UNIT ONE
THEORY OF UTILITY AND PREFERENCES
1.1. Definitions and Approaches to Utility
Utility is the power of product to satisfy the human want. It is also defined as the satisfaction a
consumer derives from the consumption of a commodity.
Here, the concept of satisfaction is not what you get after consumption of a commodity, rather
what you expect to get before actually consuming the commodity. Thus, when you decide to buy
some good/service, you predicts (pre calculate in your mind) how much the good will satisfy you
when consumed- that expected satisfaction is what is called utility.
To analyze the behavior of consumer we have to make an important assumption that each
consumer has exact and full (perfect) knowledge of all information relevant to his consumption
decisions:

Knowledge of the goods and services available

Their technical capacity to satisfy his wants

Knowledge of market prices

Knowledge of his money income
Consumers, as an objective, seek to maximize the satisfaction or utility from the consumption of
goods and services for given money income- what economists refer as rationality of consumers.
The complete list of these goods and services is the consumption bundle. To achieve the
maximize their utility, consumers must be able to compare different consumption bundles
according to their desirability. Regarding the comparison, there are two different approaches:
1.2. Cardinal utility approach
According to this approach, it is possible to measure the amount of satisfaction consumer derives
from consuming a good and hence utility can be expressed in cardinal numbers (1, 2, 3….). The
unit of measurement is referred as utils. Thus, a consumer will choose among consumption
bundiles by comparing the number of utility each bundle yields.
1
1.2.1 Assumptions of cardinal utility approach
As part of their theory, cardinal theorists make some assumptions and are discussed as follows
1. Rationality - the consumer is assumed to be rational in a sense that he/she aims at the
maximization of his/her utility subject to the constraints imposed by his/her income.
2. The cardinal measurability of utility - the exponent of cardinal utility analysis hold that
utility is measurable and quantifiable entity. Thus, a person can say that he drives utility
equals to X utils from consumption of good A, where X is a set of cardinal numbers (1, 2,
3…..,n)
3. The hypothesis of independent utilities - the utility which a consumer derives from a good
is the function of the quantity of that good only. On this assumption, the total utility
which a person gets from the whole collection of goods purchased by him is simply the
total sum of the separate utilities of the goods. This is to say that utility is additive.
I, e. U = f (X1, X2… Xn).
4. Constancy of the marginal utility of money; while the marginal utility analysis assumes
the marginal utility of a commodity diminishes as more of them are purchased or
consumed, the marginal utility obtained from one unit addition in money results in equal
increment in satisfaction (utility) to the consumer.
5. Diminishing marginal utility (DMU):- the additional satisfaction a consu```mer derivers
from consuming one more unit of a commodity diminishes as the consumer acquires more
and more of it.
1.2.2 Total utility and marginal utility
Total utility (TU) - is the total satisfaction a consumer gets from consuming commodities. It is
the summation of individual satisfaction of all units of a commodities consumed at a given time.
If, for example, a consumer consumes ten units of banana, the total utility will be the sum of
individual utilities the consumer derives from each of the ten bananas.
Suppose a consumer eats five orange and gets X amount of satisfaction, this is called total utility.
Suppose also that he consume an extra orange , the extra satisfaction he gets from consuming
this orange is called marginal utility of the six orange.
2
Marginal utility (MU)-is the extra or additional satisfaction a consumer drives from consuming
an additional unit of the product. Similarly, marginal utility is change in total utility resulting
from the consumption of one more unit of product. On the above example, if the consumer
consumes one additional banana (11th), the amount of satisfaction he/she get is considered as the
marginal utility of the eleventh banana.
Mathematically: MU = dTU/dQ
Where dTU implies change in the total utility and
dQ – change in the amount consumed
As shown on the following table, marginal utility is determined by the amount of utils added to
the total utility by consuming one more unit of avocado. For instance, the second unit of avocado
added six units of satisfaction to the total. And the total utility at this consumption level is 14-the
sum of utilities derived from the first and second units.
Quantity of avocado consumed per Total
Marginal
day
utility(utils)
utility(utils)
0
0
-
1
8
8
2
14
6
3
18
4
4
21
3
6
21
0
7
19
-2
8
14
-5
Table 1.1: TU, MU and diminishing marginal utility
1.2.3 The law of diminishing marginal utility
It states that marginal utility of a product diminishes as a consumer consumes more and more of
the product at given time period. In other word, as a consumer takes more unit of a good, the
extra utility or satisfaction that he drives from an extra unit of the good goes on falling.
3
Consider the above table again-when the consumer consumes the first avocado, he gets 8 utils of
satisfaction, which is MU of that avocado. The extra utility falls to 6 as he consumed the second
unit and further falls to 3 for the third unit. This implies that the additional unit of avocado yields
the consumer less satisfaction than the avocado consumed before it.
From the figure below we can observe that MU remains decreasing and positive up to the 6th
Avocado. For the sixth avocado, the addition to total satisfaction is zero. It implies that the sixth
avocado does not add any satisfaction for the consumer. MU becomes negative after 6 th unit of
avocado. For example, excess consumption of avocado may result in vomiting which may get the
individual unhealthy.
TU
21
14
TU
8
Q
MU
8
6
0
Q
1
2
6
MU
Figure 1.1: total and marginal utility
The relationship between TU and MU
When MU decrease but remains positive, TU is increasing- positive
When MU assumed a zero value, TU will be at a maximum level
When MU begins to assume a negative value, TU starts to decline.
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1.2.4 Consumer’s Equilibrium in Cardinal Approach
Consumer equilibrium is explained by the principle of equi-marginal utility. The law of equimarginal utility state that the consumer will distribute his money income between the goods in
such a way that the utility derived from the last birr spent on each good is the same. This
indicates how a consumer allocates his money income among various goods, i.e. his equilibrium
position.
A consumer consuming only one commodity, X, given his income level (I) will be at equilibrium
level of consumption when:
If
the consumer can increase his welfare (utility) by purchasing more of good X.
If
the consumer can increase his welfare by decreasing consumption of good X. That
is he will be better off if he reduces his consumption of good X. Thus, consumer will be at
equilibrium when the additional satisfaction obtained from a good is equal to the price of the
good, and if all of his income is spent for consumption of the good.
Suppose there are two goods X and Y on which a consumer has to spend a given income. The
consumer‟s behavior will be governed by two factors; first the marginal utility of the good;
second the price of the two goods. Suppose also that the prices of the two goods are given for the
consumer. The law of equi- marginal utility states the consumer will distribute his money income
between the goods in such a way that the utility derived from the last birr spent on each good is
the same. The law of equi-marginal utility can therefore be stated thus as; the consumer will
spend his money income on different goods in such a way that marginal utility of money
expenditure of each good is equal. That is, consumer is in equilibrium in respect of the purchases
of two goods X and Y when;
1)
2)
=
and
Px X+ PyY = I
Table 1.2 Marginal utility of good x and y and marginal utility of money expenditure
Let the price of goods x and y be birr 2 and 3 respectively. Suppose a consumer has money
income of birr 24 to spend on the two goods.
5
Unit
MUX
MUY
MUX/PX
MUY/PY
1
20
24
10
8
2
18
21
9
7
3
16
18
8
6
4
14
15
7
5
5
12
9
6
3
6
10
3
5
1
Table 1.2 consumers Equilibrium
From the table, it is clear that MUX/ PX is equal to 5 utils when the consumer purchase 6 unit of
good x and MUY/PY is equal to 5 utile when the consumer purchase 4 unit of good y. therefore
the consumer is on the equilibrium when he is buying 6 unit of good x and 4 unit of good and
will be spending (
2
). Thus in the equilibrium position where he
maximizes his utility;
=
10/2=15/3=5
Generally, extending the above for many commodity cases if consumer consumes “n” number of
goods: thus optimum of the consumer will be:
=
and PxX+PyY …+PnN=I
A rational and utility maximizing consumer consumes commodities according to their order of
utilities. He/she switches his/her expenditure from one good to another according to their
marginal utility. He/she continues to switch until he/she reaches the stage where marginal utility
of each commodity per unit of expenditure is the same.
1.2.5 Derivation of the Demand Curve of the Consumer
The derivation of demand is based on the axiom of diminishing marginal utility. The MU of
commodity X is depicted by a line with a negative slope which is the slope of total utility
function, U =f(qx). As successively increasing quantities of X are consumed, the total utility
increases but at a decreasing rate (recall the assumption of DMU), reaches a maximum at
quantity and then starts declining. Accordingly, the MUx declines continuously and becomes
negative beyond after TU reaches its maximum.
6
MUx = slope of TUx = dTU
dqx
Thus it can be shown that the demand curve for commodity X is identical to the positive segment
of the MUx curve. For example, at Q1 the MU is MU1 which is equal to P1 at the optimum point.
Hence at P1 the consumer demands Q1 quantity. Similarly at Q2 the marginal utility is MU2
which is equal to P2. Hence at P2 the consumer demands Q2 and so on. This forms the demand
curve for commodity Q. As negative price do not make sense in economics, the negative potion
of MUx does not form part of the demand curve.
P
P1
a
b
P2
P3
c
MUx
P1
P1
P2
P3
Demand curve
Q
Q1
Q2
Q3
Figure 1.3 Derivation of Demand Curve
The demand curve is simply the graphical representation of the relationship between price and
quantity demanded.
CRITIQUES OF THE CARDINAL APPROCH
7
1) The satisfaction derived from the various commodities cannot be measured objectively.
The cardinality of the utility is extremely doubtful.
2) The assumption of constant MU of money is unrealistic because as income changes the
MU of money also changes.
1.3. Ordinal Utility Approach
Unlike the cardinal approach which is based on the measurability of utility, this approach
emphasizes that consumers rank their preferences in order of their desirability, but can‟t measure
in terms of cardinal numbers. A given consumer ranks different products according to his/her
expectation and prefers one good to the other. So the logic would be- preferring one good to the
other than assigning specific numbers as the measure of the satisfaction that is believed to be
derived.
1.3.1 Assumptions of ordinal utility theory
The following are working assumptions by ordinal utility theorists
1. The consumers are assumed to be rational- they aim at the maximization of their utility,
given their income and market prices.
2. Utility is ordinal- it is assumed that consumers can rank their preferences according to the
satisfaction of each bundle. They need not know precisely the amount of satisfaction. It
suffices that they express their preference for the various bundles of commodities.
3. The total utility of the consumer depends on the quantities of the commodities consumed
U = f(q1, q2,…, qn)
4. For any two consumption bundles A and B, the consumers are able to determine the
bundle that provides the most satisfaction:

A is preferred to B if it provides more satisfaction than B. Conversely B is preferred to
A if it provides more satisfaction than A.

If both bundles provide equal level of satisfaction the consumer would be indifferent
between the two bundles.
5. Preference is transitive- if A is preferred to B and B is preferred to C, then A is preferred
to C. Similarly if A is indifferent to B and B is indifferent to C, then A is indifferent to C.
Utility functions
8
It is a preference function ordering consumer‟s desire to consume differing amount of
commodities. The use of utility functions facilitates the analysis of consumer behavior. Utility
functions provide ordinal measurement of the utility provided by consumption bundles, i.e., the
particular values assigned to consumption bundles do not have significance on their own right.
They are simply used for the purpose of ranking different consumption bundles. For example in a
utility function given by: U = XY
Utility is the product of the quantities of X and Y consumed by consumers. In this case the
consumer derives 100 units of utility from a bundle consisting of 10 units of X and 10 units of Y.
And he/she is indifferent between a bundle, which consists of 1 unit of X and 100 units of Y and
10 units of X and 10 units of Y.
1.3.2 The indifference curve
Consumers‟ preferences are such that they choose the best things they can afford. Consumers
have consumption bundle which represents the complete list of the goods they prefer.
These consumption bundles are represented by (x , y), where x represents the good of our
particular interest and y all other goods. This enables us to focus on the tradeoff between one
good and everything else. Consumers can rank these bundles according to their desirability.
In a consumer choice problem involving two consumption bundles (x1 , x2) and (y1 , y2), if the
individual:

Always prefers the former bundle to the later, we say (x1 , x2) is preferred to (y1 , y2).

Is equal satisfaction of the consumer with both bundles, i.e. the consumer is indifferent.
An indifference curve is a locus of points- particular combinations or bundles of goods- in a
commodity space, which yield the same utility to the consumer, so that he/she is indifferent
between the different consumption bundles.
If the utility function is given by U(X1, X2,…, Xn), where X1 is the amount of good 1 consumed,
X2 the amount of good 2 consumed, and so on, then an indifference curve is defined as the set of
all consumption bundles (X1, …, Xn) that satisfy the equation U(X1, X2, …, Xn) = C, where C is
the constant level of utility for that indifference curve.
9
An indifference map: it shows all the indifference curves, which rank the preferences of the
consumer. Combinations of goods situated on an indifference curve yield the same utility.
Combinations of goods lying on a higher indifference curve yield higher level of utility and are
proffered. Combinations of goods on a lower indifference curve yield a lower utility. An
indifference map is generated by choosing different values for C in the expression U(X1, X2, …,
Xn) = C.
y
y
III
II
I
0
x
0
Indifference curve
x
Indifference map
Figure 1.5 Indifference Curve and Map
Example
Assume that a consumer‟s utility function is given as U = XY. A consumption bundle with 6
units of X and 10 units of Y and a bundle with 12 units of X and 5 units of Y yield the same level
of satisfaction (60) to the consumer, therefore, lie on the same indifference curve. A bundle with
8 units of X and 8 units of Y is, however, preferred to both bundles because it yields a higher
level of satisfaction, therefore, lie on a higher indifference curve.
Characteristics of indifference curves
1. Consumers can compare any two bundles in the commodity space and decide that he/she
prefers one of them or is indifferent between them. Therefore there is an indifference curve
passing through each point in the commodity space.
10
2. An indifference curve has negative slope, which denotes that if the quantity of one
commodity (y) decreases, the quantity of the other (x) must increase, if the consumer is to
stay on the same level of satisfaction.
3. The further away from the origin an indifference curve lies, the higher the level of utility it
denotes: bundles of goods on a higher indifference curve are preferred by the rational
consumer.
4. Indifference curves do not intersect. If they did, the point of their intersection would imply
two different level of satisfaction, which is impossible.
Qy
a
d
b
c
e
0
Qx
Figure 1.6 Non-intersection of indifference curves
On the figure above, the two indifference curves intersect at point b, which implies the same
level of utility by both curves. However, the two indifference curves yield different utility at the
other points on the curve (take points a and d) which is inconsistency and hence it is impossible
for two indifferent curves to cross each other.
5. Indifference curves are convex to the origin. This implies that the slope of an indifference
curve decreases (in absolute terms) as we move along the curve from the left downwards to
the right. This is due to scarcity principle. That is, as we go down the curve, the amount of
good X increases while that of good Y decreases which gets the consumer to sacrifice only
smaller amount of good Y to get additional unit of good X.
Apart from the convex indifference curve, we have other types of indifference curves though the
previous one is preferable in analysis.
 Linear indifference curves – strait line indifference curves. These indifference curves
shows the perfect substitutability of the two goods so that we can only consume one good
11
leaving the other. The slope of the curves are constant implying that the two goods
substitute each other at a constant rate... (Draw the graph).
 Right angled indifference curves – this is the direct opposite of linear indifference curve
and hence the two goods are perfect compliments. The optimal combination only possible
at one point on the curve (at a point of kink/right angle)… (Draw the graph).
Marginal rate of substitution
The marginal rate of substitution of x for y is defined as the number of units of commodity y that
must be given up in exchange for an extra unit of commodity of x so that the consumer maintains
the same level of satisfaction. It is measured by the slope of indifference curve. As we move
from left to right on an indifference curve, the marginal rate of substitution decreases in absolute
value; this is referred to as the decreasing marginal rate of substitution. This implies that the
number of units of commodity y that the consumer is willing to sacrifice for additional unit of
commodity x declines as the quantity of x increases.
Slope of an
indifference
curve
=
dy
= MRSx, y
dx
The concept of MU is implicit in the definition of MRS, since MRS is defined by the ratio of
MRs of the commodities involved. MRS x , y 
MU y
MU x
or MRS y , x 
MU y
MU x
Example
Let us say that utility function is given by:
U = 3X + Y.
To calculate Marginal rate of substitution, we use: MRS[x,y] =
MUx = 3 and MUy = 1
MRS[x,y]
=
3/1 = 3
This implies that if we increase the consumption of good X by one unit, we should
decrease the consumption of good Y by 3 units in order to get the same level of utility.
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1.3.3 The Budget Constraint
We said that consumer‟s objective is to maximize utility- acquiring as much as utility they can
and we know that utility depends on the amount of goods consumed. If so, why consumers
acquire an infinitive amount of satisfaction by consuming very large amount of the goods they
consume? It is because consumers are limited by the income they have.
The consumer‟s income sets an upper limit to the quantities of goods and services that the
consumer can purchase. The budget line is the set of consumptions bundles that can be purchased
if the entire money income is spent. The slope of the budget line is the ratio of the prices of the
commodities involved.
Y = P1 X1 + P2 X2
X2 
the budget equation
P
1
Y  1 X1
P2
P2
X2
Y/P2
Budget line
Budget set
0
Y/P1
X1
Figure 1.7 Budget Line
The shaded area represents the different feasible combination of the two goods that can be
purchased for given income Y. This area is referred to as the budget set the consumer. The
boundary of the budget set is the budget constraint (budget line) facing the consumer.
The budget set indicates that the total expenditure by the consumer cannot exceed the total
income of the consumer for given prices of the commodities.
P1 X1 + P2 X2  Y
Properties of the budget line

Points on the budget line indicate consumption bundles that use up the household‟s entire
income.
13

Points below the budget line indicate combinations of commodities that cost less than the
household‟s income.

Points above the budget line indicate combinations of commodities that cost more than
the household‟s income. Such points imply unattainable utility level for a given level of
income.
Shifts in the budget line
The change in income of the consumer and/or the price/s of the goods, shifts the budget line.
Changes in money income
Increase in income enables the consumer to purchase more of good 1, more of good 2 or more of
both goods. Given the budget equation
X2 =
P
1
Y  1 X1
P2
P2
Increase in income changes the vertical intercept and the horizontal intercept. It does not affect
the slope of the budget line (the ratio of prices). As a result change in consumer‟s income causes
an outward shift in the budget line in a parallel fusion. A decrease in income, on the other hand,
causes a parallel shift to the left of the budget line.
X2
Y*/P2
Y/P2
Slope = -
0
P1
P2
Y*/P1
Y/P1 X1
Figure 1.8 shift of the Budget Line by change of Income
Example
Suppose a consumer has 280 birr to buy two goods, X1 and X2. Given the price per unit of X1
and X2 to be 2 and 5 birr respectively, the budget equation will be written as: 2X + 5Y = 280
Y = 56 – 0.4X………..solving for Y
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The slope of budget line is 0.4
The vertical intercept (X=O) is Y = 56 and the horizontal intercept (Y=0) is X = 140
Suppose a change in income to 350 for the previous levels of commodity prices. With the new
income, we have: 2X + 5Y = 350
Y = 70 – 0.4X………..solving for Y.
The slope of budget line is 0.4
The vertical intercept is Y = 70 and the horizontal intercept is x = 175.
These show that, a change in income will affect both vertical and horizontal intercepts, but leave
the slope unchanged. A change in income will not change consumption ratio of the two goods.
Changes in Price
The change in price could be proportional change in both prices (change by the same percentage)
or relative change in prices (change by different percentages).
Proportional Change in all Prices
Proportional rise in the prices of both goods (good 1 and good 2) will reduce the total quantity of
the two goods that the consumer can buy for a given income. For example if the prices of the two
goods under consideration doubles, this would halve the quantities of the two goods purchased.
Its effect would be the same as to that of reducing the consumer income by half. This would
cause a parallel shift in the budget line. Since the change in price is proportionate, there will be
no change in the slope of the budget line rather a change in intercepts. Similarly, a proportionate
fall in price shifts the budget line to the right.
X2
Y/P”2
Y/P2
Y/P’2
0
Y/P’1 Y/P1 Y/P”2 X1
Figure 2.9 shift of the Budget Line by proportional change in price
.
15
Example
Take the income and prices in example--- and assume further the consumer consumes 65 units of
X and 50 units of Y. Thus, 65(2) + 50(5) = 280.
Suppose, the price of both goods doubles and the new Px and Py would be 4 and 10 respectively.
Now, with the new prices, the consumer can consume 32.5 units of X and 25 units of Y with the
given level of income, which is the same as the effect of decrease in income by half. Here, the
slope has not changed (-2/5 = -4/10 = -0.4).
Changes in Relative Prices
A change in relative price can occur, and often does, as a result of changes in only one of the
prices or changes in both prices in different proportions.
First if we assume the price of good 1 changes (increase) with price 2 and income remaining
fixed. This would make the slope of the budget line steeper. The vertical intercept does not
 P1
.
P2
1
change, but the horizontal intercept will change. The resulting new slope would be
X2
Y/P2
Slope= -P’1/P2
Slope= -P1/P2
0
Y/P’1
Y/P1
X1
Figure 1.10 Inward Rotation of the Budget Line
From the above figure, we can see that the horizontal intercept (Y=0) has decreased from Y/P1
to Y/P2 implying that the consumer can now buy lower quantity of the good X if he wants to
consume the good only for the given level of income.
1.3.4 The consumer’s equilibrium in Ordinal Approach
The consumer is in equilibrium when he maximizes his utility, given his income and the market
prices. For the consumer to maximize its utility two conditions must be satisfied.
16
1. The marginal rate of substitution (the slope of indifference curve) be equal to the ratio of
commodity prices (the slope of budget constraint)necessity condition
MRS x , y 
MU x Px

