast the long-run equilibrium situations of a monopolist with that of a perfect competitor.
21.	During price discrimination, the monopolist gains hut the consumer losses, elaborate.
22.	Outline the underlying assumptions of a monopolistically competitive market structure.
23.	Describe the short-run equilibrium situations of a monopolistically competitive firm.
24.	Describe how a monopolistically competitive firm acquires long-run equilibrium.
25.	
a)	Outline the characteristics of an Oligopoly market.
b)	Distinguish between non-collusive and collusive oligopoly models.
26.	Describe how the kinked demand curve of an oligopoly firm is derived and explain why price tends to be stable in oligopoly markets.

Unit 9
Pricing of Factors of Production

9.1 	Introduction
In the previous chapter, we talked about price and out-put determination in different markets. The major emphasis was output. In this lecture however, we shall discuss the pricing of a factor input that is used to produce an output. In a competitive market, factor prices are determined in the market under the forces of demand and supply, just like commodity prices are determined. There are several factors inputs, both tangible and intangible. Traditional microeconomics however, classifies the inputs into; land, labour, capital and entrepreneurship as the major groups. Their respective prices are; rent, wages, interest and profits. We shall assume that the pricing mechanism of these factors is the same. So a single theory shall be used in the determination of the price of a factor input. This shall then be applicable to all factors of production. We shall consider labour as the factor input that shall then act as a representative factor input. We shall specifically look at the demand and supply of labour hence state the equilibrium condition for a factor input. The demand for labour and supply of labour shall be generalized into demand for productive factors and supply of productive factors. 

9.2	Factor Pricing in Perfectly Competitive Markets
In perfectly competitive inputs market, factors are paid the Value of their Marginal Physical Product (VMPP), The price of a factor is determined by its total demand and supply schedules. Factors of production include: land, labour, capital, entrepreneurship, and many others. In our discussion we shall look at labour as the variable factor, however the analysis can be extended or applied to any other factor input say land. When deriving the demand for labour (factor) in a perfectly competitive market we assume the following;

•	A single commodity X is produced in a perfectly competitive market hence its price is given for all firms in the market.
•	The goal of the firm is profit maximization.
•	There is a single variable factor labour whose market is perfectly competitive hence the price of labour service (wage rate), we is given (fixed) for all firms. This implies that the supply of labour for individual firms is perfectly elastic, (see figure 10.1).
•	Technology is given and the relevant section of the production function is the upward sloping portion. 

Figure 10.1: Supply Curve of Labour of an Individual Firm 

	Wage rate

                          We	                                          SL

	0
	Quantity of Labour 

Recll from production theory that the slope of the production function is the Marginal Product of labour or the Marginal Physical Product of labour (MPPL). MPPL declines at higher levels of employment due to the law of variable factor proportion. multiplying MPPL at each level of employment by the given output price (Px) we obtain what is known as the Value of Marginal Product (VMPL.). That is; 

		VMPL = Px. MPPL.

VMPL shows the value of the output produced by the additional unit of labour employed. 

Figure 10.2: Value of Marginal Physical Product Curve

	VMPL
	MPL

	VMPL
	MPL
	0
	Quantity of Labour		

Since the firm is assumed to be a profit maximizer, it will hire as many factor inputs as possible as long as it adds more to total revenue than to total cost. So, the firm will hire a resource up to the point Le, where the last unit of the factor or resource contributes as much as total cost (TC) as to total revenue (TR), see figure 10.3. Therefore, the condition for equilibrium of the profit maximizer in the labour market is; 

	MCL  =  VMPL.

Figure 10.3: The Demand Curve of Labour by a Firm

            Wage rate
VMPL

                          W1		SL1 = MCL1
                          We		SL = MCL

	W2	SL2 = MCL2
                                                                         VMPL

	L1 Le L2                          Quantity of Labour 

Where;	 
SL 		=	Supply of labour
MCL 		=	Marginal Cost of Labour
W		=	 wage rate
VMPL 		= 	Value of marginal physical product of labour.

The equilibrium point is denoted by point e where Le units of labour are employed at wage rate We. At levels of labour less than Le, each unit of labour costs less than the value of its product (i.e. VMPL> W), so it benefits the firm by having more workers. On the other hand, for labour levels higher than Le each additional unit of labour adds more to total cost than to total revenue (i.e. VMPL < W), hence profits are reduced so it pays the firm more if it reduces the amount of labour.. Equilibrium will be attained when VMPL = W i.e. at point e.

Suppose that market wage for labour is raised to W1, labour demand would fall to L1. Similarly if the wage rate falls to W2 the firm will maximize its profits by increasing its employment to L2, it then follows that, the demand curve of a firm for a single variable factor is also its VMPL.

From the above graphical exposition we can draw a sketch of VMPL and SL curves.

