Microeconomics I

CHAPTER ONE

THE THEORY OF CONSUMER BEHAVIOR

The theory of consumer behavior is the concern of how consumers decide on the basket
of goods and services they consume in order to maximize their satisfaction. The theory of
demand starts with the examination of the behavior of the consumer, since the market
demand is assumed to be the summation of the demand of the individual consumers.

In explaining the consumer behavior, which is the basis for the theory of demand, we
assume that:
i) The consumer is rational: - given his/her income and the market price of the
commodities, he/she plans the spending of his/her income so as to attain the
highest possible satisfaction or utility. This is the axiom of utility
maximization.
ii) The consumer has complete knowledge of all the information relevant to
his/her decision, i.e., he/she has
-Complete knowledge of all the available commodities,
-Complete knowledge of the price of the commodities,
-Complete knowledge of his/her income.

SOME BASIC CONCEPTS

CONSUMER: - A decision making unit (an individual or a household) who uses or

consumes a commodity or service.

UTILITY:-The power of a commodity to satisfy human wants. It is the satisfaction or

subjective pleasure that one gets from consuming a good or service.

RELATIVITY OF UTILITY: - The utility of a commodity is subjective to a person‘s

need. It is not absolute (objectively determined).

UTILITY AND MORAL VALUES: - Utility is free from moral values. For example,
eating a food item which may be immoral in a society yields utility as long as it satisfies
hunger. It is also the case that utility is ―ethically neutral‖ between good and bad, and
harmful and useful. For example, drug yields utility to the drug-takers.

In order to maximize utility, the consumer must be able to compare the utility of the
various baskets of goods which he/she can buy with his/her income. There are two
approaches to the problem of comparison (measurability) of utility:
i) the cardinal approach
ii) the ordinal approach

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2.1 THE CARDINAL UTILITY APPROCH

The cardinal school postulated that utility can be measured in monetary units (i.e., by the
amount of money that the consumer is willing to sacrifice for another unit of a
commodity) or by subjective unit called ―utils‖.
Assumptions

i) Rationality:- the consumer is assumed to be rational in a since that he/she

aims at the maximization of his/her utility subject to the constraints imposed
by his/her income.
ii) Cardinal utility: - the utility of each commodity is measurable, with the most
convenient measure being money.
iii) Constant marginal utility of money:- the utility that one derives from each
successive unit of money income remains constant.
iv) Diminishing marginal utility (DMU):- the MU of a commodity diminishes as
the consumer acquires mire and more of it.
v) Additively of utility: - even though dropped in the latter version of the
approach, utility was assumed to be additive in the earlier version. That is:
U = U1(X1) + U2(X2) + --- + Un (Xn)
vi) The total utility of a basket of goods and services depends on the quantities of
the individual commodities. That is:
U = f(x1, x2… xn)

EQUILIBRIUM OF THE CONSUMER

Let‘s assume that the consumer consumes a single commodity, x. The consumer can
either buy x or retain his money income Y. Under these conditions the consumer is in
equilibrium when the marginal utility of X is equated to its market price (px).
Symbolically,
MUx = Px
Mathematically, we can derive the equilibrium of the consumer as follows:
- The utility function is
U = f (qx), where utility is measured in monetary units and qx is the quantity
of x consumed by the consumer.
If the consumer buys qx, his/her expenditure is pxqx. Presumably the consumer seeks to
maximize the difference between his/her utility and total expenditure. That is:
U – Pxqx
The necessary condition for a maximum is that the partial derivative of a function with
respect to qx be equal to zero. Thus,
d (U – pxqx)
= O
dqx

═> dU d (pxqx)
- = O
dqx dqx

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═> dU dqx
- px = O
dqx dqx

═> dU = px
dqx

═> MUx = Px

If MUx > Px, the consumer can increase his/her welfare by purchasing more unit of X,
and if the MUx < Px, welfare can be increased by reducing the consumption of X.
In the case there are more commodities, the condition for optimality of the consumer is
the equality of the ratios of MU of the individual commodities to their prices, i.e. the
utility derived from spending an additional unit of money must be the same for all
commodities.

MU1 = MU2 = ….. = MUn

P1 P2 Pn

DERIVATION OF THE DEMAND CURVE

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 X* and then starts declining. Accordingly, the MUx declines
continuously and becomes negative beyond X*.