MU y Py
2. The indifference curve must be convex to the origin. This condition is satisfied by the
axiom of diminishing marginal rate of substitution, which states that the slope of the
indifference curve declines as we move from left to right.
Given an indifference map and the consumer‟s budget constraint, the consumer‟s equilibrium is
defined by the tangency of the budget with the highest possible indifference curve (at point a in
the following figure). At point a, the budget line AB and the highest attainable indifference curve
(II) are tangent. If we take point d, it is associated with higher utility compared to point a, but
unattainable for the given level of income. Likewise, though point c on indifference curve I is
attainable, it gives lower utility compared to II and thus not equilibrium point.
At this tangency (point a), the slope of the indifference curve is equal to the slope of the budget
line, i.e., MRSxy = MUx/MUy = Px/Py.
y
A
d
y*
e
III
c
II
I
0
x*
B
x
Figure 1.11 Consumer Equilibrium
The consumer maximizes his/her utility by consuming x* amount of good x and y* amount of
good y. Since the indifference curve is convex the second-order condition is also fulfilled.
Mathematical derivation of equilibrium:
Assume there are n commodities with prices p1, p2, …, pn. The consumer‟s money income is Y.
Maximize
U = f(q1, q2, …, qn)………….the objective function
17
Y = p1q1 + p2q2 + … + pnqn……….the constraint
Subject to
Rewriting the constraint
p1q1 + p2q2 + … + pnqn - Y = 0
Multiplying the constraint by Lagrangian multiplier 
(p1q1 + p2q2 +…+ pnqn - Y) = 0
Forming a composite function
 = U - (p1q1 + p2q2 +…+ pnqn - Y)
First order condition……(first order derivatives with respect to all quantities and Lagrange
multiplier be zero-equating first order derivative of a function with zero, in mathematics, implies
the point at which we the function reaches it minimum or maximum)
 U

 p1  0
q1 q1

U

 p 2  0
q 2 q 2

U

 p n  0
q n q n

 ( p1q1 + p2q2 +…+ pnqn - Y) = 0

From these equations we obtain

 p1
q1

 p 2
q 2

 p n
q n
U
 MU 1 ,
q1
U
U
 MU 2 , …,
 MU n
q 2
q n
18
Substituting

and
solving
for

we
obtain
the
equilibrium
condition:
MU n
MU 1 MU 2

 ... 
p1
p2
pn
In a case where there are only two goods this means
MU x Px

 MRS x , y
MU y Py
The second order condition for maximum requires that the second order partial derivatives of the
function with respect all quantities be negative.
 2  2U

<0
q1 2 q1 2
 2  2U

<0
q n 2 qn2
……………
The second order condition (convexity of indifference curve) is compulsory to find a single
combination of the two goods that maximize our utility. For example, in case of linear
indifference curve, the budget line and the indifference curve overlaps at their tangency and
every points on the graph shows utility maximizing levels of the two goods.
Example
A consumer consuming two commodities X and Y has the following utility function
U  XY  2 X .If the price of the two commodities are 4 and 2 respectively and his/her budget is
birr 60.
a) Find the quantities of good X and Y which will maximize utility.
b) Find the MRS X ,Y at optimum.
Solution
The Lagrange equation will be written as follows:
  XY  2 X   (60  4 X  2Y )

 Y  2   4  0 ……………………….. (1)
X

 X   2  0 …………………………… (2)
Y

 60  4 X  2Y  0 …………………… (3)

19
From equation (1) we get Y  2  4 and from equation (2) we get X  2 .Thus, we can get
that X 
Y 2
1
and equation (2) gives as   X .
2
2
By substituting X 
Y 2
in to equation (2) we get Y  14 and
2
MRS X ,Y 
X  8.
MU X Y  2

X
MU Y
At Y=14 and X=8 we get 2 which equals to the price ratio of the two goods (
PX 4
  2) .
PY
2
The value of MRSxy = 2 shows that the consumer should give up 2 quantities of Y to consume
one more of good X so that he/she remain on the previous level of utility.
We can also find the value of the maximum utility by inserting the utility maximizing levels of
the goods in the utility function.
1.4 Effects of Changes in Income and Prices on Consumer optimum
1.4.1 Changes in money income
The change in income changes the purchasing power of the consumer. Increase in income shifts
the budget line outwards while decrease in income shifts the budget line inward to the left.
M3/Py
Income consumption curve
M2/Py
M1/Py
c
b
a
X
M1/Px M2/Px M3/Px
Figure 1.12 Income Consumption Curve
If we go on increasing income we will have a set of optimum points belonging to each budget
line. As we shift budget line it gives us a curve called income consumption curve (ICC). The
shape and slope of ICC depends on the nature of commodities.
Engle curve: is a curve that shows the relationship between equilibrium quantity and the income
level. It is a derived function of ICC and its slope is the slope of ICC. The slope of Engle curve is
20
positive for normal goods and negative for inferior goods. For luxury goods which are highly
responsive Engle curve is relatively flatter and for necessity goods which are less responsive to
change in income Engle curve is steeper.
Y
M
Y3
M1
Y2
ICC
M2
Y1
Engle Curve
M3
X
X1 X2 X3
X
X1 X2 X3
Figure 1.13 Engle Curve
For each level of income, there will be some optimal choice for ach good. If we keep the price of
the two goods constant (fixed), and focus on what happens to the demand for good X as the level
income changes, we obtain what is known as the Engel curve. By plotting the different quantities
of X at different income levels against their corresponding income, we trace out the Engel curve
for X. The Engel curve may take different shapes depending on the income elasticity the goods
Panel (A) Normal goods
Income
Panel (B) Inferior goods
Income
Necessity
Luxury
X
X
Figure 1.14 Types of Engle curve
1.4.2 Change in price of commodities:
When price of the commodity changes the slope of the budget line and its intercepts will changes under
citrus paribus condition. Generally the change in consumption due to the change in price is known as price effect.
When price of a good (say, X) decreases the budget line becomes flatter i.e move from AM to AN in the fig.
bellow. The optimum choice will change from E1 to E2 and the quantity demanded increases, if we decrease price
of good X further the budget line will be AP and optimum point will shift toE3.The locus of optimum points
21
(E1, E2, E3….) associated with the new budget line formed by reducing price of X keeping price of Y and
Income of the consumer constant gives a curve called price consumption curve.
Price consumption curve (PCC)
A
Figure 1.15 Price Consumption Curve
The total price effect (PE) can be decomposed into substitution effect (SE) and income effect (IE), I.e. PE=SE+IE
Income effect: here means the change in quantity demanded of a good due to the change in real income or
Purchasing Power of the consumer resulted from decrease in price of the good. Because now one of the goods
Becomes cheaper. The Consumer‟s purchasing power increases so that the consumer has left over income to
purchase more.
Substitution effect: shows the change in quantity demanded of a good due to the consumer inherent tenders to
substitute the cheaper from the relatively expensive one. I.e. the consumer buys more of the cheaper and
less of the expensive good. These two effects occur simultaneously but can be decomposed for the purpose of
analysis using compensated budget line. Compensated budget line is an imaginary line that demarcates the
income effect from the total price effect.
22
CHAPTER TWO
CHOICE -INVOLVING RISK AND UNCERTAINTY
2.1. Introduction
So far we have assumed that prices, incomes, and other variables are known with
certainty.
However, many of the choices that people make involve considerable
uncertainty. For example, most people borrow to finance large purchases, such as a house
or a college education, and plan to pay for the purchase out of future income. But for
most of us, future incomes are uncertain. Our earnings can go up or down; we can be
promoted, demoted, or even lose our jobs. Or if we delay buying a house or investing in a
college education, we risk having its price rise in real terms, making it less affordable.
How should we take these uncertainties into account when making major consumption or
investment decisions?
Sometimes we must choose how much risk to bear. What, for example, should you do
with your savings? Should you invest your money in something safe such as a savings
account or something riskier but potentially more lucrative such as the stock market?
Another example is the choice of a job or even a career. Is it better to work for a large,
stable company where job security is good but the chances for advancement are limited,
or to join (or form) a new venture, which offers less job security but more opportunity for
advancement?
To answer questions such as these, we must be able to quantify risk so we can compare
the riskiness of alternative choices. We therefore begin this chapter by discussing
measures of risk. Afterwards, we will examine people's preferences toward risk. (Most
people find risk undesirable, but some people find it more undesirable than others.) Next,
we will see how people can deal with risk.
Sometimes risk can be reduced-by
diversification, by buying insurance or by investing in additional information. In other
situations (e.g., when investing in stocks or bonds), people must choose the amount of
risk they wish to bear.
23
24
To describe risk quantitatively, we need to know all the possible outcomes of a particular
action and the likelihood that each outcome will occur.' Suppose, for example, that you
are considering investing in a company that is exploring for offshore oil. If the
exploration effort is successful, the company's stock will increase from $30 to $40 a
share; if not, it will fall to $20 a share. Thus, there are two possible future outcomes, a
$40 per share price and a $20 per share price.
Probability refers to the likelihood that an outcome will occur. In our example, the
probability that the oil exploration project is successful might be 1/4, and the probability
that it is unsuccessful 3/4. Probability is a difficult concept to formalize because its
interpretation can depend on the nature of the uncertain events and on the beliefs of the
people involved. One objective interpretation of probability relies on the frequency with
which certain events tend to occur. Suppose we know that of the last 100 offshore oil
explorations 25 have succeeded and 75 have failed. Then the probability of success 1/4
is objective because it is based directly on the frequency of similar experiences. But what
if there are no similar past experiences to help measure probability? In these cases
objective measures of probability cannot be deduced, and a more subjective measure is
needed.
Subjective probability is the perception that an outcome will occur. This perception may
be based on a person's judgment or experience, but not necessarily on the frequency with
which a particular outcome has actually occurred in the past. When probabilities are
subjectively determined, different people may attach different probabilities to different
outcomes and thereby-make different choices. For example, if the search for oil were to
take place in an area where no previous searches had ever occurred, I might attach a
higher subjective probability than you to the chance that the project will succeed because
I know more about the project, or because I have a better understanding of the oil
business and can therefore make better use of our common information. Either different
information or different abilities to process the same information can explain why
subjective probabilities vary among individuals.
25
Whatever the interpretation of probability, it is used in calculating two important
measures that help us describe and compare risky choices. One measure tells us the
expected value and the other the variability of the possible outcomes.
2.2. Expected utility
To simplify things, we'll consider the consumption of a single commodity-the
consumer's income, or more appropriately, the market basket that the income can buy.
We assume that consumers know all probabilities, and (for much of this section) that
payoffs are now measured in terms of utility.
Table 2.1a shows how we can describe a woman's preferences toward risk. The level
of utility increases from 10 to 16 to 18, as income increases from $10,000 to $20,000
to $30,000. But marginal utility is diminishing, falling from 10 when income
increases from 0 to $10,000, to 6 when income increases from $10,000 to $20,000,
and "to 2 when income increases from $20,000 to $30,000.
Now suppose she has an income of $15,000 and is considering a new but risky sales
job that will either double her income to $30,000 or cause it to fall to $10,000. Each
possibility has a probability of .5. As table 2.1a shows, the utility level associated
with an income of $10,000 is 10 (at point A), and the utility associated with a level of
income of $30,000 is 18 (at E). The risky job must be compared with the current job,
for which the utility is 13 (at B).
To evaluate the new job, she can calculate the expected value of the resulting income.
Because we are measuring value in terms of the woman's utility, we must calculate the
expected utility E(u) she can obtain. The expected utility is the sum of the utilities
associated with all possible outcomes, weighted by the probability that each outcome
will occur. In this case, expected utility is
+ (1/2)u($30,000=) 0.5(10) +0.5(18) = 14
E(u) = (1/2)u($10,000)
26
The new risky job is thus preferred to the original job because the expected utility of 14 is
greater than the original utility of 13. The old job involved no risk-it guaranteed anincome of $15,000 and a utility level of 13. The new job is risky, but it offers both a
higher expected income ($20,000) and, more important, a higher expected utility. If the
woman wished to increase her expected utility, she would take the risky job.
Table 2.1 Differ in preferences toward risk
combination A
B
C
D
E
Income
10000
15000
16000
20000 30000
Utility
10
13
14
16
Combination A
C
E
Income
10000
20000 30000
Utility
3
8
18
Combination A
C
E
Income
10000
20000 30000
Utility
6
12
16
(a)
(b)
18
(c)
In (a) consumer’s marginal utility diminishes as income increases. The consumer is risk averse because she
would prefer a certain income of $30000 (with a utility of 16) to a gamble with a 0.5 probability of
$10,000 and a 0.5 probability of $30000 (and expected utility of 14). In (b) the consumer is risk loving,
because she would prefer the same gamble (with expected utility of 9.5) to the certain income (with a
utility of 8). Finally, in (c) the consumer is risk neutral and is indifferent between certain events and
uncertain events with the same expected income.
2.3. Risk Choice
People differ in their willingness to bear risk. Some are risk averse, some risk loving, and
some risk neutral. A person who prefers a certain given income to a risky job with the
same expected income is described as being risk averse.(Such a person has a diminishing
marginal utility of income.) Risk aversion is the most common attitude toward risk. To
see that most people are risk adverse most of the time, note the vast number of risks that
29
27
People insure against. Most people not only buy life insurance, health insurance, and car
insurance, but also seek occupations with relatively stable wages.
Table 2.1a applies to a woman who is risk averse. Suppose she can have a certain income
of $20,000, or a job yielding an income of $30,000 with probability .5 and an income of
$10,000 with probability .5 (so that the expected income is $20,000). As we saw, the
expected utility of the uncertain income is 14, an average of the utility at point A (10) and
the utility at E (18), and is shown by C. Now we can compare the expected utility
associated with the risky job to the utility generated if $20,000 were earned without risk.
This utility level, 16, is given by D in table 2.1a. It is clearly greater than the expected
utility associated with the risky job.
A person who is risk neutral is indifferent between a certain income and an uncertain
income with the same expected value. In table 2.1c the utility associated with a job
generating an income of either $10,000 or $30,000 wit$ equal probability is 12, as is the
utility of receiving a certain income of $20,000.
Table 2.1b shows the third possibility-risk loving. In this case the expected utility of an
uncertain income that will be either $10,000 with probability .5 or $30,000 with
probability .5 is higher than the utility associated with a certain income of $20,000.
Numerically,
E(u) = .5u($10,000) + .5u($30,000) = .5(3) + .5(18) = 10.5 >u($20,000) = 8
The primary evidence for risk loving is that many people enjoy gambling.
Some criminologists might describe criminals as risk lovers, especially when a robbery is
committed that has a high prospect of apprehension and punishment. These special cases
aside, few people are risk loving, at least with respect to major purchases or large
amounts of income or wealth.'
28
2.4. Risk Diversification
Suppose that you plan to take a part-time job selling appliances on a commission basis.
You can decide to sell only air conditioners or only heaters, or you can spend half your
time selling each. Of course, you can't be sure how hot or cold the weather will be next
year. How should you apportion your time to minimize the risk involved in the sales job?
The answer is that risk can be minimized by diversification-by allocating your time
toward selling two or more products (whose sales are not closely related), rather than a
single product. Suppose that there is a fifty-fifty chance that it will be a relatively hot
year, and a fifty-fifty chance that it will be cold.
Table 2.2 Income from Sales of Equipment
Hot weather
Cool weather
Air conditioner sales
30000
12000
Heater sales
12000
30000
The above table gives the earnings that you can make selling air conditioners and heaters.
If you sell only air conditioners or only heaters, your actual income will be either $12,000
or $30,000 but your expected income will be $21,000 [.5($30,000) +. .5($12000)]. But
suppose you diversify by dividing your time evenly between the two products. Then your
income will certainly be $21,000, whatever the weather. If the weather is hot, you will
earn $15,000 from air conditioner sales and $6000 from heater sales; if it is cold, you will
earn $6000 from air conditioner sales and $151000 from heater sales. Hence, by
diversifying you eliminate all risk.
Diversification is not always this easy. In our example heater and air conditioner sales
were inversely related-whenever the sales of one were strong, the sales of the other were
weak. But the principle of diversification is a general one. As long as you can allocate
your effort or your investment funds toward a variety of activities whose outcomes are
not closely related, you can eliminate some risk
29
2.5. Risk spreading
Consider the situation of an individual who had $35,000 and faced a .01 probability of a $10,000
loss. Suppose that there were 1000 such individuals. Then, on average, there would be 10 losses
incurred, and thus $100,000 lost each year. Each of the 1000 people would face an expected loss
of .01 times $10,000, or $100 a year. Let us suppose that the probability that any person incurs a
loss doesn‟t affect the probability that any of the others incur losses. That is, let us suppose that
the risks are independent.
Then each individual will have an expected wealth of .99 × $35, 000 +.01×$25, 000 = $34, 900.
But each individual also bears a large amount of risk: each person has a 1 percent probability of
losing $10,000. Suppose that each consumer decides to diversify the risk that he or she faces.
How can they do this? Answer: by selling some of their risk to other individuals. Suppose that
the 1000 consumers decide to insure one another. If anybody incurs the $10,000 loss, each of the
1000 consumers will contribute $10 to that person. This way, the poor person whose house burns
down is compensated for his loss, and the other consumers have the peace of mind that they will
be compensated if that poor soul happens to be them! This is an example of risk spreading: each
consumer spreads his risk over all of the other consumers and thereby reduces the amount of risk
he bears.
Now on the average, 10 houses will burn down a year, so on the average, each of the 1000
individuals will be paying out $100 a year. But this is just on the average. Some years there
might be 12 losses, and other years there might be 8 losses. The probability is very small that an
individual would actually have to pay out more than $200, say, in any one year, but even so, the
risk is there.
But there is even a way to diversify this risk. Suppose that the homeowners agree to pay $100 a
year for certain, whether or not there are any losses. Then they can build up a cash reserve fund
that can be used in those years when there are multiple fires. They are paying $100 a year for
certain, and on average that money will be sufficient to compensate homeowners for fires.
30 | P a g e
UNIT THREE
THE THEORY OF PRODUCTION AND COST
3.1 Theory of Production
3.1.1 Definition and Basic Concepts of Production
Production is the process of using the services of inputs to make goods and services available by
business firms at a given state of technology. Or it is the means creation of utility for sales.
Alternatively, production may be defined as the act of creating those goods/services which have
exchange value for sale (not for personal consumption). Raw materials yield less satisfaction to
the consumer by themselves. In order to get utility from raw materials, first they must be
transformed into output. However, transforming raw materials into final products require factor
inputs such as land, labor, and capital and entrepreneurial ability. Thus, no production
(transforming raw material into output) can take place without the use of inputs. These inputs can
be grouped in to fixed and variable.
Fixed vs variable inputs
Fixed inputs are those inputs whose quantity cannot readily be changed when market conditions
indicate that an immediate change in output is required. In fact no input is ever absolutely fixed,
but may be fixed during an immediate requirement. For example, if the demand for Beer shoots
up suddenly in a week, the brewery factories cannot plant additional machinery over a night to
respond to the increased demand. It takes long time to buy new machineries, to plant them and
use for production. Thus, the quantity of machinery is fixed for some times such as a weak.
Buildings, machineries and managerial personnel are examples of fixed inputs because their
quantity cannot be manipulated easily in short time periods.
On the other hand, Variable inputs are those inputs whose quantity can be changed almost
instantaneously in response to desired changes in output. The best example of variable input is
unskilled labor. In our previous example, if the brewery factory had idle machinery before the
31 | P a g e
market demand shot up, the factory can easily and immediately respond to the market condition
by hiring laborers.
Short run vs. long run
The short run or long run doesn‟t refer to period of time less than or greater than one year. The
time refers to the nature of economic adjustment in the firm to the changing economic
environment. The terms long run and short run do not necessarily refer to specific periods of
time, but to the flexibility the firm has in changing the level of output. In economics, short run
refers to that period of time in which the quantity of at least one input is fixed. For example, if it
requires a firm one year to change the quantities of all the inputs, those time periods below one
year are considered as short run. Long run is that time period (planning horizon) which is
sufficient to change the quantities of all inputs.
3.1.2 Production in the Short Run and in the Long run
A. Production in the Short Run
It is also called with one variable input because there is no fixed input in the long run.
Assumption of short run production analysis
1. Perfect divisibility of inputs and outputs: it implies that factor inputs and outputs are so
divisible that one can hire, for example a fraction of labor, a fraction of manager and we can
produce a fraction of output, such as a fraction of automobile.
2. Limited substitution between inputs: factor inputs can substitute each other up to a certain
point, beyond which they cannot substitute each other
3. Constant technology: level of technology of production available is constant.
Suppose a firm uses two inputs: Capital (which is a fixed input) and labor (which is variable
input). Given the assumptions of short run production, the firm can increase output only by
increasing the amount of labor it uses. Hence, its production function is given by Q = f (L) k
Where Q is the quantity of production (Output)
L is the quantity of labor used, which is variable, and
k is the quantity of capital (which is fixed)
The production function shows different levels of output that the firm can obtain by efficiently
utilizing different units of labor and the fixed capital. In the above short run production function,
32 | P a g e
the quantity of capital is fixed. Thus output can change only when the amount of labor used for
production changes. Hence, Q is a function of L only in the short run.
Total product, Marginal product and Average product
Total product: is the total amount of output that can be produced by efficiently utilizing a
specific combination of labor and capital. The total product curve shows the output produced for
different amounts of the variable input, labor. Here total product will change as the quantity of
the variable factor used changes. An increasing the variable input (while some other inputs are
fixed) can increase the total product only up to a certain point. Initially, as we combine more and
more units of the variable input with the fixed input output continues to increase. But eventually,
increasing the unit of the variable input may not help output increase. Even as we employ more
and more unit of the variable input beyond the carrying capacity of a fixed input, output may
tends to decline.
Marginal Product (MP); is the addition to the total product attributable to the addition of one
unit of the variable input to the production process, other inputs being constant (fixed). The
change in total output resulting from using this additional worker (holding other inputs constant)
is the marginal product of the worker. The marginal product of the variable input (slope of TP),
denoted as MPL and calculated as MPL =
Q
dTP
or MPL 
L
dL
Average Product (AP): is the total output per the unit of the variable input.
APlabour 
totalproduct TP

numberofL
L
Graphing the short run production curves
The following figures show how the TP, MP and AP of the variable (labor) input. As the number
of the labor hired increases (capital being fixed), the TP curve first rises, reaches its maximum
when L3 amount of labor is employed, beyond which it tends to decline. Assuming that this short
run production curve represents a certain car manufacturing industry, it implies that L3 numbers
of workers are required to efficiently run the machineries. If the numbers of workers fall below
L3, the machine is not fully operating, resulting in a fall in TP below TP3. On the other hand,
increasing the number of workers above L3 will do nothing for the production process because
only L3 number of workers can efficiently run the machine. Increasing the number of workers
33 | P a g e
above L3, rather results in lower total product because it results in overcrowded and unfavorable
working environment.
Output
TP
Maximum average
Productivity
0
L1
L2
L3
Labor
Point of diminishing marginal productivity
Point of diminishing average productivity
Output
0
L1
L2
L3
P
Labor
MP
Fig 3.1 Total product, average product and marginal product curves:
MP curve increases until L1 number of labor reaches its maximum at L1, and then it tends to fall.
The MPL is zero at L3 (when the TP is maximal); beyond which its value assumes zero
indicating that each additional worker above L3 tends to create over crowded working condition
and reduces the total product. The AP curve increases up to L2, beyond this level of labor it
continuously declines. The AP curve can be measured by the slope of rays originating from the
origin to a point on the TP curve. For example, the APL at L2 is the ratio of TP2 to L2.
Table 2.1 Hypothetical Production Function with One Variable Input (L)
34 | P a g e
V(Labour)
Q/Week
MPL=∆Q/∆L
APL=Q/L
0
1
2
3
4
5
0
10
30
75
100
120
10
20
45
25
20
0
10
15
25
25
24.7
6
7
8
9
10
130
136
140
140
138
10
6
4
0
-2
21.7
19.5
17.5
15.8
13.8
Notice that the APL increases as the first three units of labor are added to the fixed inputs of K
and R. The maximum APL (maximum efficiency of Labor), given our technology, plant and
natural resources is with the fourth worker. As additional units of labor are added beyond the
fourth worker the output per worker [APL] declines.
The relationship between AP and MP of the variable input
From the above graph we can observe that

when MPL > APL, Slope of APL is positive (APL rises)

When MPL = APL, Slope of APL is zero (APL is at its maximum).