Figure 10.4:  Factor Market Equilibrium
            
Wage rate

	VMPL

                       We	SL = MCL

                           VMPL = DL
                         0                                      
                                                                         Le                  Quantity of Labour 

The supply curve of labour (SL = W = MC) is a straight line passing through a given wage rate. The two curves (i.e. demand for labour DL = VMPL and supply for labour SL = W = MCL) meet at a point which defines the labour demand equilibrium point. At that equilibrium point, the profit of the firm is maximized. 

9.3  The Supply of Labour by an Individual Worker 
An individual supply curve is upward sloping showing that at higher wage rate the individual is willing to supply more labour (i.e. work more hours). However, at some higher wage rate the hours offered for work may decline. A further wage rate increase, the hours supplied for work decline further more. This pattern of response to higher wage rate produces a backward bending supply curve of labour. 

Figure 10.5: Supply Curve of Labour by an Individual

	Wage rate
	SL1

	WT

	W2

	W1

	0
	L1       L2    LT		Labour input 

From the diagram, before wage rate WT, increase in wage rates create an incentive for increased supply of labour; however above WT higher wage rates create a disincentive for long hours of work. The reason for this behaviour is that the longer working hours imply less leisure activities. So beyond a certain level of wage rate, the supply of labour decreases as the worker now prefers to spend his income on more leisure activities than acquiring more income. 

Another reason for the existence of the back-ward bending supply curve is the existence of target workers i.e. workers who aim at acquiring a certain objective or target thereafter they resign from work; this is common with labour from low income countries. 

9.4  The Market Supply Curve of Labour  
Although the supply curve of labour by a single individual may be backward bending, there is a general agreement by economist that the market (aggregate) supply curve of labour which is a horizontal summation of all the individual supply curves, is upward sloping especially in the long run as shown in figure 10.6.

Figure 10.6: The Market Supply Curve of Labour 

	Wage rate

	SLM

	0
	Labour input 	

This is so mainly because of the following; 
1.	Young people will be attracted to the market where the wages are high. 
2.	The older workers may undertake retraining and change jobs if the wage incentive is strong enough.

However, other economists maintain that the backward bending of the supply curve of labour may be typical in most markets of the rich nations. Because of higher standards of living, people (workers) demand for more holidays, longer vacation, shorter weeks and fewer hours per working day rather than demanding for higher wages.

Summary
In this lecture, we have looked at how factor inputs are priced. We considered labour as a representative input. We noted that the condition for equilibrium factor employment is the point where the demand curve for a factor meets the supply curve. At that point the price of the factor (wage rate) equals the value of the marginal physical product of the factor. We also saw that the individual supply curve of labour bends to the left at higher wages due to target workers while the market supply curve which is a summation of individual supply curves, is upward sloped.

 Review Questions
1.	Distinguish between the individual and market supply curves of labour.
2.	Why is the individual supply curve of labour backward bending while the market supply curve is not?
3.	Describe the equilibrium condition for a factor employment.
4.	Given that the price of a commodity is $ 10, and that the wage rate is $300, using the following information.
Labour 	0	1	2	3	4	5	6	7	8	9	10	
Output 	1	100	1500	1700	1800	1850	1880	1900	1910	1900	1850	

Derive;
i)	The marginal product schedule,
ii)	Derive the valve of marginal product schedule,
iii)	Determine the equilibrium labour employment level and hence the equilibrium out put level,
iv)	Obtain the total cost schedule,
v)	Obtain the total revenue schedule,
vi)	Obtain the profit level,
vii)	Determine the profit maximization out put level,

Reading Materials 
Bade, Robin; Michael Parkin (2001). Foundations of Microeconomics. Addison Wesley Paperback 1st Edition.
Baumol, W.J (1999). Economic Theory and Operations Analysis, (3rd Ed.), Prentice Hall.
Baumol, W.J and Blinder, A.A. (1991) Economics Principles and Policy, Harcourt Brace Jovanovich San Diego.
Begg, D. and Fisher, S. and Dornbusch, R. (1991), Economics. 
Colander, David. (2008). Microeconomics. McGraw-Hill Paperback, 7th Edition
Craven, J. (1990), Introduction to Economics; An integrated approach to Principles, Blackwell, Cambridge.
Dunne, Timothy, J. Bradford Jensen, and Mark J. Roberts (2009). Producer Dynamics: New Evidence from Micro Data. University of Chicago Press.
Dwived D. N, Principles of Economics, Karyan Publishers, New Delhi.
Eaton, B. Curtis; Eaton, Diane F.; and Douglas W. Allen. (2002). Microeconomics. Prentice Hall, 5th Edition.
Hyman, D.N. (1992), Microeconomics, 2nd ed. IRWIN Boston.
Lipsey R.G. (1989), An Introduction to Positive Economics.
Macmillan Publishing Co. Hongkong.
Mirrot / Mosby College Publishing St. Louis. 
Truett, J.J. and D.M. (1987), Microeconomics Times
Truett, L.J. and Truent, D.M. (1987), Economics.