MUx = slope of TUx = dTU

dqx

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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 X1 the MU is MU1 which is equal to
P1 at the optimum point. Hence at P1 the consumer demands X1 quantity. Similarly at X2
the marginal utility is MU2 which is equal to P2. Hence at P2 the consumer demands X2
and so on. This forms the demand curve for commodity X. As negative price do not make
sense in economics, the negative potion of MUx does not form part of the demand curve.

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O X1 X2 X3 X*
Panel A: The MU curve Panel B: The demand curve

The demand curve is simply the graphical representation of the relationship between
price and quantity demanded.

CRITIQUES OF THE APPROCH

1) The satisfaction derived from the various commodities can not be measured
objective. 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 changes.
3) The additivity assumption of utility is unrealistic.

2.2 THE ORDINAL UTILITY THEORY

The ordinalist school suggests that utility is not measurable, but is an ordinal magnitude.
That is, to make his/her choice, the consumer need not know the utility of various
commodities in specific unit, but be able to rank the various basket of goods(order of
preference) according to the satisfaction that each bundle gives. There are two main
theories in the ordinal approach:
1) The Indifference Curve Theory, and
2) The revealed 33preference hypothesis

2.2.1 THE INDIFFERENCE CURVE THEORY

Indifference curve(IC):- is the locus of points of different combinations of two goods (a

bundle of goods) which yields the consumer the same level of satisfaction (utility) so that
he is indifferent as to the particular combination he/she consumes.

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An Indifference Map: - shows a set of all the ICs, which rank the preference of the
consumer. Combination of goods situated on an IC yields the same level of utility.
Combination of goods lying on a higher IC yields higher level of satisfaction and are
preferred.

ASSUMPTIONS

1) Rationality: - the consumer is assumed to be rational.

2) Utility is ordinal: - the consumer can rank his/her preference (order the various
baskets of goods) according to the satisfaction of each basket.
3) Diminishing marginal rate of substitution (DMRS):- preferences are ranked in
terms of ICs, which are assumed to be convex to the origin. This implies that the
slope of IC (MRS) decreases in absolute terms.
4) The total utility of the consumer depends on the quantities of the commodities
consumed.
U = f (q1, q2… qn)
5) Consistency and transitivity of choices:-
═> If bundle A>B, then B is not greater than A
═> If bundle A >B and B>C, then A>C.

PROPERTIES OF WELL BEHAVED INDIFFERENCE CURVES

1) An indifference curve has a 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.
2) The further away from the origin an IC lies, the higher level of utility it denotes.
3) ICs do not intersect. If they did, the point of their intersection would imply two
different level of satisfaction, which is impossible.

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4) ICs are convex to the origin:- this implies that the slope of an IC (MRS)
decreases( in absolute terms) as we move along the curve from the left down
wards to the right.

THE MARGINAL RATE OF SUBISTITUTION (MRS)

The marginal rate of substitution of X and Y (MRSx,y) is defined as the number of units
of commodity Y that must be given up in exchange for an extra unit of commodity X so
that the consumer maintains the same level of satisfaction. It is the negative of the slope
of an IC at any one point and is given by the slope of the tangent line at that point:

Slope of IC = -dy
= MRSx,y
dx

The concept of marginal utility is implicit in the definition of MRS since it can be proved
that the MRS (the slope of IC) is equal to the ratio of the marginal utilities of the
commodities in the utility function.

MUx OR MUy
MRSx,y = MRSy,x =
MUy MUx

Proof:
The total utility function in the case of two commodities X&Y is
U = f(x, y)
The equation of an IC is
U = f(x, y) = K, where K is constant.
At equilibrium, the total derivative of U is equal to zero.
ӘU ӘU
═> du = dy + dx
Әy Әx
= (MUy) dy + (MUx) dx
Along any particular IC, the total differential is by definition equal to zero.
═> du = (MUy) dy + (MUx) dx = o

═> MUy dy = - MUx dx

═> - dy + MUx = MRSx,y

Dx MUy

THE OPTIMUM OF THE CONSUMER

To define the optimum of the consumer, we should introduce the concept of the budget
line. The budget line is the set of bundles of goods that cost exactly the consumer‘s
income. This implies that income acts as a constraint in the attempt of maximizing utility.