When MPL < APL, Slope of APL is negative (APL falls)
The law of diminishing marginal returns (LDMR)
The LDMR also known as short-run law of production, states that as the use of an input increases
in equal increments (with other inputs being fixed), a point will eventually be reached at which
the resulting additions to output decreases. When the labor input is small (and capital is fixed),
extra labor adds considerably to output, often because workers get the chance to specialize in one
or few tasks. Eventually, however, the LDMR operates: when the number of workers increases
further, some workers will inevitably become ineffective and the MPL falls. It is not because
highly qualified laborers are hired first and the least qualified last rather it results from
limitations on the use of other fixed inputs (e.g. machinery), not from decline in worker quality.
35 | P a g e
The LDMR applies to a given production technology (when the level of technology is fixed).
Over time, however, technological improvements in the production process may allow the entire
total product curve shift upward, so that more output can be produced with the same input.
3
Example: suppose that the production function is given by Q  8L2  L3 then
2
a. Calculate AP and MP function
b. Find the level of L that maximized TP
c. Find the level of L that equate AP and MP
d. Then find the level of L at law of diminishing marginal productivity started to operate.
Solution:
a.
TP
AP 

L
2 3
2
d (8L2  L3 )
L
dTP
2
3  8L  L2 and MP 
3

 16L  2 L2
dL
L
dL
3
8L2 
b. TP will be maximized when its slope (MP) becomes zero
Slope of TP=
dTP d (8L2  2 / 3L3 )

 16L  2L2  0 L (16-2L) =0, L=8 or L=0
dL
dL
Therefore TP will be maximized when the producer employs 8th unit of labor.
c. The MP and AP will be at equality when AP=MP i.e.
8L-2/3L2=16L-2L2 at L=0 or L=6
Since output varies with variation in L, we are restricted with positive level of labor
employment. Therefore AP and MP will be equal at L=6.
d. The law of diminishing marginal productivity starts to operate when MP of labor
becomes maximum. It will exist when the sloe of MP become zero
Slope of MP=
dMP d (16L  2 L2 )

 16  4 L  0 L=4
dL
dL
Therefore the LDMP stared to operate after employment of the 4th labor.
The Stages of Production in the Short Run
The MP of a factor may assume a positive, a negative or zero value. However, basic production
theory concentrates only on the efficient part of the production function, that is, on the range of
output over which the MPL is positive.
36 | P a g e
•
Stage I goes from the origin to the point where the APL is maximum; in this stage the
fixed inputs are underutilized.
•
Stage II goes from the point where the MPL is maximum to the point where MPL is zero;
this stage is the only meaningful and rational stage of production or efficient stage of
production. Hence, the efficient region of production is over that range of employment of
variable input where the marginal product of the variable input is declining but positive.
•
Stage III covers the range over which the MPL is negative. Here the variable input is over
employed while the fixed input is over utilized.
B. Long run Production: Production with two variable inputs
It is a period of time which is sufficient for the firm to change the quantity of all inputs. For the
sake of simplicity, assume that the firm uses two variable inputs (labor & capital). The firm can
now produce its output in a variety of ways by combining different amounts of labor and capital.
With both factors variable, a firm can usually produce a given level of output by using a great
deal of labor and very little capital or a great deal of capital and very little labor or moderate
amount of both. In this section, we will see how a firm can choose among combinations of labor
and capital that generate the same output. To do so, we make the use of isoquant.
Isoquant: is a curve that shows all possible efficient combinations of inputs that can yield
equal level of output. It shows the flexibility that firms have when making production decision:
they can usually obtain a particular output (q) by substituting one input for the other.
Isoquant maps: shows a number of isoquants combined in a single graph. An isoquant map is
another way of describing a production function. Each isoquant represents a different level of
output and the level of out puts increases as we move up and to the right. The following figure
shows isoquants and isoquant map.
37 | P a g e
Capital
3
q3
1
2
1
q2
1
3
6
q1
Labor
Fig 3.2 Isoquant and isoquant map.
Isoquants show the fact that long run production process is very flexible. A firm can produce q1
level of output by using either 3 capital and 1 labor or 2 capital and 3 labor or 1 capital and 6
labor or any other combination of labor and labor on the curve. The set of isoquant curves q1 q2
& q3 are called isoquant map.
Properties of isoquants
Isoquants have almost the same properties as indifference curves. The biggest difference
between them is that output is constant along an isoquant whereas indifference curves hold utility
constant. Most of the properties of isoquants, results from the word „efficient’ in its definition.
1. Isoquants slope down ward. Because isoquants denote efficient combination of inputs that
yield the same output, isoquants always have negative slope. Isoquants can never be
horizontal, vertical or upward sloping. As employment of one factor increases, the
employment of the other factor must decrease to produce the same quantity efficiently.
2. The further an isoquant lays away from the origin, the greater the level of output it
denotes. The more inputs used, more outputs should be obtained if the firm is producing
efficiently. Thus efficiency requires that higher isoquants must denote higher level of output.
3. Isoquants do not cross each other. This is because such intersections are inconsistent with
the definition of isoquants. Consider the following figure.
38 | P a g e
Capital
Q=20
q=50
K*
Labor
L*
Figure 3.3 Non-crossability of Iso-quant curves
This figure shows that the firm can produce at either output level (20 or 50) with the same
combination of labor and capital (L* and K*). The firm must be producing inefficiently if it
produces q = 20, because it could produce q = 50 by the same combination of labor and capital
(L* and K*). Thus, efficiency requires that isoquants do not cross each other.
Marginal Rate of Technical Substitution (MRTS)
It is the slope of an isoquant (-K/L) which indicates how the quantity of one input can be
traded off against the quantity of the other, while output is held constant. The MRTS of labor for
capital, denoted as MRTS
L, K
shows the amount by which the input of capital can be reduced
when one extra unit of labor is used, so that output remains constant.
MRTS
L,K
decreases as the firm continues to substitute labor for capital (or as more of labor is
used). The reason is that when the number of capital is large and that of labor is low, the
productivity of capital is relatively lower and that of labor is higher (due to the law of
diminishing marginal returns). Thus, at this point relatively large amount of capital is required to
replace one unit of labor (or one unit of labor can replace relatively large amount of capital). As
the employment of labor increases and that of capital decreases, quite the reverse will happen.
That is, productivity of capital increases and that of labor decreases. Hence, the amount of capital
that needs to be reduced increase when one extra labor is used decreases. Hence slope of an
isoquant is decreasing makes an isoquant convex to the origin.
39 | P a g e
MRTSL,K (the slope of isoquant) can also be given by the ratio of marginal products of factors.
That is, MRTS L , K  
K MPL

. This can be shown algebraically as follows:
L MPK
Let the production function is given as: q= f (L, K), the equation of a specific isoquant can be
obtained by equating the production function with a given level of output, say q as q = f (L, K)
Total differential of q measures the total change in q that happens as a result of a simultaneous
change in L and K. i.e, dq 
q
f
.dL  .dk  d q
L
k
But since q is constant, d q is zero (d q =0)
So,
q
q
.dL  dk  0
L
k
(But,
q
q
 MPk )
 MPl and
k
L
Thus, the above equation can be written as: MPL. dL + MPK.dk = 0 i.e.
MPL  dK

MPk
dL
Therefore, the slope of an isoquant can be given as the ratio of marginal products of inputs.
The Efficient Region of Production: Long run
The efficient region of production in the long run prevails when the marginal product of all
variable inputs is positive but decreasing. Graphically this can be represented by the negatively
slopped part of an isoquant. The locus of points of isoquants where the marginal products of
factors are zero form the ridge lines. The upper ridge line implies that the MP of capital is zero.
MPk is negative for all points above the upper ridge line and positive for points below the ridge
line. The lower ridge line implies that the MPL is zero. For all points below the lower ridge line
the MPL is negative and positive for points above the line. Production techniques are technically
efficient inside the ridge lines symbolically; in the long run efficient production region can be
illustrated as:
MPL >0, but
40 | P a g e
MPL
<0
L
MPk >0, but
MPk
<0
K
Graphically, efficient region of production is shown as follow:
Capital
Upper ridge line
Lower ridge line
q3
q2
q1
Labor
Fig 3.5: Efficient Region of Production
Thus efficient region of production is defined by the range of isoquants over which they are
convex to the origin.
The long run law of production: The law of returns to scale: it describes the
technically possible ways of increasing the level of production. Output may increase in various
ways. In the long run output can be increased by changing all factors of production. This long
run analysis of production is called Law of returns to scale.
In the short run output may be increased by using more of the variable factor, while capital (and
possibly other factors as well) are kept constant. The expansion of output with one factor (at
least) constant is described by the law of variable proportion or the law of (eventually)
diminishing returns of the variable factor.
In the long run all inputs are variable. Expansion of output may be achieved by varying all
factors of production by the same proportion or by different proportions. The traditional theory
of production concentrates on the first case, i.e. the study of output as all inputs change by the
same proportion. The term returns to scale refers to the change in output as all factors change by
the same proportion.
41 | P a g e
Suppose initially the production function is X0 = f (L, K). If we increase all factors by the same
proportion t, we clearly obtain a new level of output X* where, X* = f (tL, tK)

If X* increases by the same proportion t or if X* = tX0, we say that there is constant
returns to scale. Here along any isocline the distance between successive multipleisoquant is constant. Doubling the factor inputs doubles the level of initial output;
trebling inputs trebles output, and so on.

If X* increases less than proportionally with the increase in the factors (or if X* increases
by a proportion less than t), we have decreasing returns to scale. Here, the distance
between consecutive multiple- isoquants increases. By doubling inputs, output increases
by less than twice of its original level.

If X* increases more than proportionally with the increase in the factors (by a more than t
proportion), we have increasing returns to scale. The distance between consecutive
multiple isoquants decrease, by doubling the inputs, output is more than doubled.
Causes of increasing returns to scale
Technical and /or managerial indivisibility: it will expand the production system and increase
productivity of inputs than an increase in level of input.
Causes of decreasing returns to scale
If we expand the output beyond optimum, the top management personnel will be overburdened
and the productivity of additional unit of the variable inputs decline eventually.
Equilibrium of the firm: Choice of optimal combination of factors
To determine the economically efficient input combinations we need to have the prices of inputs.
Iso-cost line: is the locus point denoting all combination of factors that a firm can purchase with
a given monetary outlay, given prices of factors.
Suppose the firm has C amount of cost out lay (budget) and prices of labor and capital are w and
r respectively. The equation of the firm‟s isocost line is given as:
C  rK  wL , where K and L are quantities of capital and labor respectively.
Given the cost outlay C , the maximum amounts of capital and labor that the firm can purchase
are equal to
42 | P a g e
C
C
and
respectively. The straight line that connects these points is iso-cost line.
r
w
Capital
Iso cost
line
C/r
C/w
Labor
Figure: 3.6 the Isocost Line
It shows different combinations of labor and capital that the firm can buy given the cost out lay
and prices of the inputs.
Case1: Maximization of output subject to cost constraint
Suppose a firm having a fixed cost out lay (money budget) which is shown by its iso-cost line.
Here, the firm is in equilibrium when it produces the maximum possible output, given the cost
outlay and prices of input. The equilibrium point (economically efficient combination) is
graphically defined by the tangency of the firm‟s iso-cost line (showing the budget constraint)
with the highest possible isoquant. At this point, the slope of the iso cost line (
slope of the isoquant (
w
) is equal to the
r
MPL
).
MPK
The condition of equilibrium under this case is, thus:
w MPL

r MPK
or
MPL MPK
-------------- the first order (necessary) condition.

w
r
The second order (sufficient) condition is that isoquant must be convex to the origin.
43 | P a g e
Capital
A
Q3
K1
E
Q2
Q1
L1
B
Labor
Figure: 3.7 Equilibrium of the Firm for Output Maximization
The optimal combination of inputs ( L1 and K1 ) is defined by the tangency of the iso-cost line
(AB) and the highest possible isoquant ( Q2 ), at point E. At this point the slope of iso-cost line (
w
MPL
) is equal to the slope of isoquant Q2 (
).The second order condition is also satisfied by
r
MPK
the convexity of the isoquant.
Case -2: Minimization of cost for a given level of output
Dear learner, as cases of output maximization here also the equilibrium will exist when the two
lines become tangent. Consider an entrepreneur (a firm) who wants to produce a given output
with minimum cost outlay. That is, we have a single isoquant which denotes the desired level of
output, but there are a set of isocost lines which denotes the different cost outlays. Higher isocost
lines denote higher production costs. The production costs of a desired level of output will
therefore be minimized when the isoquant line is tangent to the lowest possible isocost line.
At the point of tangency, the slopes of isoquant= slope of isocost lines. That is
44 | P a g e
w MPL

r MPK
Capital
e
c
a
E
K1
Q
L1
b
d
f
Labor
Fig: 3.8 Equilibrium of the Firm for Cost Minimization
The equilibrium combination of factors is K1 and L1 amounts of capital and labor respectively.
Lower isocost lines such as „ab‟ are economically desirable but unattainable given the desired
level of output. So point E shows the least cost combination of labor and capital to produce X.
45 | P a g e
UNIT FOUR
Theory of Cost of Production
4.1 Basic Concepts of Cost of Production
As you know in theory of production to produce goods and services, firms need factors of
production or simply inputs. To acquire these inputs, they have to buy them from resource
suppliers. Cost is, therefore, the monetary value of inputs used in production of an item. We can
identify two types of cost of production: social cost and private cost.
Social cost: is the cost of producing an item to the society. This cost is realized due to the fact
that most resources used for production purpose are scarce and some production process, by their
nature, release dangerous chemicals, bad smell, etc to surrounding society.
For example, when a Harar beer factory wants to produce beer, the society as a whole also incurs
a cost. Because, the next- best alternative of the raw material (such as barely) used for the
production of beer is sacrificed. When the beer factories buy barley from the market, the amount
of barely available for consumption by society may be reduced and the price may become dearer.
Hence, the production of beer imposes an indirect cost on the society, moreover, by its nature;
the production of beer emits bad chemicals to the environment, which pollutes waters, air, etc.
Private cost: This refers to the cost of producing an item to the individual producer. It is the cost
that the beer factory incurs to produce the beer, in our example:
Private cost of production can be measured in two ways either by economic cost or by
accounting cost:
i) Economic cost
In economics the cost of production to the individual producer includes the cost of all inputs used
for the production of the item. The producer may buy part of the inputs from the market. For
example, he/ she hire workers, buy raw materials, the necessary machines, etc. the actual or out46 | P a g e
,of- pocket expenditures that the firm incurs to purchase these inputs from the market are called
explicit costs.
But, the producer can also use his/ her own property as an inputs which are not purchased from
the market for the production purpose. For example, the producer may use his/ her own building
as a production place, he/she may also manage his firm by himself instead of hiring another
manager, etc. since these inputs are used for the purpose production, their value has to be
estimated and included in the total cost of production. As to how to estimate the cost of these
non- purchased inputs is concerned, we usually estimate their cost from what these inputs could
earn in their best alternative use. For instance, if the firm uses his own building for production
purpose, the cost of using this building for production is estimated by the rent income foregone.
If the producer is a teacher with salary of 5000 birr per month and fruits his job to manage his
factory, then the next best alternative of his labor is the salary that he sacrificed to be the
manager of his factory. The estimated cost of non- purchased inputs are called implicit costs.
Thus, in economics the cost of production includes the costs of all inputs used in the production
process whether the inputs are purchased from the market or owned by the firm himself.
Economic cost: Explicit cost plus Implicit cost
ii) Accounting Cost
For accountant, the cost of production includes the cost of purchased inputs only. Accounting
cost is the explicit cost of production only. Moreover, accountant‟s doesn‟t consider the cost of
production from the opportunity cost of the resources point of view. To clarify the difference
between accounting cost and economic cost on this regard, consider the following example.
Suppose Harar Brewery factory purchases 5000 quintals of barely for 600 birr per quintal in
2005 to use this barley for production purpose in the year 2006. However, suppose that the price
of the barely has been increased to 700 birr per quintal in the year 2006. Now shall we use the
actual price with which the barely was bought in 2005 or the current price (2006 price) to
estimate the cost of barely in 2006?
47 | P a g e
In economics, the 2006 price should be taken because, though the barley was bought for 600 birr
per quintal in 2005, the cost of using this barely for the production purpose in 2006 is the 700
birr per quintal, the amount of income that could be obtained if the barely were sold in the
market. But accountants use the 2005 price to estimate the cost of production in the year 2006.
4.1.2 Cost Functions
Cost functions are derived functions. They are derived from the production function, which
describes the available efficient methods of production at any one time. Cost function shows the
algebraically relation between the cost of production and various factors which determine it.
Economic theory distinguishes between short-run and long-run costs. Both in the short-run and
in the long-run, total cost is a multivariable function, that is, total cost is determined by many
factors.
Among others, the cost of production depends on the level of output produced,
technology of production, prices of factors, etc.
Symbolically,
C = f (x, t, pi)
Where c- is total cost of production
x - is the amount of output
T – is the available technology of production.
Pi – is the price of input
Short-run Cost Function
The short run is the period during which some factor(s) is fixed; usually capital equipment and
entrepreneurship are considered as fixed in the short run. In the traditional theory of the firm,
total costs (TC) are split into two groups: total fixed costs (TFC) and total variable costs (TVC):
TC = TFC + TVC
By fixed costs are costs which don‟t vary with the level of output. The fixed costs include:
a. Salaries of administrative staff
b. Expenses for building depreciation and repairs
c. Expenses for land maintenance
d. The rent of building used for production , etc
48 | P a g e
 All the above costs are regarded as fixed costs because whether the firm produces much
output or zero output, these costs are unavoidable, and the firm can avoid fixed costs only
if he / she shut down the business.
Variable costs are all costs which directly vary with the level of output and it includes:
a. The cost of raw materials
b. The cost of direct labor
c. The running expenses of fixed capital such as fuel, electricity power, etc.
Graphical illustration of Total Cost Functions
A. Total fixed cost (TFC)
TFC is denoted by a straight line parallel to the output axis. The point of intersection of the TFC
line with the cost axis (vertical axis) shows the amount of the fixed. For example if the level of
fixed cost is $ 100, it can be shown as.
B. Total variable cost (TVC)
The total variable cost of a firm has an inverse s- shape. The shape indicates the law of variable
proportions in production or the law of diminishing marginal returns. According to this law, at
the initial stage of production with a given plant, as more of the variable factor (s) is employed,
its productivity increases. Hence, the TVC increases at a decreasing rate. This continues until the
optimal combination of the fixed and variable factors is reached. Beyond this point, as increased
quantities of the variable factors(s) are combined with the fixed factor (s) the productivity of the
variable factor(s) declined, and the TVC increases by an increasing rate.
C. Total Cost (TC)
The total cost curve is obtained by vertically adding the TFC and the TVC i.e., by adding the
TFC and the TVC at each level of output. The shape of the TC curve follows the shape of the
TVC curve i.e. it is an inverse S-shape. But the TC curve doesn‟t start from the origin as that of
the TVC curve. The TC curve starts from the point where the TFC curve intersects the cost axis.
49 | P a g e
Cost
TC
TVC
100
TFC
Figure 4.1 the graph of total cost functions
Q
Per unit costs (average costs)
Average fixed cost (AFC) - is found by dividing the TFC by the level of output. Graphically,
the AFC is a rectangular hyper parabola. The AFC curve is continuously decreasing curve, but
decreases at a decreasing rate and can never be zero.
Average variable cost (AVC): is obtained by dividing the TVC with the corresponding
level of output. Graphically, the AVC at each level of output is derived from the slope of a line
drawn from the origin to the point on the TVC curve corresponding to the particular level of
output. The short run AVC falls initially reaches its minimum and then starts to increase. Hence,
the AVC curve has a U-shape and the reason behind is the law of variable proportions.
Average total cost (ATC) or Simply, Average cost (AC)
AC is obtained by dividing the TC by the corresponding level of output. It shows the amount of
cost incurred to produce each unit of successive outputs. AC 
Or equivalently, AC 
TC
Q
TVC  TFC TVC TFC


= AVC + AFC
Q
Q
Q
Graphically, AC curve can be obtained by vertically adding the AVC and AFC for each level of
successive outputs. Alternatively, the AC curve can also be derived in the same way as the
SAVC curve. The AC curve is U-shaped because of the law of variable proportions. Observe the
figure that follows.
50 | P a g e
Marginal Cost (MC): is defined as the additional cost that the firm incurs to produce one
extra unit of the output. One thing to be noted here is that, the additional cost that the firm incurs
to produce the 10th unit of output is not equal to the additional cost of producing the 1000th unit.
They would be equal if the TC curve is straight line.
To sum up, the MC is the change in total cost which results from a unit change in output i.e. MC
is the rate of change of TC with respect to output, Q or simply MC is the slope of TC function
and given by: MC 
dTC
dQ
In fact MC is also the rate of change of TVC with respect to the level of output.
MC 
dTFC
dTFC  dTVC dTVC
0

, since
dQ
dQ
dQ
Graphically, the MC the slope of TC curve (or equivalently the slope of the TVC curve)
obviously, the slope of curved lines at a given point is measured by constructing a tangent line to
the curve at each point. So, the slope of the curve at a given point is equal to the slope of the
tangent line at that specific point. Given the inverse S-shaped TC (or TVC) curve, the MC curve
will be U-shaped. Thus given inverse S-shaped TC or TVC curve, the slope of the TC or TVC
curve (i.e. MC) initially decreases, reaches its minimum and then starts to rise.
From this, we can logically infer that the reason for the U-shappedness of MC is also the law of
variable proportion. That is, had the TC or TVC curve not been inverse S-shaped, the MC curve
51 | P a g e
have would never assumed the U-shape, and obviously, the TC or TVC is inverse S-shaped.
C
AC
MC
AVC
AFC
Q
Q1
Q2
Figure 4.2 Average Cost Curves
In summary, AVC, ATC and MC curves are all U-shaped due to the law of variable proportions.
The simplest total cost function which would incorporate the law of variable proportions is the
cubic polynomial of the following form.
TC  bo  b1Q  b2Q 2  b3Q 3
Where Q- is the level of output and b0, b1, b2 &b3 – are none zero constants.
From this type of total cost function,
TFC=bo and AFC = b0/Q
TVC= b1Q  b2 Q 2  b3 Q 3 and AVC 
ATC = AFC + AVC 
b1 Q  b2 Q 2  b3Q 3
 b1  b2 Q  b3Q 2
Q
b0
 b1  b2Q  b3Q 2
Q
The relationship between AVC, ATC and MC
Given ATC = AVC + AFC, AVC is part of the ATC. Both AVC and ATC are u – shaped,
reflecting the law of variable proportions however, the minimum of ATC occurs to the right of
the minimum point of the AVC ( see the following figure) this is due to the fact that ATC
includes AFC which continuously decreases as the level of output increases.
52 | P a g e
After the AVC has reached its lowest point and starts rising, its rise is over a certain range is
more than offset by the fall in the AFC, so that the ATC continues to fall (over that range)
despite the increase in AVC. However, the rise in AVC eventually becomes greater than the fall
in AFC so that the ATC starts increasing. The AVC approaches the ATC asymptotically as
output increases.
Finally, the MC curve passes through the minimum point of both ATC and AVC curves.
This can be shown by using calculus.
Suppose the TC = f (Q)
MC 
d ( f (Q))
 f (Q)
dQ
AC  d
Slope of
AC 
TC f (Q)

Q
Q
d (f (Q)) ( f (Q))Q  Q. f (Q)

dQ
Q2
But f (Q) MC and Q1 (or dQ/dQ) =1
Thus, slope of
Slope AC =
MC f (Q)

MC.Q - f(Q)
Q
Q
AC 

Q2
Q
1
MC  AC , where f (Q)  AC
Q
Q
i) When MC<AC, the slope of AC is negative, i.e.
AC curve is decreasing (initial stage of production)
ii) When MC >AC, the slope of AC is positive, i.e. the AC curve is increasing (after optimal
combination of fixed and variable inputs.
iii) When MC = AC, the slope of AC is zero, i.e. the AC curve is at its minimum point.
The relationship between AVC and MC can be shown in a similar fashion.
LONG-RUN COSTS
In the long – run all factors are assumed to become variable. It is known that the long-run cost
curve is a planning curve, in the sense that it is a guide to the entrepreneur in his decision to plan
53 | P a g e
the future expansion of his output. The long run average cost curve is derived from short-run cost
curves. Each point on the LAC corresponds to a point on a short-run cost curve, which is tangent
to the LAC at that point.
The long-run marginal cost is derived from the SRMC curves, but does not envelope them. The
LRMC is formed from the points of intersection of the SRMC curve with vertical lines (to the xaxis) drawn from the points of tangency of the corresponding SAC curves and the LRA cost
curve.
4.2 The relationship between short run production and cost curves
The short run AVC is the mirror reflection of the short run AP of the variable input. When AP
variable input increases, AVC decreases; when AP variable input reaches its maximum, the AVC
reaches its maximum point, and finally when AP variable input starts to fall, the AVC curve
starts to rise. The same relationship exists between the short run MP of variable input curve the
MC curve. This can be shown algebraically by using a linear short run cost function.
AP, MP
APL
MPL
AVC, MC
54 | P a g e
MC
AVC
Q
Figure 4.3 Relation of Production and Cost curves
As shown above we can conclude that the short run AVC and MC curves are the mirror
reflection (along the horizontal axis) of short run APL and MPL curves
55 | P a g e
UNIT FIVE
MARKET STRUCTURES
Market structure refers to the nature and degree of competition within a particular market. It
indicate the number and relative share of the firm in the industry and it can be characterized by
sellers, buyers or both, but most economic book classified based on sellers. Based on this criteria
market can be classified as perfect competitive and imperfect competitive.
Perfect competition is a market structure characterized by a complete absence of rivalry among
the individual firms. A perfectly competitive market model is constructed assuming that there are
large number of buyers and sellers in the industry/market, so that no individual buyer or seller,
however large, can influence the price by changing the purchase or output; all firms in the
industry produce a homogenous product; entry and exit of firms is free for the industry.
Imperfectly competitive is a market in which the actions of one or more buyers and sellers have
a perceptible influence on price. This broad definition of imperfect competition encompasses
markets of many different types, which can be distinguished by further classification as:
monopoly, monopolistic competitive and oligopoly.
5.1 BASIC CONCEPTS OF PERFECT COMPETITIVE MARKET
Definition: perfect competition is a market structure characterized by a complete absence of
rivalry among the individual firms. Thus, perfect competition in economic theory has a meaning
diametrically opposite to the everyday use of this term.
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Most of the time, we see business men using the word “Competition” as synonymous to
“rivalry”. However, in theory, perfect competition implies no rivalry among firms.
Assumptions
The model of perfect competition was constructed based on the following assumptions
1. Large number of sellers and buyers: it is to extent that the market share of each firm
(and buyer) is too small to have a perceptible effect on the price of the commodity. That
is the action of a single seller or buyer cannot influence market price of the commodity.
2. Products of the firms are homogeneous: products supplied by all the firms in the market
have uniform physical characteristics (are uniform in terms of quantity, quality etc) and
the services associated with sales and deliveryare identical. Thus buyers can not
differentiate the product of one firm from the product of the other firm.
 The two assumptions imply that the individual firm in pure competition is a price
taker: their demands curve to be infinitely elastic, indicating that the firm can sell any
amount of output at the prevailing market price.
Market P
P=AR=MR
Out put
Figure 5.1 the demand curve of a perfectly competitive firm
3. Free entry and exit of firms
There is no barrier to entry and exit from the industry. Entry or exit may take time, but firms
have freedom of movement in and out of the industry.
57 | P a g e
4. The goal of all firms is profit maximization.
Some firms may have the aim of making their product wise, others may want to maximize
their sales even by cutting price, etc. But, in this model, it is assumed that the goal of all
firms is to maximize their profit and no other goal is pursued.
5. No government regulation: that is there is no tax, subsidy etc.
 A market structure in which all the above assumptions are fulfilled is called pure
competition. It is different from perfect competition which requires the fulfillment of
the following additional assumptions.
6. Perfect mobility of factors of production: Factors of production (including workers) are
free to move from one firm to another throughout the economy.
7. Perfect knowledge; It is assumed that all sellers and buyers have a complete knowledge of
the conditions of the prevailing and future market. That is all buyers and sellers have
complete information about the price and quality of the product.
Thus, a perfectly competitive market is a market which satisfies all the above conditions
(assumptions). In reality, perfectly competitive markets are scarce if not none. But since the
theory of perfectly competitive market helps as a bench mark to analyze the more realistic
markets, it is very important to study it.
Demand and revenue functions under perfect competition
Due to the existence of large number of sellers selling homogenous products, each seller is a
price taker in perfectly competitive market. Given the horizontal demand function at the ongoing
market price, the total revenue of a firm operating under perfect competition is given by the
product of the market price and the quantity of sales, i.e., TR = P*Q. Since the market price is
constant at P*, the total revenue function of a firm is linear and the amount of TR depends on
the quantity of sales. To increase his total revenue, the firm should sell large quantity.
58 | P a g e
Graphically, the TR curve is as shown below.
_
TR=PQ
TR
Q
Figure 5.2 total revenue of perfect competitive firm
MR and AR of a firm operating under perfect competition are equal to the market price. i.e.
MR 
TR P.Q
dTR

 P and AR 
 P Hence, AR = P=MR (look the figure 4.1 above).
Q
dQ
Q
5.2 Short run Equilibrium of the firm
A firm is said to be in equilibrium when it maximizes its profit (). Profit is defined as the
difference between total cost and total revenue of the firm = TR-TC
Determination of equilibrium of the firm operating in a perfectly competitive market means
determination of the profit maximizing output since the firm is a price taker. The level of output
which maximizes the profit of the firm can be obtained in two ways: either in total approach or
marginal approach
A. Total approach
Here, the profit maximizing level of output is that level of output at which the vertical distance
between the TR and TC curves is maximum given that the TR curve lies above the TC curve at
this point.
59 | P a g e
Graphically
TC TR
TC, TR
Q
Q0
Qe
Q1
Figure: 5.3 Equilibrium Determinations (Total Approach)
Here the profit maximizing output level is Qe because it is at this output level that the positive
vertical distance between the TR and TC curves (or profit) is maximum. For all output levels
below Q0 and above Q1 profit is negative because TC is above TR. At Q0 and Q1 the firm neither
generates profit nor incurs a loss.
B. Marginal Approach
In this approach the profit maximizing level of output is the level of output at which: MR=MC
and MC is increasing. It is directly derived from the total approach. In figure 4.3, the level of
profit maximized when the vertical distance between the TR and TC curve is maximum or the
slope of the two curves is equal. The slope of the TR curve constant and is equal to the MR or
market price. Similarly, the slope of the TC curve at a given level of output is equal to the slope
of the tangent line to the TC curve at that level of output, which is equal to MC. Thus the
distance between the TR and TC curves () is maximum when MR equals MC.
Graphically, the marginal approach can be shown as follows.
60 | P a g e
MC, MR
MC
MR
Q*
Qe
Q
Figure 5.4 Determination of Equilibrium (Marginal Approach)
As we can look in the above figure the profit maximizing output is Qe, where MC=MR and MC
curve is increasing. At Q*, MC=MR, but since MC is falling at this output level, it is not
equilibrium output. For all output levels ranging from Q* to Qe the marginal cost of producing
additional unit of output is less than the MR obtained from selling this output. Hence the firm
should produce additional output until it reaches Qe.
Mathematical derivation of the equilibrium condition
TC is a function of output, TC=f (Q) and TR is also a function of output, TR=f (Q). Thus, profit
is a function of output, = f (Q) =TR-TC. To determine the profit maximizing output we find
the first derivative of the  function and equate the result to zero.
d
dQ

dTR dTC

0
dQ
dQ
= MR – MC = 0 MR = MC -------------------- (1st order or necessary condition)
The equality of MC and MR is a necessary, but not sufficient condition.
d 2
dQ 2
 0
d 2TR d 2TC

 0
dQ 2
dQ 2
d 2TR
dMR

0
dQ 2
dQ
d 2TC
 0 i.e slope of MC > 0 or Mc is increasing……………. Sufficient condition
Hence,
dQ 2
61 | P a g e
A firm is in the short run equilibrium does not necessarily mean that the firm gets positive profit.
Whether the firm gets positive or zero or incurs a loss depends on the level of ATC at
equilibrium thus;
 If the ATC is below the market price at equilibrium, the firm earns a positive profit equal to
the area between the ATC curve and the price line up to the profit maximizing output; here
the level of profit the firm generated is equivalent to the area ABCP (see figure 4.5).
MC, AC, MR
AC
MC
A
C
P
L
A
P=AR=MR
Profit
B
1
Q
li
Figure 5.5 Equilibrium under perfect competitive market
Q*
 If the ATC is equal to the market price at equilibrium, the firm gets zero profit. It is also
called the breakeven point or neither profit nor loss.
 If the ATC is above the market price at equilibrium, the firm earns a negative profit (incurs
a loss) equal to the area between the ATC curve and the price line.
The firm will continue to produce irrespective of the existing loss as far as the price is sufficient
to cover the average variable costs or the TR sufficiently covers the total variable costs. This is
so because if the firm stops production he will incur a loss which equals the total fixed cost. But,
if it continues to produce the loss is less than total fixed costs because the TR will cover some
portion of fixed costs in addition to the whole variable costs as far as it is greater than TVC.
However, if p< AVC or alternatively, if the TR of the firm is not sufficient to cover at least the
TVC, the firm should close (shut down) its factory (business). It will only lose the TFC; but if it
continues operation, the loss is greater than the TFC since part of the variable cost is also not
covered by the existing revenue.
Numerical example
62 | P a g e
Suppose that the firm operates in a perfectly competitive market. The market price of his product
is Br10. The firm estimates its cost of production with the following cost function:
TC=10q-4q2+q3
A)
What level of output should the firm produce to maximize its profit?
B)
Determine the level of profit at equilibrium.
C)
What minimum price is required by the firm to stay in the market?
Solution
Given: p=$10 and TC= 10q - 4q2+q3
A) The profit maximizing output is that level of output which satisfies the following
condition
MC= MR, & MC is rising. Thus, we have to find MC& MR first
 MR in a perfectly competitive market is equal to the market price. Hence, MR=10 = P
MC=
dTC d (10q  dq 2  q 3 )

 10  8q  3q 2
dq
dq
 To determine equilibrium output just equate MC& MR and then solve for q.
10 – 8q + 3q2 = 10  - 8q + 3q2 = 0 q (-8 + 3q) = 0  q = 0 or q = 8/3
Now we have obtained two different output levels which satisfy the first order
(necessary) condition of profit maximization i.e. 0 & 8/3
 To determine profit maximizing level of output we have to use the second order test at
the two output levels, condition of increasing MC. Slope of MC =
dMC
= -8 + 6q
dq
 At q = 0, slope of MC is -8 + 6 (0) = -8 which implies that MC is decreasing at q = 0.
Thus, q = 0 is not equilibrium output
 At q = 8/3, slope of MC is -8 + 6 (8/3) = 8, which is positive, MC is increasing at q =
8/3. Thus, the equilibrium output level is q = 8/3
B) To determine the firm‟s equilibrium profit we have calculate the TR and TC of
producing the equilibrium level of output.
TR = Price * Equilibrium output = Br 10 * 8/3= $ 80/3
TC = 10 (8/3) – 4 (8/3)2 + (8/3)3  23.12
 = TR – TC = 26.67 – 23.12 = Br 3.55
63 | P a g e
C) To stay in operation the firm needs the price which equals at least the minimum AVC.
AVC is minimal when derivative of AVC is equal to zero. That is:
dAVC
=0
dQ
Given the TC function: TC = 10q – 4q2 +q3, since TFC=0 i.e. TC = TVC.
Hence, TVC = 10q – 4q2 + q3 and AVC =
TVC
10q  4q 2  q 3
=
= 10 – 4q2 + q2
q
q
d (10  4q  q 2 )
dAVC
 0  = -4 + 2q = 0 q = 2
0 
dq
dq
The minimum AVC is obtained by substituting 2 for q in the AVC function i.e.,
Min AVC = 10 – 4 (2) + 22 = 6
Thus, to stay in the market the firm should get a minimum price of $ 6.
5.3 The short run supply curve of the firm and the industry
A. The short run supply curve of the firm
The profit maximizing level of output is defined by the point of equality of MC and market price
(because market price is equal to MR in the perfectly competitive market). By repeating this
analysis at different possible market prices, we observe how the equilibrium quantity supply of
the firm varies with the market price. Look figure 4.6 below.
Suppose that initially the market price and MR is Birr 6 and the demand curve is shown by line
P1. Given the MC curve, the level of output which maximizes the firm‟s profit is defined by the
point of intersection of the MC curve and the demand line (P1), which is equal to 50 units.
When the market price increases to Birr 7 (an upward shift of the demand curve or MR to P 2)
and given the positive slope of MC, this higher demand (MR) curve cuts the MC curve at higher
output level, 140. That is, when the market price increases from $6 to $7, the equilibrium
quantity supplied by the firm increases from 50 units to 140 units. As the price increases further
(say to Birr 8), the equilibrium output increases to 200 units.
64 | P a g e
The firm, given its cost structure, will not supply any quantity (will shut down) if the price falls
below $6, because at a lower price than $6, the firm cannot cover its variable costs. Thus, supply
is zero for all price levels below $6 (minimum AVC). If we plot the successive equilibrium
points on a separate graph we observe that the supply curve of the individual firm over laps with
(is identical to) to part of its MC curve to the right of the shutdown point.
P, C
P
MC
Supply
curve
AC
AVC
E2
$8
P3= MR3
$8
E2
$7
P2= MR2
$7
E1
$6
P1= MR1
50
Q2
140
200
Q
$6
50
140
200l
Q
Figure 5.6: The short run supply curve of a perfectly competitive firm
B. Short run supply curve of the industry
The industry supply curve is the horizontal summation of the supply curves of the individual
firms in the market. That is, the total quantity supplied in the market at each price is the sum of
the quantities supplied by all firms at that price. This is based on the assumption that the factor
prices and the technology are given.
Let us look how the short run industry supply curve derived from the supply of individual firms
by considers the following figure. Suppose S1, S2 and S3 denote the supply curves of firms
existing in a given industry. The industry supply curve is obtained by adding the quantities
65 | P a g e
supplied by all the firms at each price. For example, at price which equals Br 6, firm 1 supplies
50 units, firm 2 supplies 80 units & firm 3 supplies 120 units. The market supply at Br 6 price is
thus 250 units (50+80+120 units). The short run industry supply is derived by repeating the
above process at each price levels and it is given bellow.
P
SS1
SS3
SS2
Industry
Supply
P4=7
P3=6
P2=5
P1=4
Q
Q1
Q2
Q3
Q4
Figure 5.7: The industry- supply curve of perfectly competitive Market
When the market price falls below Br 4, only firm 2 exist in the market. Thus, for prices below
Br 4, the industry supply curve is identical with the supply curve is identical with the supply
curve of firm 2. Similarly, for price levels ranging from Br 4 to Br 5, only firm1 and firm2 are
producing and searching in the market. Thus, the industry- supply cusrve for this range of price
is the sum of the quantities supplied by firm 1 and firm 2, and so on.
5.4 Short run equilibrium of the industry
Short run equilibrium of the industry is defined by the intersection of the market demand and
market supply and determines the equilibrium price and quantity of the commodity in the
market. The demand curve that an individual firm faces is horizontal line while the market
demand curve (the total demand curve that the industry faces) is down-ward sloping.
66 | P a g e
Firm 1
SS
P1
DD
AC1
Q
MC2
P
MC1
P*
Q*
Firm 2
P
C
P
AC
P=MC
P2
P=MC
AC2
AC2
XM
Q*
Q
Figure 5.8: short run equilibrium of the industry
Q
Q*
In fig.5.8 the industry is in equilibrium at price P*, at which the quantity demanded and supplied
is Q*. At this equilibrium market price, individual firms can earn a positive profit, zero profit
(normal profit) or even can incur a loss depending on their cost structures. Short run equilibrium
of the industry is defined by the intersection of the market demand and the industry supply
Curve. At equilibrium price, P* firm 1 gets a positive profit because the average cost of the firm
at equilibrium is less than the market Price, P*. On the other hand, firm 2 is incurring a loss as its
average cost is higher than the market price.
5.5 Long-run Equilibrium of Perfect Competitive Market
5.5.1 Equilibrium of an individual firm in the long run
In the long run, firms are in equilibrium when they have adjusted their plant size so as to produce
at the minimum point of their long run average cost (LAC) curve, which is tangent to the demand
curve defined by the market price (or when the market price is equal to the minimum LAC).
Since price is equal to LAC at the long run equilibrium, firms will be earning just normal profits
(zero profits). This is due to two reasons.
First, if the firms existing in the market are making excess profits (the market price is greater
than their LACs) new firms will be attracted to the industry seeking for this excess profit. The
entry of new firms results a fall in market price of the commodity (which is shown by the down
67 | P a g e
ward shift of the individual demand curve) and an upward shift of the cost curves. These changes
will continue until the LAC becomes tangent to the demand curve defined by the market price.
At this time, entry of new firms will stop since there is no positive profit (since P = LAC) which
attracts new firms in to the market.
Second, if the firms are incurring losses in the long run (P < LAC) they will leave the industry
(shut down). This will result in higher market price (because market supply of the commodity
decreases) and lower costs (because the market demand for inputs decreases as the number of
firms in the market decreases). These changes will continue until the remaining firms in the
industry cover their total costs inclusive of the normal rate of profit.
The following figure shows how firms adjust to their long run equilibrium position. When the
market price is p, the firm is making excess profit working with plant size whose cost is denoted
by SAC1. It will therefore have an incentive to build new capacity or larger plant size and it
moves along its LAC. At the same time new firms will be entering the industry attracted by the
excess profits. As quantity supplied in the market increases (by the increased production of
expanding old firms and by the newly established ones) the supply curve in the market will shift
to the right and price will fall until it reaches the level of P1, at which the firms and the industry
are in the long- run equilibrium. The condition for the long run equilibrium of the firm is that the
long run marginal cost (LMC) should be equal to the price and to the LAC i.e. LMC = LAC = P.
P
M
P
C
SS1
LRAC
APL1
SMC
X1
SS2
LRMC
SAC1
P1
SAC2
Pe
P2
put
_
DD
Q
68 | P a g e
Q
Qe
Qe
Figure 5.9: Long run equilibrium of the firm.
At equilibrium the short – run marginal cost is equal to the long run marginal cost and the short –
run average cost is equal to the long run average cost. Thus, given the above condition, we have:
SMC = LMC = SAC = LAC = P = MR. This implies that at the minimum point of the LAC the
corresponding short run plant is worked at its optimal capacity so that the minimum of the LAC
and SAC coincide.
Long run shut down decision
In the short-run the firm should continue production as far as the market price is greater than the
minimum AVC. If the market price falls below the minimum AVC, the firm is well advised to
shut down because if it shut down it well loose only the fixed costs but if it continues production
the loss is greater than the fixed cost.
In the long run all costs are variable because the firm can change the quantity of all inputs. Thus,
in the long run the firm shuts down when its revenue falls below the long run total cost or if the
market price falls below the minimum LAC of the firm.
5.5.2The long-run supply curves of the firm
Previously, we have noted that in the long run the firm shuts down if the market price is below
the its minimum long run average cost. Thus, the firm will not supply for all price levels below
the minimum LAC. On the other hand, the firm's long run equilibrium output is defined by the
equality of the MR and its LMC. As a result, a firm‟s long- run supply curve is its LMC curve
above the minimum of its long-run average cost curve.
5.5.3 Long run supply curve of the industry
The long run supply curve of the industry is the horizontal sum of the supply of individual firms
just like the case of short run supply curve of the industry. Thus, the long run supply curve of the
industry is up ward sloping, provided that the firms are of different size. This is because, firms
69 | P a g e
with relatively lower minimum LAC, are writing to inter the market than others. So that as the
market price increased in the long run more firms will find it profitable to inter the market,
resulting in upward sloping long-run supply curve of industry.
5.5.4 Long-run equilibrium of the industry
An industry is in the long-run equilibrium when the price is reached at which all firms are in
equilibrium. That is, when all firms are producing at the minimum point of their LAC curve and
making just normal profits, the industry is said to be in the long-run equilibrium. Under these
conditions there is no further entry or exit of firms in the industry (since all the firms are getting
only normal profit), so that the industry supply remains stable.
Panel (A): Industry equilibrium
Panel (B):
Firm’s equilibrium
P
P
LRAC
B
SS
LRMC
MC
Pe
m
Pe
DD
Qe
Q
Qe
Q
Figure 5.9: long-run equilibrium of the industry
As shown in the above figure long-run equilibrium of the industry is defined by the price (p) at
which all individual firms are in equilibrium, marking just normal profit. At this price all firms
are in equilibrium because LMC=SMC=P=MR and they get only normal profit because
LAC=SAC=P.
70 | P a g e
5.6 Perfect competition and optimal resource allocation
In the perfect competition, the market mechanism leads to an optimal allocation of resources.
The optimality is shown by the following conditions all of which prevail in the long run
equilibrium of the industry;
a. The output is produced at the minimum feasible cost. That is all firms produce at the
minimum of their LAC.
b. Consumers pay the minimum possible price which just covers the marginal cost of
production, that is, price equals just opportunity cost so that the consumers are not
exploited.
c. Plants are used at full capacity in the long- run so that there is no waste of resources. That
is, at the long run equilibrium the short run average cost is also minimum.
d. Firms earn only normal profits.
5.5 Theory of price in Pure Monopoly Market
5.5.1 Definition and source of monopoly
Definition of monopoly
Monopoly is defined as: a market situation in which a single seller sells a product or provides a
service for which there is no close substitute. In monopoly there are no similar products whose
prices or sales will influence the monopolist price or sales. In another words, cross elasticity
between monopolist product and other commodities is zero or low. Since there is a single seller
in monopoly market structure, the firm is at the same time the industry.
Common characteristics of monopoly
Monopoly market structures share the following characteristics in common.
1-Single seller and many buyers
There is a single seller in the market (industry) who sells the product to many buyers.
2-Absence of close substitutes
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A product produced by a monopolist has no close substitute so that consumers have no
alternative choices to substitute one product for another.
3-Price maker
Under perfectly competitive market, we have said that, both sellers and buyers are price takers.
However, the monopolist is a price maker or price setter. Facing a down ward sloped demand
curve for its product, the monopolist can change its product price by changing the quantity of the
Product supplied. For example, the monopolist can increase the price of its product by decreasing
the quantity of supply and vice-versa.
4-Barrier to entry
In monopoly, new competitors cannot freely enter in to the market due to some barriers which
can be economical, technical, legal or other type of barriers.
Sources of Monopoly Power
1. Ownership of strategic or key inputs: A firm may own or control the entire supply of a raw
material required for the production of a commodity. Such firms are not willing to sell the raw
materials to another firm.
2. Exclusive knowledge of production technique.
Most beverage (soft drink) companies such as East Africa Beverage Company have maintained
monopoly power over supply of their products (Coca Cola, Fanta and Sprite) partly due to
exclusive knowledge of the ingredient chemicals required for the production of their product.
3. Patents, Copyrights and Trademarks
A patent is a legal protection which prevents original inventions from being copied, and once a
patent is granted it is protected by law for a period of time. Copyright protects written work like
plays, books, music, and films which are all protected from copying by copyright laws.
Trademarks can be names of logos, and sometimes shapes. The Coca-Cola bottle, for example, is
actually a trade mark and it is illegal to copy it without permission of the company.
Protection of patents, copyrights, and trademarks come from a country‟s legal system and from
international agreements. In countries where we have these laws, owners of the indicated
intellectual property rights will have some monopoly power on their products or services.
72 | P a g e
4. Government Franchise and License
Another source of monopoly is government franchise. Franchise is a promise by the government
for a firm to prohibit the establishment of another firm (by another person) that produces the
same product or offers the same service as the original one.
For example, when the first Bank in Ethiopia, Abyssinia Bank was established, Emperor Minilik
has promised for the Egyptian firms (the owner of the Bank) that they will monopolize the
Banking service in Ethiopia for 50 years. Telecommunication service and hydroelectric power
supply are other examples of monopoly in Ethiopia.
5. Economies of scale may operate (i.e. the long run average cost may fall)
Another cause for the emergence of monopoly is economies of scale in production. A firm is said
to have economies of scale if its long run average cost is declining. In such a situation, when the
incumbent firm observes that new firms are entering into the market, it will produce large
amount of output to minimize its unit cost of production and will charge a lower price than the
new firms to deter entry. Such a monopoly is called natural monopoly.
Aside from the cases of monopoly mentioned above, pure monopoly is rare and most
governments discourage pure monopoly because monopoly is deemed to create inefficiency. For
example, had it been the case that the telecommunication services are not monopolized in our
country, their prices would have been lower. But though pure monopoly is rare, the pure
monopoly model is useful for analyzing situations that approach pure monopoly and for other
types of imperfectly competitive markets (i.e. monopolistic competition and oligopoly).
5.5. 2The demand and revenue curves of the monopoly firm
A monopolist firm is at the same time the industry and thus, it faces the negatively sloped market
(industry) demand curve for the commodity. In other words, because a monopolist is the sole
seller of a commodity, it faces a down ward sloping demand curve. This means, to sell more
units of the commodity, the monopolist must lower the commodity price. Conversely, if the
monopolist decides to raise the price of the product, it will reduce the quantity of supply without
worrying about the competitors. The monopolist who charged lower prices would capture a large
share of the market (customers) at the expense of him. So the monopolist can manipulate the
price of its commodity by changing the quantity of supply. To sell more units of the commodity,
73 | P a g e
the monopolist will charge lower price and vice-versa. Hence, the demand curve facing the
monopolist is negatively sloped, showing the inverse relationship between market price and
quantity demanded.
P
P1
dd
P2
Q
Q1
Q2
Fig.5.10 the demand curve of the monopolist
The demand curve facing the monopolist firm is down wards sloping. At price p1, the firm sells
only Q1 outputs. To sell more units of the product the firm should reduce its price.
The MR curve of monopolist firm is down ward sloping (decreases with quantity of sales). The
fact that the monopolist must lower the price to increase its sales causes the MR to be less than
price except for the first unit. This is so because when the firm reduces the commodity price to
sell one more unit all units which would have been sold at the original higher price will now be
sold at the new (lower) price. Note that the AR of a monopolist is always identical to the P or
demand curve.
In general, the MR curve of a monopolist firm is negatively sloped. The MR will be positive
over the elastic range of the demand curve (because TR is increasing over this range), zero when
the price elasticity of demand is unitary ( because the TR is at its maximum level) and will have
a negative sign over the inelastic range of the demand curve( because TR is decreasing). The
following figure illustrates the relationship between price elasticity of demand and MR
74 | P a g e
P
Ep>1
P1
Ep=1
Ep<1
DD
Q
MR
Fig: 5.11 The relationship between MR and P.
The MR of a monopolist lies below the commodity price for each unit sold (except the first unit)
and it is negative over the inelastic range of the demand curve. Mathematically, it can be shown
that MR is less (steeper) than the AR or demand curve.
Suppose a monopolist‟s demand curve is given by P = a – bQ
TR = P.Q = (a - bQ) = aQ – bQ2 hence MR 
dTR d (aQ  bQ2)