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Assuming two goods (x,y), the budget line will have the equation:
Px.X +Py.Y= M
Y = 1/Py.M – Px/Py.X
Where M= is fixed money income
Px = is the price of good X
Py = is the price of good Y
Assigning successive values to X (given income, M and the commodities price, Px and
Py), we may find the corresponding values of Y. Thus,
If X = O (if the consumer spends all his/her income on Y), the consumer can buy
M/Py units ofY.
If Y = O, the consumer can buy M/Py units of X.
If we join these two points by a line, we obtain the budget line.
Y

M
Py

O M X
Px

M/Py M Px
Slope of the budget line = = .
M/Px Py M

= Px
Py
Mathematically, slope of the budget line is the derivative of the budget equation:
ӘY Ә (1/Px.M – Px/Py.X)
=
ӘX ӘX

ӘY Px
=
ӘX Py
The consumer is in equilibrium when he/she maximizes his/her utility, given income and
the market prices. Two conditions must be fulfilled for the consumer to be in equilibrium.
1) MRSx,y = MUx/MUy = Px/Py, which is the necessary condition.

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2) The IC be convex to the origin (decreasing MRSx,y)

Graphically, the equilibrium of the consumer is at the point of tangency of the budget line
and the highest possible IC (at point e).

At the point of tangency (point e) the slope of the budget line (Px/Py) and of the IC
(MRSx,y = MUx/MUy) are equal.

MRSx,y = MUx/MUy = Px/Py, which is the FOC.

The SOC is implied by the convex shape of the IC. Thus, the consumer maximizes utility
by buying X* & Y* of the two commodities.

Mathematical derivation of the equilibrium of the consumer is as follows:

- Assume that there are two commodities, X&Y. The consumer is in equilibrium
when he/she maximizes utility given hi/her income and the market price of the
commodities.
- Formally the problem can be stated as:
Maximize U = f(x,y)
Subject to M = Px.X + Py.Y
- By using the lagrangian method, the steps involved are:
a) rewrite the constraint as
Px.X + Py.Y – M = O
b) Multiply the constraint by a constant  (lagrangian multiplier)
(Px.X + Py.Y – M) = O
C) Subtract from the objective function to obtain a composite function.
L = U - (Px.X + Py.Y – M)

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D) Derivate L with respect to X, Y, & and equate to zero.

L/X = U/X - Px = O
=> U/X = Px
=>MUx = Px
=>  = MUx/ Px………………………………………… (1)
L/y = U/y - Py =O
=> U/y = Py
=>MUy = Py
=>  = MUy/Py………………………………………….. (2)
L/ = Px.X + Py.Y – M = O…………………………... (3)
From (1) and (2), we can infer that
 = MUx/ Px = MUy/Py
 MUx/ Px = MUy/Py
 MUx/MUy = Px/ Py = MRSx,y

We observe that the equilibrium conditions are identical in the cardinal‘s approach and in
the Indifference curve approach. In both theories we have:
MUx/ Px = MUy/Py = ---- = MUn/Pn
EXAMPLE

Let us assume that an individual, whose income is birr 10 consumes two types of goods,
X & Y, whose prices are Px = 2 and Py = 1, spend all his income on these goods. By
using the above information and the MU table for the two goods, determine the following
things/ answer the following questions.
(A) Indicate how much of X & Y the individual should purchase to maximize utility.
(B) Show that the condition for constrained utility maximization is achieved.
(C) Determine how much total utility the individual receives when he /she maximizes
utility. How much utility would the individual get if he/she spent all income on
X/Y?

Qx MUx Qy MUy MUx/Px MUy/Py

1 10 4 5 5 5
2 6 5 4 3 4
3 4 6 3 2 3
4 2 7 2 1 2
5 0 8 1 0 1
Solution:
(A) the individual maximizes his/her utility when he/she consumes 2 units of X and 6
units of Y since at this point MUx/Px = MUy/Py, i.e, 6/2 = 3/1.
(B) The condition for utility maximization is that MUx/Px = MUy/Py, give that all
the consumer income is spent.
Thus at the optimum of the consumer,
MUx/Px = MUy/Py i.e. 6/3 = 3/1 => 3 = 3 and
PxX + PyY = I
 2(2) + 1(6) = 10

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 10 = 10
(C) TU = ∑MUs = ∑MUx + ∑Muy
 TU = (10 + 6)x + (5 + 4 + 3)y
 TU = (16)x + ( 12 )y
 TU = 28
 If the individual spend all his/her income, he/she will get the total utility of:
Tux = ∑MUx
Tux = 10 + 6 + 4 + 2 + 0
Tux = 22
This is because the consumer can consume 5 units of X given that his/her income is
10 birr and Px is 2 birr.

 if the consumer spend all his/her income on Y:

Tux = ∑MUx
Tux = 5 + 4 + 3 + 1
Tux = 13

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INCOME CONSUMPTION CURVE (ICC)

Increase in income shifts the budget line outward in a parallel manner (if commodities prices are kept
constant). If we go on increasing income (i.e., shifting the budget line outward), we will have a set of
optimum points corresponding to each budget line. The curve which connects these optimum points is
called the Income Consumption Curve (ICC). It is the locus consumer optimum points resulting only
when the consumer income changes. The ICC is also known as the Income Offer Curve or the Income
Expansion Path. From the ICC we can then derive the consumer Engle Curve. The Engle curve shows
the amount of a good (X) that the consumer would purchase per unit of time at various income levels.
To derive the Engle curve we keep the same horizontal scale as in the top panel but measure money
income on the vertical axis.
Y A‘‘

A‘

A ICC
E2 E3
E1
U2 U3
U1

O X1 X2 X3 B B‘ B‘‘ X
M

Engle curve

M3
E3‘
M2
E2‘
M1
E1‘

O X
X1 X2 X3
At income level M1, the consumer is in equilibrium at point E1 by consuming X1 units of X and this is
shown by point E1‘ on the M-X plane. When income of the consumer increases to M2, the budget line
shifts to A‘B‘ and the consumer will a higher IC U2 at point E2 by purchasing X2 units of X. this is
shown by point E2‘ on the second panel. Similarly, when income increase to M3, the consumer is in
equilibrium at point E3 by purchasing X3 of X and this is shown by point E3‘ on the second panel.

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If we connect equilibrium points of the consumer in the first panel we obtain the Income Consumption
Curve. Similarly, if we connect the points on the second panel, we obtain the Engle Curve.

NORMAL AND INFERIOR GOODS

A normal good is one of which the consumer purchases more with an increase in income.
An inferior good is one of which the consumer purchases less with an increase in income.
Good X in the above figure is a normal good because the consumer purchases more of it
with an increase in income. This is shown by a positively sloping income consumption
curve and the Engle curve. However, for an inferior good, the income consumption curve
and the Engle curve are negatively sloping because as income increases, the consumer
purchases less of these commodities. This can be shown by the following graph.

A‘
ICC
E2
A
U2

E1

U1

O X
X2 X1 B B‘
M

M2 E2

E1
M1

Engle curve

O X
X2 X1
 The classification of goods as normal or inferior depends only on how a specific consumer views the
particular good.
Thus, the same good X can be regarded as a normal good by another consumer.
 Furthermore, a good can be regarded as a normal good by a consumer at a particular level of income
and as an inferior good by the same consumer at a higher level of income.

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 A normal good can be further classified as a necessity or a luxury depending on whether the quantity
purchased increases proportionately more or less than the increase in income.

PRICE CONSUMPTION (OFFER) CURVE

When the price of a good (say X) decreases the budget line becomes flatter (rotates to the right) from its
initial position (AB) to a new position (AB‘) due to the increase in the purchasing of the given income
of the consumer. The new budget line is tangent to a higher IC at point E2 showing that as price of X
falls, more of commodity X will be bought. If we allow price of X to fall continuously and we join the
points of tangencies of successive budget lines and the higher ICs, We form the so called price
consumption curve from which we derive the demand curve for commodity X. at point E1 the consumer
buys quantity X1 at price P1. At point E2 the price P2 is lower than P1 and the quantity demanded has
increased to X2 and so on.
Y

PCC
E3
E2
E1 I3
I2
I1
O
X1 X2 B X3 B‘ B‘‘ X
P

P1

P2

P3
DD-Curve

O X
X1 X2 X3
Thus, we derive the demand curve by plotting the price quantity pairs defined by the points of
equilibrium (on the price consumption curve) on the price quantity space.
The demand curve for normal goods (goods whose demand increases with increase in income) will
always have a negative slope denoting the law of demand which states that the quantity demanded
increases as price increases and vice versa. In the case of giffen goods the demand for a good decreases
when its price decreases.