 a  2bQ
dQ
dQ
Thus, MR = (a – 2bQ) has a slope which equals twice the slope of demand (average revenue)
curves. This implies that MR is less than AR or demand or price.
Example 1
Consider that the monopolist firm faces a demand function which given as Q= 48-2P, then based
on the given find
a. Total revenue function
b. Marginal revenue function and
c. Price elasticity at Q=24
Solution
To find the solution for the above functions first we should convert the demand function which
given as a function of price to quantity.
75 | P a g e
Q = 48-2P  2P= 48 - Q P = 24-1/2Q
a. TR  P * Q  (24  1 / 2Q)Q  24Q  1 / 2Q 2
b. MR 
dTR d (24Q  1 / 2Q 2 )

 24  Q
dQ
dQ
As we can observe from the P and MR functions we can conclude that MR is less than P
except at zero level of output at which both of them becomes 24.
c. As we know e p 
Q P dQ P
* 
*
P Q dP Q
Therefore first we should find the value
dQ
and value of P at Q=24
dP
dQ d ( 48  2 P )

 2 and at Q=24, P=24-1/2(24) =24-12=12
dP
dP
ep 
dQ P
12
*  2 *
 1
dP Q
24
This means the price elasticity of demand is unitary.
5.6 Monopoly supply in the short run
Under Perfect competition, you remember that firms have unique supply curve. That is there is
unique supply price for each unit of output supplied. In monopoly supply price is not unique. A
given quantity could be supplied at different prices and different quantities can be sold at the
same price, depending on market demand and marginal revenue. Hence there is no one to one
correspondence between P and Q under monopoly.
76 | P a g e
P
MC
MC
P1
P
E1
P
E2
D
D1
Q*
MR1
D2 D1
D
Q
Q2
MR2
MR
Fig 5.12 supply curve of the monopoly
Panel-1
In this panel, the same quantity Q* is sold at
different prices depending on the market demand.
If the market demand is D1 and the MR curve is
MR1, equilibrium occurs when MR1 cuts MC
curve and the equilibrium price and quantity are
P1 and Q*. If the market demand for the
monopolist product decreases to D, the monopolist
can still sell the same quantity Q* by lowering the
price. So, there is no unique (or one to one
correspondence) between P&Q, as the same Q* is
matched with two different price, P&P1
Q1
MR1
Panel-2
In this panel, initially equilibrium is E1
(Where MR1=MC) and equilibrium P&Q1.
When the demand for monopolist product
decreases to D the new equilibrium becomes
E2 where the new MR2=MC. At the new
equilibrium, price is the same, but the
monopolist sell only Q amount of output i.e.
the monopolist sells lower quantity at the
original price when the dd decreases.
Therefore, there is no unique supply curve
under monopoly.
5.7 Short run and Long run Equilibrium of the monopolist
5.7.1 Short run and Long run Equilibrium
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Q
Profit maximization under monopoly involves determination of both price and output
combination that yields the firm the maximum possible profit. Price and output combination that
maximizes the monopolist profit can be determined in the similar fashion as that of the perfectly
competitive firm. That is, price- output combination that yields the monopolist the maximum
profit can be determined either using total approach or marginal approach
A. Total approach
In this approach the profit maximizing unit of output is defined as that level of output where the
positive difference between TR and TC is maximal or the negative difference between TR and
TC is minimal. The equilibrium price can be determined by dividing the TR corresponding to the
equilibrium output level to the equilibrium output.
B. Marginal approach
In this approach there are two condition of profit maximization. These are:
1) MC = MR. This means the slope of cost curve is the same as the slope of revenue curve.
2) Slope of MC is must be > slope of MR i.e. MC curve cuts MR curve from below.
P
MC
AC
G
Pm
A
A
A
H
E
MR
O
QQm
AR
=D
= dd
Q
Figure 5.13: Short-run equilibrium of the monopolist
At point E, MR=MC and MC cuts MR from below, and hence it is equilibrium point for the
monopolist. This equilibrium point determines monopoly output Qm. In order to determine
78 | P a g e
monopoly price, trace up through the equilibrium point to the demand or AR line to point G and
correspond to the price axis. Therefore, monopoly price is Pm.
Revenue R = P x Q = area of OQmGPm. and Cost C = AC x Q = area of rectangle OQmHA.
  R  C = area of rectangle AHGPm. The shaded area is, therefore, profit for the monopolist.
The monopolist may get a positive profit or incurred a loss depends on the value of AR and short
run AC at the equilibrium point. When AR>AC, the monopolist get a positive profit; if AR=AC
the firm get neither profit nor loss while if AR<AC, the firm incurred a loss.
Mathematically, the profit maximizing conditions are same to perfect competitive market:
MR = MC ………………………….. First order condition and
Slope of MC > slope of MR ---------- second order condition
Example 2
Suppose the monopolist faces a market demand function given by P=40-Q. The firm has a fixed
cost of Birr 50 and its variable cost is given as TVC=Q2
determine:
a) the profit maximizing unit of output and price
b) the maximum profit
Solution
Given:
p=40-Q, TFC=50 and TVC= Q2
a) equilibrium condition is MR=MC, and slope of MC>slope of MR.
TR=P.Q = (40-Q) Q =40Q- Q2
TC=TFC+TVC =50 + Q2
Now,
MR 
dTR d (400  Q 2 )

 40  2Q
dQ
dQ
MC 
At equilibrium MR=MC
40-2Q=2 →40=4Q → Q=10
Second order condition
dMC
dMR

dQ
dQ
MR 
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dMR
 2
dQ
MC 
dTC d (50  Q 2 )

 2Q
dQ
dQ
dMC
2
dQ
Slope of Slope of
Since both first and second order conditions are satisfied, the profit maximizing level of output is
10 units and the profit maximizing price is obtained by substituting the profit maximizing
quantity (10) in the demand function. .Hence, P = 40 – Q = 40 – 10 = Birr 30.
b) The maximum profit is the level of profit obtained from selling 10 units at Birr 30 each.
∏ = TR – TC But TR = P.Q = Birr 30 * 10 = Birr 30 and TC = 50 + Q2 = 50 + 102 = Birr 150
The maximum ∏ is thus Birr 300 - Birr 150 = Birr 150.
Example 3
Ethio-telecom is the sole provider of a telephone service in Ethiopia. The demand function for its
service is P = (8300 – Q)/2.1 and its total cost function is TC = 2200 + 480Q + 20Q2 where P is
price in Birr. Based on the given information, calculate the maximum possible profit that the
monopolist can achieve.
Solution
The corporation will maximum its profit when MC = MR
Total Revenue (TR) = Price x Quantity = (8300–Q)/2.1*Q = 3952Q – 0.476Q2
MR 
dTR d 3952Q  0.476Q 2

 3952  0.952Q
dQ
dQ
MC 
dTC d (2200  480Q  20Q 2 )

 480  40Q
dQ
dQ
At profit maximizing point MC = MR
480 + 40Q = 3952 – 0.952Q 40.952Q = 3472  Q = 84.8
At Q = 84.8, P = 3952 + 0.476(84.8) = 3,912. Thus the price should be Br. 3912.
The firms monthly profits () is given by TR – TC
= 80(3,914) – [2200+480(80) +20(80)2] = Br.144520.
Therefore the maximum profit that the monopolist can achieved will be 144,520 Birr.
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5.7.2 Long – run Equilibrium under Monopoly
The monopolist‟s long run condition is different from the perfectly competitive firms‟ long run
situation in respect of the entry of new firms into an industry. In perfectly competitive market,
there is free entry in the long run. Nevertheless, entrance is barred by several factors in
monopoly. Moreover, we have seen that a perfectly competitive firm can earn only normal profit
in the long run. The monopolist firm can, however, get a positive profit even in the long run
because there are entry barriers that discourage new firms to enter to the industry.
A monopolist maximizes its long run profit when it produces and sells that output level where
LMC = MR , slope of LMC being greater than the slope of MR at the point of intersection, and
the optimal plant size is the one whose SAC curve is tangent to the LAC at the point
corresponding to long run equilibrium with price and quantity of Pe and Qe respectively.
SMC1
P1
LAC
SMC2
LMC
SAC1
Pe
SAC2
DD
MR
Q
Q1
QE
Fig 5.14 Long run Equilibrium of the Monopoly Firm
Finally, it should be noted that there is no certainty in the long run that the monopolist will reach
the optimal plant size (minimum LAC), as in perfectly competitive case. The monopolist may
reach optimal plant size or even may exceed the optimal size if the market demand allows him
(or if there is enough demand which absorb that level of output).
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5.8 The multi- plant monopolist
We have seen that a monopolist maximizes its profit by producing that level of output where MR
equals MC. For many firms, however, production takes place in two or more different plants
whose operating costs can differ. To minimize transport cost, to approach the consumers or for
different reasons a monopolist may establish more than one plant in different areas. The
operating costs of these plants can also vary due to many reasons such as variation in prices of
raw materials, wage of labors etc. we call such firm a multi-plant monopolist.
In short, the condition of equilibrium in multi- plant monopolist is: MR = MC of multi plant
monopolist and to allocate the total output among each plant, the condition must satisfy:
MC1 = MR = MC or MC2 = MR = MC of multi plant monopolist. In short it can be given as
MR = MC1 =MC2
Example 4
Suppose Ethiopian Electric Light and Power Corporation (EELPC) is a multi-plant monopolist
having two plants, Tekeze plant (plant1) and Fincha plant (Plant2). The operating costs of the
two plants are given as follows:
Plant 1: TC1 = 10 Q12 and
where Q1 - Amount of electric power produced in Tekeze
Plant 2: TC2 = 20 Q22
Q2 – amount of electric power produced in Fincha
EELPC estimates the demand for electric power by the following function i.e. P= 700 – 5Q
where P - is price (total in million birr) per Giga watt and
Q – is the total amount of Giga watt sold and Q = Q1 + Q2
Note that a Giga watt of electric power, whether it comes from Fincha or Tekeze plant worth
equal price, based on the given answer the following questions accordingly
a) What level of output (electric power) should EELPC produce and what price per Kilowatt
should it charge to maximize its profit?
b) How much of the total output should be produced in each plant?
Solution
a) The equilibrium condition is:
MR = MC1 and MR = MC2
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TR = P.Q = (700 – 5Q) Q = 700Q-5Q2
MR =
dTR
= 700- 10Q, where Q = Q1+Q2. Thus, MR = 700 – 10 Q1 – 10 Q2
dQ
MC1 =
dTC1
dTC 2
= 40 Q2
 20Q1 and MC2 =
dQ2
dQ2
Now the equilibrium occurs when:
700 – 10Q1- 10Q2 = 20Q1 and
700 – 10Q1 – 10Q2 = 40Q2
Re-arranging the above equations we get the following simultaneous equation.
30Q1 + 10Q2 = 700 and 10Q1 + 50Q2 = 700
Solving the above equations simultaneously, we get
Q1 = 20 giga watts and Q2 = 10 giga watts
The profit maximizing level of output is, thus, Q1+Q2 = 30 giga watt
To determine the equilibrium price we substitute the total output (30) in the demand function:
Accordingly, P = 700 – B (30) = 550 mill birr
b) The Tekeze plant should produce 20 giga watts and Fincha plant should produce 10 giga watts
5.9 Price Discrimination
Price discrimination refers to the charging of different prices for the same good. But not all price
differences are price discrimination. If the costs of offering a certain uniform commodity
(service) to different group of customers are different (say due to difference in transport costs),
price of the commodity may differ for each group owing to this cost difference. But this cannot
be considered as price discrimination. A firm is said to be price discriminating if it is charging
different prices for the same commodity without any justification of cost differences. By
practicing price discrimination, the monopolist can increase its total revenue and profits.
Necessary conditions for price discrimination
1- There should be effective separation of markets for different classes of consumers, so
that buyers of low price market cannot resale the commodity in high price market.
A market is said to be effectively separated if one of the following points is met:
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 Geographical variation with high transport cost so that the inter market price margin is
unable to cover the transport expense. E.g. Domestic Vs international markets.
 Exclusive use of the commodity. For some services resale is inherently difficult. For
example you cannot resale Doctor‟s services, Entertainment shows.
 Lack of distribution channels
2- The price elasticity of demand should be different in each sub market.
 For example, a movie theatre knows that college students and old people differ in their
willingness to pay for a ticket and can exercise discrimination by charging the college
students a higher price.
3- Lastly, the market should be imperfectly competitive.
 The seller of the product should have some monopoly power (it should not be price taker)
to practice price discrimination.
Degrees (types) of price discrimination
The degree of price discrimination refers to the extent to which a seller can divide the market and
can take advantage of it in extracting the consumer Surplus. In economics literature, there are
three degrees of price discrimination. These are discussed one by one here under.
5.9.1 First degree price discrimination (Perfect price discrimination)
This is a price discrimination in which the monopolist attempts to entirely take away the
consumers surplus. Ideally, a firm would like to charge each customer the maximum price that
the customer is willing and able to pay for each unit bought. We call this maximum price the
consumer‟s reservation price and obviously, the consumers‟ reservation prices are different due
to the differences in their economic status or the value they attach to a commodity. Note that the
consumer‟s willingness to pay reservation price for a given commodity varies with the quantities
of the commodity the consumers own. The LDMU implies that a consumer‟s willingness to pay
for successive units of a commodity declines because the marginal utilities of these successive
units decline. Hence, in the first degree price discrimination differs across customers and a given
customer may pay more for the initial units than for others (successive units).
First degree price discrimination is the limiting case of price discrimination, the monopolist, in
this case, individually negotiate with each buyer and sell each unit of the output at the
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corresponding price given on the demand curve of the consumer, then receiving the entire of
consumer‟s surplus.
For example, a doctor who knows his patients’ paying capacity charges high price for the
richest patients’ and low price for the poor patients for identical services. This is practiced to
increase revenue. If the doctor fixes the price at the richest patients’ level, no poor will
afford to pay and the doctor will not get revenue from the poor. On the other hand, the
doctor would not fix the price at the poorest patients’ level for all patients because he
knows that the rich can pay more and he will exploit the rich. Lawyers also practice the
same discrimination for identical legal service.
Perfect price discrimination is efficient as it maximizes the total welfare, where welfare is
defined as the sum of consumer surplus and producer surplus. That is, there is no welfare loss
associated with first degree price discrimination equilibrium. The problem with perfect price
discrimination is that it hurts consumers because the monopolist will take the entire of the
consumer surplus. The other problem with perfect discrimination is that it involves high
transaction costs; it is too difficult and costly to gather information about each customer‟s price
sensitively.
5.9.2 Second degree price discrimination (block pricing)
Many firms are unable to determine which customers have the highest reservation prices. Such
firms may know, however, that most customers are willing to pay more for the first unit than for
successive units. This is due to the fact the typical customer‟s demand curve is down ward
sloping. Such a firm can discriminate price by letting the price each customer pays vary with the
number of units the customer buys. The act of charging different prices for different quantities of
purchases is called second degree price discrimination or sometimes called quantity
discrimination. In second degree price discrimination, the price various only with quantity: all
customers pay the same price for a given quantity. In second degree price discrimination, the
monopolist attempts to take the major part of the consumer surplus instead of the entire of it.
Block pricing can feasibly be implemented where:
 The number of consumers is large and price rationing can be effective
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 The demand curves of all customers are identical and
 A single rate is applicable for a large number of buyers.
Graphically, block pricing can be explained as follows:
A monopolist that practices second degree price discrimination charges the price OP1, for the
first OQ, units, OP2 for the next Q1 Q2 units and OP3 for Q2 Q3 units. By doing so, the
monopolist will increase its total revenue by extracting the major part the consumer surplus.
P
P1
A
B
P2
P3
C
DD
Q1
Q2
Q3
Fig.5.15 Second price degree price discrimination.
The monopolist receives a price OP1, for each unit sold to a given customer for the first OQ,
units, OP2 for the next Q1 Q2 units and OP3 for the next Q2 Q3 units. By so doing, the
monopolist will receive total revenue of OP, A B C . If the monopolist charges a uniform price of
OP3, its total revenue will only be OP3 EQ3. Hence, block pricing will enable him receive large
total revenue than uniform pricing.
Note that not all quantity discounts are a form of price discrimination. Sometimes selling in large
quantities may reduce the unit costs of sales and as a result a firm may charge a relatively lower
per unit price for large sales than small sales. Such an action cannot be regarded as price
discrimination.
5.6.3 Third degree price discrimination (multi-market price discrimination)
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An action of charging different prices in different markets is called third degree price
discrimination. All units of the good sold to customer with in a group (in one market) are sold at
a single price, but prices will differ among the different groups or markets.
For simplicity, let us assume that there are only two markets. To maximize profits, the
monopolist must produce the level of output (defined by MC=MR) and sell that output in the
two markets in such a way that the marginal revenue of the last unit sold in each market is the
same. This will require the monopolist to sell the commodity at higher p rice in the market with
the less elastic demand. The equilibrium condition for a third degree price discriminating
monopolist is: MC=MR1=MR2.
Example 5
Suppose Ethiopian Airlines (EAL) flies only one route: from Addis Ababa to Dubai. EAL knows
that two different types of people fly to Dubai. Type A consists of rich merchants flying to Dubai
for business purposes with demand for flight of
QA = 260-0.4PA. Type B consists of poor ladies flying to Dubai in search of jobs ( such as house
maid) whose total demand is QB = 240-0.6PB.
Assume that EAL has a running cost of $30,000 plus $100 per passenger and it has decided to
charge different prices for the two groups of passengers.
a. How many tickets should EAL sell to each group?
b. How much price should EAL charge each group?
c. Suppose now that EAL is prohibited by the Ethiopian government to exercise such
discrimination. How many tickets should the EAL sell to maximize its profit and at what price?
Solution
Given
TC = 30,000 + 100Q
Where Q = QA+QB
QA = 260 – 0.4PA PA = 650 – 2.5QA………..…. Merchants inverse demand function:
5
QB = 240 – 0.6 PB. PB  400  Q B …………….Ladies inverse demand function
3
a) The equilibrium condition is that
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MC=MRA = MRB But MC =
MRA =
dTC
 100
dQ
then we should find MRA and MRB
dTRA
, and TRA = QA.PA = 650QA – 2.5 Q 2A
dQ A
Thus, MRA = 650 – 5QA. Likewise MRB = 400 -
10
QB
3
The equilibrium condition is thus presented as:
100 = 650 – 5QA and 100 = 400 -
10
QB
3
Solving the above equations simultaneously, we get QA = 110 and QB = 90
Therefore, EAL should sell 110 tickets of A type and 90 tickets of B type passengers.
b) Substituting the above quantities in their respective demand functions, we get
PA = 650 – 2.5 QA = 650 – 2.5 (110) = $ 37 and PB = 400 -
5
5
QB = 400 - (90) = $ 250
3
3
Hence, the EAL should charge $ 375 for the merchant and $ 250 for the leady passengers.
C) If EAL decides to charge a uniform price, the equilibrium price will be obtained first by
deriving the market demand function and then by using the usual method (MC = MR)
Market demand (Q) = QA + QB  Q = 260 – 0.4 PA + 240 – 0.6 PB
Since PB = PA = P, thus the market demand becomes = 500 – P or P = 500 – Q
TR = P.Q = 500 Q – Q2 hence MR = 500 – 2Q
Given MC = 100, Equilibrium occurs when MC = MR, i.e.
100 = 500 – 2Q Q = 200, and P = 500 – Q = $300
That is, EAL should sell 200 tickets at a price of $ 300 each to maximize its profit.
5.10 Social costs of monopoly: The dead weight loss
In a competitive market, price equals MC of production. Monopoly power, on the other hand,
implies that price exceeds MC. Because monopoly power results in higher prices and lower
quantities produced, we would expect it to make consumers worse off and the firm better off.
Consider the following figure. Suppose DD represents the market demand curve, MR represents
the corresponding marginal revenue. Here, we use consumers‟ and producers‟ surplus as a
measure of welfare of each. Consumer surplus is the area between the demand curve and
88 | P a g e
equilibrium price and producer surplus is the area between the equilibrium price and marginal
cost curve.
A perfect competitor‟s equilibrium occurs when MC = P= MR at Ec with PC &QC. Here
-
the consumer‟s surplus is the area above the dropped line Pc Ec and below the demand
curve i.e. area of the rectangle Pc F Ec while producer‟s surplus is area below the
dropped line PcEc and above the MC curve.
-
A monopolist equilibrium occurs when MC = MR i.e. at Em with Pm and Qm
respectively. Hence, in monopoly lower quantity is sold at higher price. The new
consumers‟ welfare is the area above the dropped line PmD and below the demand curve
(i.e. area of the rectanglePmFD) whereas the producers surplus becomes the area below
the dropped line PmD and above MC curve to the left of Qm (i.e. the area GPm
p
F
41 = pm
Dead
weight
loss
D
MC
A
B
25 = pc
Ec
Em
C
DD= Price = MR (for perfect competitor)
G
Em
MR
0
Qm
Qc
6
10
Q
Fig.5.16 the Dead Weight Loss of the Monopolist
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Thus monopoly power reduces the consumers‟ surplus by the amount which equals area A+B.
But increases the producers‟ surplus by the area A-C. The net welfare effect (loss) is obtained by
deducting the welfare loss of consumers from the welfare gain of producers i.e
Net welfare = Welfare gain by producers – Welfare loss by consumers
= A-C – (A+B) = A-C – A-B = -C –B or – (C +B)
Thus monopoly results in a welfare loss which is given by the area (C+B). This area is called
dead weight loss. It is gained neither by producers nor by consumers. The other disadvantage
(Social cost) of monopoly is that is discourages innovations. Monopolist may feel secure and
have no incentive to innovate new product (technology) since there are no competitors.
5. 11 Monopolistic Competitions
5.11.1 Assumptions monopolistic Competitive
Monopolistic competition is a market structure with many buyers and sellers in which product
differentiation exists and in which there are elements of both monopoly and perfect competition.
Assumptions of Monopolistic Competition
Chamberlin‟s model of monopolistic competition works under many of the assumptions of pure
competition.
1. There are large number of sellers and buyers in the group
2. The products of the sellers are differentiated, but they are close substitutes of one another.
3. There is free entry and exit of firms in the group.
4. The goal of the firm is profit maximization.
5. The prices of factors and technology are given.
6. The firm is assumed to behave as if it knew its demand and cost curves with certainty.
7. The long run consists of a number of identical short run periods, which are assumed to be
independent of one another, in the sense that decisions in one period do not affect future
periods and will not be affected by past decisions. The optimum decision for one period
is the optimum decision for any other period.
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8. Heroic Assumptions – Both demand and cost curves of all products are uniform
throughout the group. This requires that consumer’s preference be evenly distributed
among the different sellers, and that differences between the products be such as not to
give rise to differences in costs. This assumption is made in order to be able to show the
equilibrium of the firm and the group on the same diagram. But this assumption leads to
a model that is very restrictive, because it excludes the inclusion of the firm in the group
which has similar products but different cost of production.
5.11.2 Product Differentiation, Demand and Cost Curve
Product differentiation is any feature of a product of sellers that makes buyers to prefer one
product or sellers to that of another. It leads to different consumer‟s preference. It is also the
basis for establishing a downward sloping demand curve. Chamberlin suggested that the demand
for a product is not only determined by the price – but also by the style of the product, the
services associated with it and the selling activities of the firm. Thus, Chamberlin introduced
two additional policy variables in the theory of the firm: the product itself and selling costs.
Hence, the demand curve shifts if:
1. The style, services, or the selling strategy of the firm changes,
2. Competitors change their price, output, services or selling policies of a product;
3. Tastes, incomes, prices or selling policies of products from other industries change.
Product differentiation is intended to distinguish the product of one producer from that of the
other producer in the „industry‟ (in the group).
It can be real differentiation or fancied
(artificial) differentiation. Real differentiation: exists when the inherent characteristics of the
products have slight differences (slight difference in quality, durability), in the specification of
products (terms of credit, transportation, guarantee, location of the firm), which determine the
convenience with which a product is accessible to the consumer. Example: chemical differences
existing in shampoos or conditioners. On the other hand, fancied differentiation is established by
advertising or differences in packaging or differences in design (color or shape) or simply by
brand name. Product differentiation leaves firms under monopolistic competition with some
degree of monopoly power. Because of this the firm is not a price – taker.
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Panel B
DD curve for a monopoly
firm and the industry
Panel A
DD curve for a firm
In perfect comp. mkt
P
Panel C
DD curve for a firm in
monopolistic comp mkt
P
d curve
P
d curve
Q
d curve
Q
Q
Figure 5.17 demand curves of different market structures
Cost structure of a firm under monopolistic competition is similar to that of any other firm
(perfectly competitive and monopoly firm). The AVC, MC, ATC are all U-shaped implying that
there is only single level of output which can be optimally produced. There is another cost, the
cost of selling activities, which is introduced in the theory of the firm by Chamberlin. The
recognition of product differentiation provides the rationale for the selling expenses incurred by
the firm. With advertising and other selling activities the firm seeks to differentiate more his
product from the products of other firms in the group. Chamberlin assumes that advertising will
shift the demand and will make the demand less elastic.
Total cost = Production cost + Selling cost.
Like any other costs the average selling cost is U-shaped. That means there are economies and
diseconomies of selling cost as output increases.
Cost
Average Selling Cost Curve
o
Q
Figure 5.18 selling cost of monopolistic competitive firm
Initially, expansion of output will not require an equi-proportional increase in selling costs, and
this leads to a fall in the average selling expenditure. However, beyond a certain level of output,
the firm will have to spend more per unit in order to attract customers from other firms this
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makes the average selling cost to be U shaped. The U shaped average selling cost, added to U
shaped average production cost, yields a U shaped ATC curve.
5.18 The Concept of Product Group and Industry
In perfectly competitive market, firms included in an industry are easy to determine because they
all produce same product.
But product differentiation creates difficulty in the analytical
treatment of the industry.
Strictly speaking, firms under monopolistic competition do not
constitute an industry because they produce differentiated products.
PRODUCT GROUP: It refers to a group of sellers in an industry, supplying different brand of
commodities or services, but are very much (closely) related and hence consumers are unable to
differentiate them based on some state of quality, such as shape, test, colour etc. For instance, within
automobile industry cars with brand name Fiat and Lada, Corolla DX and Toyota DX are alike in
their shape many people cannot differentiate them precisely simply by looking them distant without
getting close and search for some clues, such as looking at their brand names.
Chamberlin uses the concept of „product group‟, which includes products which are „closely
related‟. The products should be close technological and economic substitutes. Technological
substitutes are products which can technically cover the same want. For example, Motor cars
are all used for transportation, all powder soaps are used for washing purpose. On the other
hand, Economic substitutes are products which cover same want and have similar prices.
Products with different cost structure are not economic substitutes.
INDUSTRY: The concept industry refers to broader classification and hence consists of several
product groups. If all firms in a monopolistic competition market produce very close products as the
brewery industry or supply very close service as the banking and insurance industry in Ethiopia all
the firms in can be regarded as product group and industry. On the other hand, if all firms in an
industry produce highly differentiated products, we say there is no product group. Thus, product
group is a sub set of industry.
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5.19 Equilibrium of Monopolistic Competitive Firms
5.19.1 Short Run Equilibrium
The short run MR (derived from the perceived demand curve) that will be equated with the MC
curve in order to find the optimal-profit maximization (loss minimization)-output and price and the
MC curve must be rising..
Numerical Example 1
Assume a firm engaging in selling its product and promotional activities in monopolistic
competition face short run demand and cost functions as Qd=20-0.5P and TC= 4Q2-8Q+15,
respectively. Having this information
A. Determine the optimal level of output and price in the short run.
B. Calculate the economic profit (loss) the firm will obtain (incur).
C. Show the economic profit (loss) of the firm graphically.
Solution
B.∏=TR-TC or Q (P-ATC)
A. Q=20-0.5P
Q-20= -0.5P
= (40Q-2Q2) – (4Q2-8Q+15) or 4(32-11.75)
*P=40-2Q
=(40(4)-2(4) 2) - (4(4) 2-8(4)+15) or 4(20.25)
TR=PQ
= (160-64) – (64-32+15) or 81
= (40-2Q) Q
=128 - 47 or 81
2
=40Q-2Q
MR=
=81=81
dTR
= 40-4Q
dQ
TC=4Q2-8Q+15
TC
MC=
=8Q-8
Q
MR=MC
40-4Q=8Q-8
P
MC
ATC
32
24
Q=20-0.5P or P=40-2Q
11.75
MR=40-4Q
48=12Q
Q=4
*P=40-2Q
P=40-2(4)
94 | P a g e
4
Q
C. Graphical illustration of economic profit of the firm
P=40-8=32
5.19. 2 LONG RUN EQUILIBRIUM
In order to be able to analyze the equilibrium of the firm and of the industry on the same diagram
Chamberlin made two „heroic assumption‟, namely that firms have identical costs, and
consumers‟ preferences are evenly distributed among the different products. That is, although
the products are differentiated, all firms have identical demand and cost curves. Under these
assumptions the price in the market will be unique.
Chamberlin develops three models of equilibrium.
Model 1: Equilibrium with new firms entering the industry
Assumption: Each firm is in short run equilibrium with excess profit.
The firm in the short run is in equilibrium at point C where MC = MR. See the graph above. At
equilibrium point a given firm attains abnormal profit, area of PmCBA. The excess profit
attracts firms to come in to the market with competing brands. The result of new entry is a
downward shift of the demand curve dd‟, since the market is shared by a larger number of
sellers. The process will continue until the dd‟ curve is tangent to the average cost curve at its
equilibrium. i.e. until the abnormal profit is eliminated and excess profit is wiped out. In the
final equilibrium of the firm, the price will be Pe and the ultimate demand curve will be dd‟. In
the long run the equilibrium occurs at P=LAC, at this point there will be neither entry nor exit,
and the equilibrium is stable.
95 | P a g e
LMC
d
d
Pm
Pe
A
C
LAC
E
B
d‟
Qe Qm
d
Q
MR2
MR1
Figure 5 .19 Long-run Equilibrium Monopolistic competitive firms with price competition
Model 2: Equilibrium with price competition
In this model, the number of firms in the industry is assumed to be compatible with long run
equilibrium, so that neither entry nor exit will take place. But the ruling price in the short run is
assumed to be higher than the equilibrium price.
The analysis of this case is done by the introduction of a second demand curve, labeled DD‟,
which shows the actual sales of the firm at each price after accounting for the adjustments of the
prices of other firms in the group. DD‟ is sometimes called actual sales curve or share of the
market curve. It is a locus of points of shifting dd curves as competitors change their price.
96 | P a g e
Assume the firm is at a non-equilibrium position Po and Xo. The firm, in an attempt to
maximize its profit, lower the price to P1 expecting to sell X 'o . This level of sales is not actually
realized because all other firms faced by the same demand and cost condition have an incentive
to act in the same way simultaneously. Thus, all firms acting independently reduce their price
simultaneously to P1. As a result, the dd curve shifts downward and the firm instead of selling
expected quantity X 'o sales actual quantity X1 (whish is less than the expected quantity)on the
shifted dd curve dd‟ along the share curve DD.
Actual Sales curve or share of the Market Curve
d
D
P0
LMC
d|1
P1
d||1
LAC
P2
d|||e
d
d|1
Pe
d||1
D
d|||e
e
Q
X0 X1X2Xe
MR Xol
Figure 5.20Long-run Equilibrium with price competition
According to Chamberlin, the firm suffers from myopia and does not learn from past experience
and may further reduce price expecting that the others will not react. Thus the firm lowers its
price again in an attempt to reach equilibrium, but instead of the expected sales Xo, the firm
achieves actual sales of X2, because all other firms act identically, though independently. The
97 | P a g e
process stops when the dd‟ curve has shifted so far to the left as to be tangent to the LAC curve.
Equilibrium is determined by the tangency of d|||e d|||e and the LAC. At the point of tangency the
DD curve cuts the d|||e d|||e curve. Obviously it will pay no one firm to cut the price beyond that
point, because its costs of producing the larger output would exceed the price at which this
output could be sold in the market.
Model 3: Equilibrium through Entry and Price Competition.
D|
D*
D
LMC
d
P
e2
C
A
d|
P1
B
d*
e1
LAC
d||
d
P*
E
d|
D
D|
D*
d*
d||
X X1 X2
X*
MR*
Q
Figure 5.11 Long-run Equilibrium with Entry and Price Competition
Chamberlin suggests that in the real world adjustment towards long run equilibrium takes
place through both entry/exit and price competition. Price adjustments are shown along
the dd| curve while entry/exit cause shifts in the DD‟ curve. Equilibrium is stable if the
dd| curve is tangent to the AC curve and expected sales are equal to actual sales, i..e, DD |
curve cuts dd| curve at the point of tangency of dd‟ & LAC.
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Let‟s start from e1 where there is an abnormal profit. This excess profit attracts other firms to
enter into the market. When they enter in to the market, the market will be shared by larger
number of firms then DD (market share curve) keeps on shifting left ward until it becomes
tangent to LAC.
Although, firms earn normal profit, e2 does not constitute stable equilibrium, because the firm
believes that dd is its demand curve. By taking dd as its sales planning function the firm will feel
that it can expand sales and earn excess profit by reducing price to P1. But all the firms will be
doing the same thing simultaneously. As price is reduced by all firms demand shifts down to d |d|
and each firm realizes a loss of area CABP1 instead of positive profit.
The firm is still in myopia assumption, now also he believes that he can obtain positive profit by
cutting its price. However, all the firms do the same. One might think that the process would
stop when dd becomes tangent to the LAC, dd*. This would be so if the firm could produce X*.
However, there are so many firms and the share of the firm is only X2. The frim still on the
myopia assumption believes that it can reach X* if he reduces to P*. However, all firms do the
same and dd* falls below the LAC with ever increasing losses. At this time, the financially
weakest firms will leave the market. So that the surviving firms will have a higher market share
then DD| will move to the right with dd | . Exit will continue until the dd becomes tangent to the
LAC curve and the market share curve, DD, cuts the dd curve at the point of tangency, point E.
Equilibrium is then stable at point E with normal profits earned by all firms and no entry or exit
taking place. The equilibrium price is P*, which is unique and each firm have a share equal to
OX* at E, expected share is equal to actual sale.
CRITICISM OF CHAMBERLIN’S LARGE GROUP MODEL
1. The assumption of product differentiation is incompatible with the assumption of
independent action and free entry.
2. It is hard to accept the myopic behavior of business men implied by the model. For sure
some firms learn from their past mistakes.
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3. The concept of industry was destroyed by the recognition of product differentiation.
Heterogeneous products can not be added to give industry.
4. The model assumes large number of firms & high cross price elasticities among the
products in the industry but the model does not objectively define the number of firms
and the magnitude of elasticity required to have monopolistic market structure.
Despite his critics chamberlin‟s contribution to the theory of pricing are:
a) Introduction of product differentiation and selling strategy as two additional policy
variables in the decision process of the firm. These factors are the basis for the non price
competition which is a typical form of competition in the real world.
b) Introduction of the share of the market demand curve as a tool of analysis.
5.20 Excess Capacity and Welfare Loss
Under perfectly competitive firm MC = MR = LAC = P = AC at the minimum point of LAC and
resources are efficiently allocated. On the other hand, under monopolistic competition MC = MR
and P = AC, but P > MC (because P > MR). As a result price will be higher and output will be
lower in monopolistic competition as compared to the perfectly competitive market.
In monopolistically competitive market structure there are too many firms in the industry each
producing less than the optimal (at a higher cost) because of
1. The tangency of the long run average cost and demand occurs at the falling point of the
average cost curve.
2. Firms incur selling cost which is not presented in perfectly competitive market structure.
Therefore, firms in monopolistically
competitive market have an excess capacity
measured by the difference between the ideal output (YF) corresponding to the minimum
cost level on the LAC curve and the output actually obtained in the long run (YE).
100 | P a g e
P
LMC
d
Excess
Capacity
PE
LAC
PF
d
YE
MR
YF
Y
Figure 5.21 Monopolistic Competitive Excess Capacities
Chamberlin argues that the excess capacity and misallocation of resources is valid only if one
assumes that the demand curve of each individual firm is horizontal. If demand is downward
sloping and firms enter into active price competition and entry is free in the industry. YF cannot
be considered as a socially optimal level of output. Consumers desire a variety of products. And
product differentiation reflects the desire of consumers to pay higher price for differentiated
product. Therefore, the difference between the actual output YE and the minimum cost output YF
is not a measure of excess capacity but rather a measure of the “social cost of producing and
offering the consumers a greater variety of output.”
D|
P
D
d
D|
LAC
D
Y
YE YF
Excess Capacity Social Cost
Figure 5.22 chamberlain’s Excess Capacity
101 | P a g e
d
Y
Chamberlin‟s argument is based on the assumption of active price competition and free entry.
He argues that the equilibrium output will be very close to the minimum cost output, because
firms will be competing along their individual dd curves which are very elastic.
Chamberlin divides the competition into two, price and non-price competition. If firms avoid
price competition and instead enter into a non-price competition there will be an excess capacity
in each firm and inefficient product capacity in the industry and that is an inexhaustible economy
of scale for the firms in the industry. Chamberlin argues “excess capacity in monopolistically
competitive market structure comes because of the non-price competition coupled with
free entry”. Excess capacity is the difference between YE and Y shown in figure 6.8 above.
102 | P a g e
5.21 Price and Output Determination under Oligopoly Market
Introduction
Definition
The term oligopoly has been derived from Greek words, oligo meaning ‘few’ and polein meaning
‘sellers’ from this; oligopoly means a market with few sellers. Oligopoly can synonymously be
used for competition among few firms. Markets are said to be oligopolistic whenever a small
number of large firms supply the dominant share of an industry‟s total output. How few should
be the sellers' to make an industry or market oligopolistic is not easy to define numerically. It is
rather difficult task to fix a definite number of sellers for the market to be oligopolistic in its
form. The number of sellers depends on the size of the market. Given the size of the market, if
number of sellers is such that each seller has command over a sizable proportion of the total
market supply, then there exists oligopoly in the market.
Firms in an oligopoly market trade products that may be identical/homogenous or
differentiated/heterogeneous. If the firms in an industry produce a standardized or identical
product the industry is called pure oligopoly. The most common examples of virtually uniform
products marketed under conditions of oligopoly include steel, aluminum, cement, fuel oil, etc. If
a few firms dominate the market for differentiated product, the industry is called a differentiated
oligopoly. The most visible differentiated oligopolies involve the production of automobiles,
tooth paste, cereal, cigarettes, TV sets, computers, refrigerators, soft drinks, beer, etc.
In oligopoly market entry is difficult or impossible for new firms to the market. Barrier to entry
may arise as a result of
1. Scale of economics and large capital requirement than other markets except monopoly,
2. Patents or access to technology or raw materials may exclude potential competitors,
3. Pricing and advertizing strategies of firms and the like
DUOPOLY is a special case of oligopoly in which there are only two firms in the industry. The
duopoly case allows as capturing many of the important features of firms engaging in strategic
103 | P a g e
interaction without the notational complication involved in models with a large number of firms.
Also, we will limit ourselves investigation of the case in which each firm is producing an identical
product. This allows us to avoid the problems of product differentiation and focus only on strategic
interaction.
If one firm reduces its price it will attract consumers and increases its sells, leading to a substantial
loss of sales by other firms in the industry. The other firms may or may not reduce their price, but
the firm that reduces price can no longer assume other firms do not notice his/her action. The
outcome of his/her decision depends on the reaction of other firms. The outcomes (consequences) of
price changes by the firm under consideration are uncertain. Firm under oligopoly market may
1. Spend a lot of time to guess each other‟s action or reaction
2. Be bitter rivals of each other, competing by price changes (price war may be started)
3. Tacitly (informally or implicitly) agree to compete by advertising but not by price changes
4. Form a collusion or cooperation (some kind of agreement) rather than competing. Therefore,
there are many solutions to oligopoly problem. This means that there is no unique solution
like that of perfect competition, Monopoly and monopolistic competition.
The Distinguishing Features of Oligopoly
So as to enrich your understanding of what oligopoly means let us discuss the distinguishing
features of oligopolistic market from other markets as follows:
1. Keen competition: - The fact that there are only few sellers in the market brings the
firms (oligopolies) in to keen competition. Under oligopoly, the number of sellers is so
small (or few) that any move by one seller immediately affects the rival sellers. As a
result each firm is curious enough about the acts of the rival firms in order to react in an
aggressive or defensive way. To an oligopolistic business is „constant struggle of life‟
that urges action and reactions or moves and counter moves. Such kind of competition is
not found in the other forms of market. So, fierce (keen) competition is key
characteristics of the oligopoly market structure.
2. Interdependence: - Each firm closely and carefully watches the moves of its rival firms‟
as it is affected by the competing firms‟ act. So, a typical firm‟s decisions are
interdependent with the decision of other firms since the typical firm knows that its
decision (action) results in reaction.
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One of the characteristics of oligopolistic market structure, which is interdependence among the
firms, makes the behavior of the firms uncertain or unpredictable. Hence, it becomes extremely
difficult to formulate model that could explain the behavioral pattern of oligopolistic firms.
Under the oligopoly market, various behaviors can be observed that some firms collude to
undertake optimum decision regarding price and output setting. While some act independently
without collusion and in some other cases the collusion may not last long and some other
situations. Thus, we find no nice, neat and clear-cut equilibrium position toward which all firms
tend to move-just like we find for the previously discussed market structures: perfectly
competitive, monopoly, and monopolistic competition. Accordingly, our survey of the oligopoly
will consist a series of models developed by various economists based on different behavioral
assumptions and competitive conditions.
Types of Oligopoly Market
A. Non-Collusive Oligopoly: here firms do not enter in to any form of collusive agreement.

The Cournot‟s Duopoly model (1838)

The Kinked demand (Sweezy‟s) model (1839)

The Stackelberg‟s model (1920)

The Bertrand‟s Duopoly model (1883)
B. Collusive Oligopoly: here firms enter in to collusive

Cartels

Price leadership.
5.22 Non Collusive Oligopoly
5.22.1 The Kinked Demand Curve Model
This model developed by Paul M. Sweezy in his analysis of price stability in oligopolistic
market. The kinked demand curve model seeks to establish that once a price-quantity
combination is determined, an oligopoly firm will not find it profitable to change its price even
in response to the small changes in the cost of production. The kinked demand curve model
developed to explain why prices often remain stable in oligopoly markets, even when costs rise.
105 | P a g e
Consider a firm in an oligopolistic market structure which behaves that:
1. If it raises price above the ongoing market price, none of its rivals will follow suit. But, the
firm will lose a considerable part of its consumers. Hence, the demand curve confronting the
firm is very elastic above the ongoing price.
2. If it reduces its price, its competitors will follow suit, matching the price cut. That is to say
all rivals will reduce their prices. So the share of the competitors in the market demand
remains unchanged. Therefore, for price reduction below the ongoing market price, the
relevant curve for decision making is the proportional demand curve (D).
In short, oligopolies rivals will ignore a price rise and follow a price cut. This in turn cause
1. The oligopoly‟s DD curve to be kinked. That is CED.
2. His/her MR curve to have a vertical break or gap.
3. Furthermore, since any shift in MC between MC1 and MC2 will cut the vertical segment
(dashes) of the MR curve, no change in either Pk or Qk will occur.
P
C
MC1
E
MC2
Pk
A
d
D
B
Qk
MR
Q
Figure 5.23: The kinked demand curve in oligopoly market
The equilibrium of the firm is defined by the kink because at any point to the left of the kink, MC
lies below MR which implying output must increase while to the right of the kink, MC lies above
MR implying output must decrease. Thus, total profit is maximized at the point of the kink by the
intersection of d and D curves at point E.
106 | P a g e
The discontinuous segment AB on the MR curve implies that there is a range within which cost may
change without affecting the equilibrium price (Pk) and output (Qk) of the firm. So long as the MC
passes through the segment AB the firm maximizes profits by producing Qk and selling at Pk.
Hence, oligopoly price is said to be very sticky, changing only infrequently (rarely).
The kinked demand model has the following limitations;
1. The model implies that price rigidity (stickiness) coincides with quantity rigidity (stickiness).
In reality this may not be the case. For example, in our country the price of Coca Cola and
Pepsi are rigid for the last many years but the SS of the products has been increasing from
time to time due to aggressive promotion. In other word, the model ignores the impact of
non-price competition (advertising and sales promotion) in increasing output sold.
2. The analysis does not explain how the ongoing price gets to be Pk or why firms in oligopoly
market are reluctant to deviate existing price that yields them higher (substantial) profits.
3. The model explains only as to how the kink occurs but doesn‟t explain where it occurs.
5.21.2 Cournot’s Duopoly Model
This model is the pioneering oligopoly (or duopoly) model formally developed in 1838 by
French economist, Augustin Cournot. In his model, he put forth some basic assumptions, and
after logically deducing the assumptions he conclude about the behavior of duopolists.
Basic Assumptions:
1. There are only two firms, A & B in the market; each owning mineral water wells;
2. Both operate their wells at zero marginal cost.
3. Both face a downward sloping straight-line demand curve.
4. Each firm acts on the assumption that its competitor will not react to its decision to change
in its output and price. This assumption is the behavioral assumption of Cournot.
Conclusion:
Deducing the assumptions logically, Cournot has concluded that each firm attains equilibrium by
ultimately selling one-third of the market, and charging the same price. And one-third of the
market remains unsupplied.
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The Analysis:
Tabular Illustration of the Cournot Model:
Table 5.5: Tabular Illustration of the Cournot Model
Period
Firm „A‟
Firm „B‟
Unsupplied Portion of the Market
1st
½(1) = ½
½ (½)=1/4
1/4
2nd
½ (1-¼) = ⅜
½(1-3/8)=5/16
5/16
3rd
½ (1- 5/16 ) = 11/32
½ (1-11/32) = 21/64
43/64
:
:
:
:
:
:
:
:
:
:
:
:
Nth
½ (1 – 1/3)= ⅓
½
(1- 1 /3) = 1/3
1
/3
As you can see it from the table, the process of adjustment continues and ultimately a point will
be attained, where any further changes gets back to the original position that is the equilibrium
point for the duopolists. If firm „A‟ at period N+1 wants to adjust price and output in search for
better position, it assumes that firm „B‟ continues to supply 1/3rd of the market so the relevant
market demand for „A‟ is 2/3rd of the market and attempts to optimize given this. To optimize
profit, firm „A‟ should offer half of the available market demand (½ (2/3) = 1/3) that is one-third
of the market which is the same as firm A‟s position at period N. Hence, any further attempt of
adjustment result in no change in the firm‟s position hence is equilibrium position.
Example
Suppose that there are only two firms, A and B, and with the demand curve of P = 120 – Q and
retain the condition of no cost. Assume that firm A is the first to start producing and selling
mineral water. In order to maximize his / her profit, he/ she sells quantity 60 where his/her
MC=0=MR, at price 60 birr. As a result his /her total profit is 3600 Birr. The elasticity of
market demand at this level of output is equal to unity and the total revenue of the firm is the
maximum which is equal to 3600 birr.
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Then firm B will take A's output as given and seek the output that maximizes B's profits in the
remainder of the market, so B's demand curve begins at R of the following figure. The output of
firm B is found to be 30. The price in the market is 120 – (30 + 60) = 30 birr. Taking this
segment as the relevant demand curve, firm B maximizes profit by selling 30 units at price 30
Birr. The maximum profit will be 900 birr which is equal to the maximum of the total revenue.
Note that firm B supplies only 30 = ¼ of the market demand (120 – 60) ½ = 60 X ½ = 30 units.
Let us now relax the assumption of zero marginal cost and see the equilibrium of a duopoly
market (Cournot‟s equilibrium) based on the reaction-curves approach. Reaction curve is a
curve that shows the relationship between a firm‟s profit maximizing output and the amount it
thinks its competitor will produce. For instance, if we have two firms (A&B), firm A‟s reaction
function (curve) shows how much output A must produce in order to maximize its own profit for
every specific level of output of its rival (B).
Example:
Assume that the market demand and cost functions of the duopolies are P =100 - 0.5Q,
Where Q = q1+q2, TC1= 5q1, TC2 = 0.5q22. Based on the given answer the following questions
accordingly.
A. Determine the short run equilibrium output and price of each duopoly ignoring their
interdependence (with naive assumption)
B. Find the demand functions for each duopolies
C. Calculate the short run profits of each duopoly and the industry profit.
D. Verify the profit level of each duopoly graphically
Solution
The same to the precious market structures here also the equilibrium of the cournot duopoly exists
when the marginal revenue and the marginal cost becomes equal.
A. To determine the short run equilibrium output and price of each duopoly first we should find the
marginal revenue and marginal cost of each firm
TR1 = Pq1 = (100 – 0.5 (q1+q2))q1 = 100q1 –0.5q12 – 0.5q1q2
From this total revenue we can find marginal revenue as MR1 =
109 | P a g e
TR
= 100 –q1 – 0.5q2
q1
From the total cost we can find marginal cost as MC1 =
TC1
=5
q1
Equate MR1 = MC1 100 – q1 – 0.5q2 = 5 100 – 5 - q1 – 0.5q2 = 0
95 – q1 – 0.5q2 = 0  95 = q1 + 0.5q2 ------------------------------ (1)
TR2 = Pq2 = (100 – 0.5 (q1+q2)) q2 = 100q2 – 0.5q22 – 0.5q2q1
MR2 =
TR2
TC2
= 100 – q2 – 0.5q1 and MC2 =
= q2
q2
q2
Equate MR2 = MC2 100 – q2 – 0.5q1 = q2 100 – q2 – q2 – 0.5q1 = 0
100 – 2q2 – 0.5q1 = 0 100 = 2q2 +0.5q1 --------------------------- (2)
The profit maximizing (loss minimizing) output of q1 and q2 can be solved from the two
equations using simultaneous equation method. That is
q1 + 0.5q2 = 95
(0.5q1 + 2q2 = 100) (–2)
q1 + 0.5q2 = 95
-q1 – 4q2 = -200
-3.5q2 = -105
q2 = 105/3.5 = 30, substituting this in any one of the above equation gives value of
q1. That is q1 + 0.5q2 = 95 q1 + 0.5 (30) = 95  q1 = 95 – 15 = 80
Q = q1 + q2 = 80 +30 = 110
Market price: P = 100 – 0.5Q, where q1 + q2
= 100 – 0.5 (80 + 30) = 100 – 0.5 (110) = 100 – 55 = 45
B. The demand functions (reaction curves) of the duopolies are obtained by solving for q 1 and
q2 from the two equations as follows.
95 = q1 + 0.5q2  q1 = 95 – 0.5q2, is the demand function for firm 1.
100 = 2q2 + 0.5q1  q2 = 50 – 0.25q1, is the demand function for firm 2.
C. The economic profits of each duopoly
Π1 = Pq1 – TC1
Π2 = Pq2 – TC2
= 45(80) – 5(80)
= 45 (30) – 0.5 (30) 2
= 3600 – 400 = 3200
=1350 – 450 = 900
The total industry profit naïve assumption calculated as
Π = Π1+ Π2 = 3200 + 900 = 4100
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D. To verify the profit level of each duopoly graphically we should find the two intercepts of
the firms demand functions as follow
q1 = 95 – 0.5q2,  If q2 = 0, then q1 = 95 and if q1 = 0, then q2 = 190
This implies firm1 reaction function cross the x-axis at q1=95 and the y axis at q2=190
q2 = 50 – 0.25q1,  If q1 = 0, then q2 = 50 and if q2 = 0, then q1 = 200.
This implies that firm1 reaction function cross the x-axis at q1=200 and the y axis at q2=50
Therefore the reaction curves (graphic solution of Cournot‟s model) is given as follow
q2
Firm 1‟s reaction curve
190
Equilibrium
Firm 2‟s reaction curve
50
30
80
95
200
q1
Criticism of Cournot Model:
The Cournot model has been criticized on the following ground:
Cournot assumed the behavior of firms as they never learn from their past experience which is
far-cry from reality. In general, the behavioral assumption of Cournot is naïve
5.21.3 THE BERTRAND’S MODEL:
Dear students, this model assumed a model of competitive bidding and hence is the opposite of
the Cournot‟ model (simultaneous price setting). Bertrand, a French Mathematician, criticized
cournot's model and developed his own model of duopoly in 1883. Bertrand's model differs
from cournot's model in respect of its behavioral assumption. While under cournot's model, each
seller assumes his rival's output to remain constant; under Bertrand's model each seller
determines his price on the assumption that his rival's price remains constant.
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This model states that when firms are selling identical (homogenous) products and have significant
effect on the price, the Bertrand equilibrium is a competitive equilibrium for they engaged in
strategic interaction. That is, the Bertrand equilibrium is where price equals MC. What do you think
the reason for such situation?
First, we note that price can never be less than MC. As a result, either firm would increase its profits
by producing less output. So let us consider the case where P >MC. Suppose that both firms are
selling at some P >MC. Consider the position of firm 1. If it lowers its price by any small amount ε
and if the other firm keeps it price at P , all the consumers will prefer to purchase from firm 1. By
cutting its price by an arbitrary small amount, firm 1 can steal all the consumers from firm 2.
On the other way if firm 1 really believes that firm 2 will charge a price P that is greater than MC, it
will always pay firm 1 to cut its price to P - ε. But firm 2 can reason the same way. Thus, any price
higher than MC cannot be equilibrium. The only equilibrium is then the competitive equilibrium.
This result seems paradoxical when you first encounter it. You may wonder how we can get a
competitive price if there are only two firms that produce identical products in the market. If we
think of the Bertrand model as a model of competitive bidding it makes more sense. Suppose that
one firm “bids” for the consumers‟ business by quoting a price above MC. Then the other firm can
always make a profit by undercutting this price with a lower price. It follows that the only price that
each firm cannot rationally expects to be undercut is a price equal to MC. Thus, it is often observed
that competitive bidding among firms that are unable to collude can result in prices that are much
lower than it can be achieved by other means. This phenomenon is simply an example of Bertrand
competition.
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Numerical Example:
Given P = 100 – 0.5Q, where Q = q1+q2, TC1= 5q1, TC2 = 0.5q22 find the Bertrand‟s equilibrium.
Solution:
Firm 1
Firm 2
Since TC1=5q1 MC1=5
TC2=0.5q22  MC2=q2
At equilibrium P = MC1
P = MC2
100 – 0.5Q = 5
-95 = -0.5Q
Q = 95/0.5 = 190
100 – 0.5Q=q2, since Q=190
100-0.5(190) = q2
q2=5
Its criticisms:

It is a static model which does not explain the time period involved in the action and
reaction process of price moves by the duopolists.

It is a closed model which does not allow entry of firms. This assumption that entry of
firms is blocked makes the model unrealistic because price increases in the duopoly
market lead to entry of firms.

The assumption that each duopolist can act without any price reaction from the other is
unrealistic. It is, in fact, a no- learning by-doing model.
5.21.4 THE STACKELBERG MODEL (Quantity leadership)
The German economist developed his leadership model of duopoly in 1930 based on the
assumption that each seller recognizes the interdependence of other's actions. His model is an
extension of cournot's model. In this model each seller determines the maximum profits he can
get both by being a leader and a follower. He/she will then choose to play whatever role brings
him/her greater profits. Stakelberg assumes that one of the duopolists (Say A) is sophisticated
enough to play the role of a leader and the other (say B) acts as a follower. The leading duopolist
A recognizes that his rival seller, B, has a definite reaction function which A uses into his own
profit function and maximizes his profits.
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This model often used to describe industries in which there is a dominant firm or a natural leader.
For example, IBM is often considered to be a dominant firm in the computer industry. A commonly
observed pattern of behaviour is for the smaller firms in the computer industry to wait for IBM‟s
announcements of new products and then adjust their own product decisions accordingly. In this
case we might want to model the computer industry with IBM playing the role of a Stackelberg
leader and the other firms in the industry being Stackelberg follower.
Suppose that firm 1 is the leader and that it chooses to produce q1. Firm 2 responds by choosing a
quantity q2. Each firm knows that the equilibrium price in the market depends on the total output
produced. That is by substituting Q (q1 +q2) in the inverse demand function (curve).
What output should the leader choose to produce to maximize profits? The answer depends on how
the leader thinks the followers will react to its choice. Presumably, the leader should expect that the
follower will also attempt to maximize profits as well, given the choice made by the leader. In order
for the leader to make a sensible decision about its own product, it has to consider the follower‟s
profit maximization problem as its own.
Numerical example:
Consider the example we have used to describe Cournot‟s model. That is,
P = 100 – 0.5Q, where Q=q1 + q2, TC1 = 5q1, and TC2 = 0.5q22. Given this,
i. Find the equilibrium q1, q2, market price, Π1, and Π2
a. Firm 1 being Stackelbrg‟s sophisticated leader and firm 2 the follower
b. Firm 2 being Stacklberg‟s sophisticated leader and 1 the follower
ii. From the view point of profit obtained is it better for the firms to be a leader or a
follower?
Solution:
i. The reaction (DD) functions or curves are found by taking the partial derivatives w.r.t. q1
and q2 and equating to zero.
Π1= Pq1 – TC1= (100 –0.5 (q1+q2)) q1 –5q1
= 100q1 – 0.5q12 – 0.5q1q2 – 5q1 = 95q1 – 0.5q12 - 0.5q1q2 ----------------------------- (1)
Π2 = Pq2 – TC2 = (100 – 0.5 (q1+q2) q2 –0.5q22
= 100q2 – 0.5q1q2 – 0.5q22 – 0.5q22 = 100q2 – 0.5q1q2 – q22 ---------------------------- (2)
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The partial derivatives w.r.t. q1 and q2
 1
= 95 – 0.5q2 – q1 q1= 95 – 0.5q2 ---- firm 1 reaction (DD) function----------- (3)
q1
 2
= 100 – 0.5q1 – 2q2  q2= 50 – 0.25q1 --- firm 2 reaction (DD) function------- (4)
q 2
a. Stakelberg’s solution with firm 1 being the sophisticated leader;
Firm 1 will substitute firm 2‟s reaction (DD) function in its own profit equation to
produce an output that will maximize profit as if it were a monopoly. That is
Π1= Pq1 – TC1
= 95q1 – 0.5q12 – 0.5q1q2, substituting firm 2‟s DD function given in eq (4)
= 95q1 – 0.5q12 – 0.5q1 (50 – 0.25q1)
= 95q1 – 0.5q12 – 25q1 + 0.125q12
= 70q1 – 0.375q12------------------------------------------------------------------------ (5)
The first order condition of the profit function w.r.t. q1
 1
= 70 – 0.75q1 70= 0.75q1  q1 = 70/0.75 = 93.333
q1
Π1= 70q1 – 0.375q12
= 70 (93.333) – 0.375 (93.333) 2
= 6533.333 – 3266.666 = 3266.66
 Firm 2 will substitute firm 1‟s output in its own DD as a follower. That is
q2 = 50 – 0.25q1 = 50 – 0.25 (93.333) = 50 – 23.333 = 26.666
Π2 = 100q2 – q22 – 0.5q1q2
= 100 (26.666)2 – 26.6662 – 0.5 (93.333) (26.666)
= 2666.66 – 711.1 – 0.5 (2488.8)
= 2666.7 – 711.1 – 1244.4 = 711.1
 P = 100 – 0.5 Q
= 100 – 0.5 (93.33 + 26.666)
= 100 – 0.5 (120)
= 100 – 60 = 40
b. Stakelberg’s solution with firm 2 being the sophisticated leader;
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It will substitute firm 1‟s DD function in its own profit function to produce an output that
will maximize its profit as it were a monopoly. That is
 Π2 =Pq2 – TC2
 Π2 = 100q2 – q22 – 0.5q1q2, substituting firm 1‟s DD function
= 100q2 – q22 – 0.5q2 (95 – 0.5q2) = 100q2 – q22 – 47.5q2 + 0.25 q22
= 52.5q2 – 0.75q22
 The first order condition of Π2 w.r.t.q2 gives
∂ Π2 = 52.5 – 1.5q2  52.5 = 1.5q2  q2 =52.5/1.5 = 35
∂q2
Π2 = 52.2q2 – 0.75q22 = 52.2 (35) – 0.75 (35) 2 = 1837.5 – 918.75 = 918.75
 As a follower firm 1 will substitute the output produced by firm 2 on its DD function.
That is q1 = 95 – 0.5 q2 = 95 – 0.5 (35) = 95 – 17.5 = 77.5
Π1 = 95q1 – 0.5q12 – 0.5q1q2 = 95 (77.5) – 0.5 (77.5) 2 – 0.5 (35) (77.5) = 3003.125
P = 100 – 0.5 (35 + 77.5) = 100 – 0.5 (112.5) = 100 – 56.25 = 43.75
As can be seen from the profits as a leader and follower, both are better off as a leader
5.22 COLLUSIVE OLIGOPOLY MODELS
Rationales for Collusion and Types of Collusion
Some of the factors that can be taken as rationales for collusion of an oligopoly firms are;
A. Collusion reduces the degree of competition between the firms and helps them act
monopolistically in their effort of profit maximization.
B. It reduces the oligopolistic uncertainty (risk) surrounding the market
C. It forms a kind of barrier to the entry of new firms.
5.22.1 CARTELS:
As it is indicated, the firms under oligopoly are independent in decision-making. However, their
actions are not unnoticed by the rivals and in this sense they are independent. In this situation,
best interest of the firms can be served through mutual cooperation rather than competition.
Cooperation in the market by the competing firms is called collusion.
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Cartel is the most effective form (type) of collusion as seen in practice. Cartel is a formal
organization of the oligopoly firms in an oligopoly. It is a combination of firms whose object is to
limit the scope of competitive forces within a market. A cartel is a cooperation of firms whose
objective is to limit (reduce) the scope of competitive environment that arises due to mutual
interdependence of firms within the market and act as a monopoly.
A general purpose (objective) of cartels is to centralize certain managerial decisions and
functions of individual firms in the industry with a view to promoting common benefits.
Producers in a cartel explicitly agree to cooperate in setting prices and output levels. In other
words, formation of a cartel by the firms means creation of a single body to take pricing and
output decisions for the firms. Whether cartel may take form of open or secret collusion, Cartel
agreements are explicit and formal in the sense that agreements are enforceable on member firms
not following the cartel rules. In most countries cartels and cartel type agreements between the
firms in manufacturing and trade are illegal. Yet, Cartels in the broader sense of the term exist in
the form of trade associations, professional organizations and the like.
Cartels are often international. For example, the OPEC Cartel is an international agreement
among oil-producing and exporting countries, which for over a decade succeeded in raising
world oil prices far above what they would have been otherwise. Others also succeeded, for
example during the mid 1970s the International Bauxite Association (IBA) quadrupled bauxite
prices, and a secretive international Uranium cartel pushed up Uranium prices. Some cartels had
longer successes. From 1928 through the early 1970s, a cartel called Mercurio Europeo kept the
price of Mercury close to monopoly levels, and an international cartel monopolized the iodine
market from 1878 through 1939. However, most cartels have failed to raise prices. An
International Copper Cartel operates to this day, but it has never had a significant impact on
copper prices. And cartel attempts to drive up the prices of tin, coffee, tea, and cocoa have also
failed. DeBeers is one of the largest cartels in trading Diamond.
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Successful cartelization requires two things:
1. The total demand for the good must not be very price elastic.
2. Either the cartel must control nearly all the world's supply or if it does not the supply of
non-cartel producers must not be price elastic.
There are two forms of cartel. These are
a) Cartel aiming at joint profit maximization
b) Cartel aiming at sharing the market
A. CARTEL AIMING AT JOINT PROFIT MAXIMIZATION:
The aim of this particular form of cartel is to set prices and outputs together so as to maximize total
industry (joint) profit not profit of individual firms. In this cartel solution the firms act together to
restrict output so as not to “spoil” the market. They recognize the effect on joint profits from
producing more output in either firm. This situation is similar to the multi plant monopoly case that
seeks (wants) the maximization of his profit.
For simplicity we will consider two oligopoly firms (firm A and B) producing identical
(homogenous) products. The firms appoint a central agency (cartel) to which they delegate to:
1) The total quantity and the price level at which each quantity should be sold so as to attain
maximum group (joint) profit
2) The allocation of production among the members of the cartel and
3) The distribution of the maximized joint profits among the participating members
The authority of the central cartel agency is complete. The central agency:
Has access to the cost figures of individual firms.
It calculates the market demand and the corresponding MR. Given the market demand, the
cartel (monopoly) solution output and price levels- that maximizes joint industry profit is
determined by equating MR = MC.
Next the central agency allocates the production among firm A and B by equating the MR to
individual firm‟s MC. That is MR = MCA and MR = MCB.
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 The first-order condition for maximization of the joint profit П requires the
allocation of output in such a way that the MC of each firm is equal.

R  c1
R C1


0 

X 1 X X 1
X X 1
MR = MC1= MC2
 The Second-order condition for maximization of joint profit:
 2 R  2C1
 2 R  2C2

and

X 2
X 12
X 2 X 22
Consider a numerical example for a profit-maximizing cartel
Suppose the market price of a homogeneous product which produced by to joint profit maximizing
cartel given as p = 100 – 0.5Q, where Q = q1 +q2, and their costs as TC1 = 5q1, and TC2 = 0.5q22
then determine Q, q1, q2, P, and joint profit.
Solution:
First the central agency of the cartel computes the joint profit function as
П = П1 + П2 = TR1 – TC1 + TR2 – TC2 = (Pq1+Pq2) – (TC1 + TC2)= P (q1+q2) – (TC1+TC2)
= 100 – 0.5 (q1+q2) (q1+q2) – (5q1+0.5q22)
= 100q1+100q2 – 0.5q12 – 0.5q1q2 – 0.5q1q2 – 0.5q22 – 5q1 – 0.5q22
= 95q1+100q2 – 0.5q12 – q1q2 – q22
Find the partial derivative of the profit function w.r.t q1 and q2 and equate them to zero.
∂ П = 0 = 95 – q1 – q2 = 0
∂ П = 100 – q1 – 2q2 = 0
∂ q1
∂ q2
= q1+q2 = 95 -------- (1)
= q1+2q2 = 100 --------- (2)
To obtain the level of output and price that maximizes joint profit, the central agency of the
cartel solves q1 and q2 using the above two equations simultaneously as follows
q1+q2 = 95
(q1+2q2 = 100) –1
q1+q2 = 95
-q1 – 2q2 = -100
-q2 = -5, q2 = 5. Substituting this in one of the two equations above will give us
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q1+q2 = 95q1+ 5 = 95  q1 = 95 – 5 q1 = 90.
Then joint profit maximizing P = 100 – 0.5Q = 100 – 0.5 (95) = 100 – 47.5 = 52.5.
 The second order condition for maximization states the slope MR < slope of the MC
2R
 2C1
2R
 2C2
 1 
 0and
 1 
1
X 2
X 12
X 2
X 22
Thus, Q = 95 and P = 52.5 are the output and price levels that maximizes joint profit.
Finally, the joint profit will be obtained by substituting the values of q1 and q2 in the above П
function or alternatively as follows
П = TR1+TR2 – TC1 – TC2 = Pq1+Pq2 – TC1 – TC2= 52.5 (90) + 52.5 (5) – 5 (90) – 0.5 (5) 2
= 4725 + 262.5 – 450 – 12.5 = 4525.
Difficulties of a joint profit maximizing cartel
1. It is difficult to estimate demand curve accurately since each firm thinks that the demand
for its own product is more elastic than the market demand curve because its product is a
perfect substitute for the product of other firms.
2. An accurate estimation of industry's MC curve is highly improbable for lack of adequate
and correct cost data. If industry's MC is incorrectly estimated, industry output can be
only incorrectly determined. Hence joint profit maximization is doubtful.
3. Cartel negotiations take a long time. During the period of negotiation, the composition of
the industry and its cost structure may change. This may render the estimates irrelevant,
even if they are correct. Besides, if the number of firms increase beyond 20 or so, cartel
formation becomes difficult, or even if it is formed, it soon breaks down.
4. If Cartel price, like monopoly price is very high, it may invite government attention and
interference. For the fear of government interference, members may not charge the cartel
price.
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5. There are "Chiselers' who have a strong temptation to give secret concessions to their
customers. This tendency in the cartel members reduces the prospect of joint profit
maximization.
6. Another reason for not charging the cartel price is the fear of entry of new firms. The
high cartel price which yields monopoly profit may attract new firms to the industry. To
prevent the entry of new firms some, firms may, decide on their own not to change the
cartel price.
Yet another reason for not charging the cartel price is the desire to build a public image or
good reputation. Some firms may, to this end, decide to charge only a fair price and realize
only a fair profit.
B. CARTEL AIMING AT SHARING THE MARKET: This is the most common type of cartel.
The two methods of sharing the market are through
I. NON-PRICE COMPETITION: Under this kind of arrangement between firms, a uniform
price is fixed and each firm is allowed to sell as much as it can at the cartel price. The only
requirement is that firms are not allowed to reduce the price below the cartel price. The
Cartel price is a bargain price. While low-cost firms press for a low price, the high -cost
firms press for a higher price. But the cartel price is so fixed by mutual consent that all
member firms are able to make some profits. But the firms are allowed to compete with one
another in the market on a non-price basis. That is, they are allowed to change the style of
their product, innovation of new designs and promote their sales without reducing their price
below the level of cartel price. For example
b. Doctors charge the same price
c. Barbers charge the same price
d. Gasoline stations charge the same price
e. Cinema halls charge the same price etc.
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II. SHARING THE MARKET BY AGREEMENT ON QUOTAS: Here, cartel members agree
explicitly on the common price and quantity each member may sell in the market (national or
international). The best example of this cartel is OPEC.
If all firms have identical cost, a monopoly solution will emerge with the market being shared
equally. That is equal quotas will be allocated. This will happen if and only if firms have identical
costs. However, if costs are different, the quotas (shares) of the market will differ. Again, allocation
of quotas on the basis of cost is unstable. Therefore, the quotas will be decided by bargaining.
During the bargaining process to decide the quotas of members of the cartel, the main criterions are;
Bargaining ability of a firm and its relative importance in the industry,
The relative sales of the firm in some pre-cartel price,
The production capacity of the firm,
The geographical division of the market, and the like
The best example of this kind of agreement is what the Japanese, Malaysian, and Chinese companies
producing Sony products have agreed. Note that cartel models of collusive oligopoly are closed
models. That is they assume no entry. However, if entry is free, the inherent instability of cartel will
be intensified. This is because new entrant firms may charge lower prices in order to secure a
considerable share of the market. Besides, if either firm is not sure the other firm keeps track on
prices and production levels, price war and eventually the dissolution of the cartel is inevitable
It may be mentioned at the end that cartels do not necessarily create the conditions for price
stability in an oligopolistic market. Most cartels are loose. Cartel agreements are generally not
binding on the members. Cartels do not prevent the possibility of entry of new firms. On the
contrary, by ensuring monopoly profits, cartels in fact create conditions, which attract new firms
to the industry. Besides; 'Chiselers' and 'free riders' create conditions for instability in price and
output.
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5.22.2 Price Leadership
Collusion through price leadership is an imperfect form of collusion between oligopoly firms.
Price leadership is an informal position of a firm in an oligopolistic setting to lead other firms in
pricing. This leadership may emerge spontaneously due to technical reasons or out of tacit or
explicit, agreements between the firms to assign leadership role to one of them. The spontaneous
price leadership may be the result of such technical reason as size, efficiency, economies of scale
or firm‟s ability to forecast market conditions accurately or a combination of these factors. The
three common types of price leaderships: - low-cost firm, dominant firm, and barometric Price.
A. Low Cost Price Leadership
Consider we have two firms (duopoly) that produce identical products at different costs but sell
their products at the same market price. However, firms may have equal or unequal share.
Assumptions to this model:
a. There are only two firms, firm 1 and firm 2. firm 2 is the low cost firm and firm 1 is the high
cost firm
b. The product produced by the two firms is identical (homogenous) products.
c. Each of the two firms have equal share in the market. In other words demand curve facing
each firm will be the same and will be half of the total market demand.
d. The two firms may have different costs but sell their products at the same market price.
e. The market industry demand curve for the product is known to both the firms.
P
MC1
MC2
P1
P2
D (market demand)
E
d
q1
q2 MR
Figure 5.24 the low cost firm equilibrium
123 | P a g e
Q = q2+q1 Q = 2(q2)
Firm 2 have lower cost and hence it charges lower price, p2, and produce q2 to maximize profits.
Firm 1, with the highest cost, on the other hand would like to charge p1 and produce q1. However,
firm 1 prefers to follow the leader because if it charges p1 its sells will be zero implying no one will
pay a higher price for identical products. Therefore, the high cost firm 1 must be willing (satisfied)
to accept the price decision of the low cost firm. Thus, it changes P2 and produces the same quantity
as firm 2, q2. The two together then produce output level, which is equal to q2 + q2 = 2q2. It is only
in this case the antitrust monopoly legislation, which forbids monopoly production will work. In
short the high cost firm must tolerate to the price and output level equal to the low cost firm to avoid
the uncertainty that may arise when firm 2, reduces price lower than p2.
Mathematical approach for the low-cost price leader
The market demand is defined by the function P = a-b(X) a-b(X1+X2)
Where X1= Output of firm A and X2= Output of firm B
The firms costs defined by the functions: C1= f1(X1) and C2=f2 (X2) Where C1 < C2
The leader will be the low-cost firm, A. It assumes that the rival firm will produce an equal
amount of output to his own; i.e. X1=X2
With this assumption, the demand function relevant to the leader's decision is: P= a-2b (X1)
The low-cost leader will set the price, which maximizes his own profit.
π1= R1- C1= PX1 - C1
R1= (a-2bX1) X1-C1
The first-order condition for the maximization of π1 requires
R1
1
C1
R1 C1
R
C1


0 1 

 MR1  MC1
 0 =>
X 1 X 1
X 1 X 1 X 1
X 1 X 1
The second - order condition requires.
 2 1
 2 R1  2C1

0


X 12
X 12 X 12
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The solution of this problem yields the price P and output X1 that the leader must produce in
order to maximize his profit. The follower would adopt the same price and will produce an equal
amount of output (X1=X2). Given that C2>C1, the follower does not maximize his profit. He
would prefer (under the above assumptions) a lower level of output and sell it at a higher price.
Numerical example:
Given P = 24 – 0.1Q, where Q = q1+q2 and q1 = q2, TC1 = 0.1q12, TC2 = 0.05q22,
a) Determine the output and price of low cost firm
b) Calculate the profit of the low cost firm
c) What is the profit maximizing price level the high firm would like to charge but that
doesn‟t realize in the market
d) Compare the profits of the price taker at its own profit maximizing output and low cost
firm‟s output
Solution
a) Since q1 = q2, 0.075q12 > 0.05q22. This implies that firm 2 is a low cost price leader.
Hence,
П2 = Pq2 – TC2
P = 24 – 0.1Q, where q1 = q2
= (24 – 0.1(q1+q2)) q2 – 0.05q22
P = 24 – 0.1 (2q2)
= (24 – 0.1 (q2+q2)) q2 – 0.05q22
= 24 – 0.2q2
= (24 – 0.1 (2q2)) q2 – 0.05q2
2
= (24 – 0.2q2) q2 – 0.05q22
= 24q2 – 0.2q22 – 0.05q22
= 24 – 0.2 (48)
= 24 – 9.6 = 14.4
b) П2 = Pq2 –TC2
= 24q2 – 0.25q22
dП2 = 0 = 24 – 0.5q2 = 0
= 14.4 (48) – 0.05 (48) 2
dq2
= 691.2 –115.2 = 576
= q2 = 24/0.5 = 48
c) П1 = Pq1 – TC1
d) П1= Pq1 – TC1
= (24 – 0.1(q1+q2)) q1 – 0.075q12
= 14.4 (43.63) – 0.075 (43.63) 2
= (24 – 0.1 (q1+q1)) q1 – 0.075q12
= 628.36 –142.77= 485.59 and
= (24 – 0.1 (2q1) q1 – 0.075q12
= (24 – 0.2q1) q1 – 0.075q1
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2
П1= Pq1 – TC1
= 14.4 (48) – 0.1 (48) 2
= 24q1 –0.2q12 – 0.075q12
= 24q1 – 0.275q12
= 691.2 – 230.4 = 460.8
though, 485.59>460.8
firm
1 will
produce 48 than 43.63
dП1 = 0 = 24 –0.55q1 = 0
dq1
q1= 24/0.55 = 43.63
Exercise: Given P = 300 – 5X, where X = x1+x2, TC1= 0.5x12, TC2 = 3x22 answer the
questions above.
Answer: X1 = 14.29, P1 = 157.96, X2 =11.54, and P2 = 184.62
B. Price- Leadership by the Dominant Firm
This is a typical case of price leadership where there is one large dominant firm and a number of
small firms in the industry. The dominant firm fixes the price for the entire industry and the
small firms will sell as much product as they like and the remaining market is filled by the
dominant firm itself. The dominance of the large firm is indicated by the fact that it could
possibly eliminate all its rival firms by price-cutting. In that case, the large firm gains the status
of a monopoly, which may invite legal problems. The dominant firm therefore compromises with
the existence of rural firms in the market. The smaller firms recognize their position and behave
just like a firm in a perfectly competitive market; i.e., the smaller firms assume that their demand
curve is a straight horizontal line.
Assumptions of the model:
- The oligopolistic industry consists of a large dominant firm and a number of small firms.
- The dominant firm sets the market price
- All other firms act like pure competitors, which act as price takers.
- The dominant firm alone is capable of estimating the market demand curve for the product.
- The dominant firm is in a position to predict supplies of other firms at each price set by it.
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Given these assumptions, when each firm sells its product at the price set by the dominant firm,
its demand curve is perfectly elastic at that price. Thus its MR curve coincides with the
horizontal demand curve.
The problem confronting the dominant firm is to determine the price that will maximize its profit
while allowing the small firms to sell all they wish at that price. To do this, it is necessary to find
the demand curve for the dominant firm. It is assumed that the dominant firm knows the market
demand curve DD' and the MC curve of the small firms. The summation of the MC curves of the
small firms is MCs. Since the small firms equate MC and price, MCs is also the collective supply
curve of the small firms.
P
S small
MCL
D1
PS
SSsm
B
PL1
SSsm
A
P2
SSsm
C
SSL1
D2
SSL2
D3
P3
DD
SSL3
Q
Smaller firms
dL
MRL
qL
q2
Dominant firm
q3
Figure 5.25The dominant firm price leader ship
Knowing the market DD and the SS of the smaller firms the dominant firm calculates its DD curve
as follows. At each price the dominant firm will be able to SS that section of the total market DD not
supplied by the smaller forms. That is, the DD for the product of the firm will be the difference
between the total dd (D) and the total SS of the smaller firms.
At ps, market DD is equal to the market SS of smaller firms. This is equal to PSD1 amount. The dd
for the product of the leader will be zero. As price falls below PS, the dd for the leader increases, for
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instance, at P2, total market dd is P2D2 amount of which P2A is supplied by the smaller firms. The
share of the dominant is AD2. At P3, total market dd is P3D3 of which the share of smaller firms is
zero, while P3D3 (all) is the share of the dominant firm. Below Ps the market dd coincides with the
leader dd curve.
Having derived the dd curve of the leader (dL) and given its MC, the dominant firm will set the price
p at which MRL = MCL and output is qL. At price PL1 the total market dd is PL1C of which PLB is the
share of smaller firms while BC is the share of the dominant firm. The dominant firm maximizes its
profit be equating its MR to MC, but the smaller firms or price taker may or may not attain the point
where MRS = MCS.
Numerical example: Given Q = 120 – 0.2P, SSsm = 4.8P, and TCL = 4qL determine the supply,
price, and profit of the dominant (large) firm, finally, the supply of smaller (followers) firms.
Solution:
First we should derive the demand function of the dominant firm (qL) which is the difference of
the market demand (Q) and the small firms supply (SSsm)
qL (dL ) = Q – SSsm)= 120 – 0.2P – 4.8 = 120 – 5P  qL – 120 = -5P  P = 24 - 0.2qL
TRL = p*qL= (24 – 0.2 qL) qL= 24qL-0.2qL2
ПL = TRL – TCL = 24qL-0.2qL2– 4qL = 20qL - 0.2qL2
 Once we have derived the profit function of the dominant firm, it maximized its profit by
calculating the first order derivative of its profit with respect to qL and equate to zero.
d L
 20 – 0.4qL = 0  20 = 0.4qL qL = 20/0.4 = 50
qL
P = 24 – 0.2 qL = 24 – 0.2 (50) = 24 – 10 = 14, this is the equilibrium price
ПL = PqL – TCL = 14 (50) – 4 (50) = 700 – 200 = 500
Then the supply of smaller firms will (SSsm) = Q – dL. That is
SSsm = (120 – 0.2P) – 50 = (120 – 2.8) – 50 = 117.82– 50 = 67.2 or
SSsm = 4.8P=4.8*14=67.2
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C. Price-Leadership by the Barometric Firm
The barometric price leadership is that in which there is no leader firm as such but one firm
among the oligopolistic firms with the wisest management which announces a price change first
which is followed by other firms in the industry. The barometric price leader may not be the
dominant firm with the lowest cost or even the largest firm in the industry. It is a firm, which
acts like barometer in forecasting changes in cost and demand conditions in the industry and
economic conditions in the economy as a whole. On the basis of a formal or informal tacit
agreement, the other firms in the industry accept such a firm as the leader and follow it in
marketing price changes for the product.
The barometric price leadership develops due to the following reasons:
a) Most firms do not possess the expertise to calculate cost and demand conditions of the
industry. So they leave their estimation to one leader firm, which has the ability to do so.
b) Oligopolistic firms accept one among them as the barometric leader firm which possesses
better knowledge and predictive power about changes in direct costs or style and quality
changes and changes in the economic conditions as a whole
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