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Mathematical derivation of the demand curve:

Derive the demand function for good X and Y given
U(x, y) = 1/4QxQy, Px, Py, &M.
Solution
=> M = QxPx + QyPy
At the optimum choice, the slope of IC (MRSx,y = MUx/MUy) is equal to the slope of the budget
line(Px/Py). That is,
MUx/ MUy = Px/ Py
But MUx = U/ X = ¼ Qy and
MUy = U/ Y = ¼ Qx
 ¼ Qy/ ¼ Qx = Px/ Py
 QyPy = QxPx----------------------------------------(1)
The budget constraint is
M = QxPx + QyPy
=> Qy = M/ Py – Px/ Py Qx------------------------------ (2)
Substitute (2) in to (1)
 Py ( M/ Py – Px/ Py Qx) = Qx Px
 M – PxQx = QxPx
 2PxQx = M
 Qx = 1 M
2Px
To obtain the demand function for Y:
M = PxQx + PyQy
=> PxQx = M – PyQy
Qx = 1/ PxM – (Py/Px)Qy--------------------------------(3)
Substitute (3) into (1)
 PxQx = PyQy
 Px(1/PxM – Py/PxQy) = PyQy
 M – PyQy = PyQy
 2PyQy = M
 Qy = 1 x M  is the demand function for Y.
2Py

Example: given utility U(x, y) = X1/3Y2/3 , Px = 2, Py = 5 and M = 400, find:

(1) The demand equation for X and Y.
(2) The utility maximizing levels of X and Y.
(3) The maximum utility
(4) The MRSx,y at the optimum level.
Solution:1
U(x, y) = X1/3Y2/3
At equilibrium, MUx/MUy= Px/Py
But, MUx = U/ /X = 1/3 X-2/3Y2/3
MUy = U/ /Y = 2/3X1/3 Y-1/3
=> 1/3 X-2/3Y2/3 Px
=

2/3X1/3 Y-1/3 Py

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=> X-2/3Y2/3 . 3 Px
=
3 2X1/3 Y-1/3 Py

=> X-2/3Y2/3 Px
2X1/3 Y-1/3 = Py

=> X-1Y Px
=
2 Py

=> Y Px
=
2X Py

=> Py Y = 2 Px X-------------------------------------------------(1)

But, M = Py Y + PxX  Is the budget constraint.

=> PyY = M – PxX

=> Y = M/ Py – Px/ Py X-----------------------------------------(2)

And PxX = M – PyY
=> X = M/Px –(Py/Px)Y-------------------------------------------(3)
Substitute equation (2) into (1)
 PyY = 2 PxX
 Py(M/Py – Px/Py X) = 2PxX
 M – Px X = 2PxX
 3PxX = M
 X=M
 Is the demand equation for X.
3Px
Similarly, substitute equation (3) into (1).
PyY = 2PxX
 2Px(M/Px – Py/PxY) = PyY
 2M – 2PyY =PyY
 3PyY = 2M
 Y = 2M
 Is the demand function for commodity Y.
2Py

(2) The above functions of X & Y are derived from the equilibrium position of the consumer. Thus,
substitute the value of M, Px and Py in the demand equations to find the optimum value of X and Y.
X = M/ 3Px = 400/ 3(2) = 400/6 = 200/3=66.7
Y = 2M/3Py = 2(400)/3(5) = 160/3 = 53.3
(3) U = X1/3Y2/3
= (66.7)1/3(53.3)2/3 = 57.5 is the maximum utility.
(4) At the equilibrium or at the optimum point,
MRSx,y = MUx/MUy = Px/Py
=>MRSx,y = 2/5 = 0.4
OR MRSx,y = MUx/MUy =1/3 X-2/3Y2/3 Y 160/3
= =
2/3X1/3 Y-1/3 2X 2(200/3)

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= 160/3 80 40
= = = 0.4
400/3 200 100

DERIVATION OF THE MARKET DEMAND

In our previous discussion we have derived the individual demand curve from the utility
maximization behavior of consumers. Now we will derive the market demand from this
individual demand curves. As it has been proved, the individual demand is negatively
related to the price commodity in the sense that when price decrease, the individual
consumer purchases more of the commodity in order to maximize his/her utility. The
market demand curve for the commodity is simply the horizontal summation of the
demand curve of all the consumers in the market. In other words the quantity demanded
in the market at each price is the sum of the individual demands of all consumers at that
price.

EXAMPLE:
Assume that there are two consumers in the market for a particular commodity X ( say
hamburger) and their demand at each price is given as follow:
Price ($) Qx dded by A Qx dded by B Market demand
2 2 2 4
1 6 4 10
0.5 10 6 16

Graphically the market demand can be derived as follows:

Px Px Px
Individual A Individual B Market demand

2------ --------------------------- ------------------------------------- -------------

1--------------------------------- ------------------------------------ ------------------------

0.5-------------------------------- ------------------------------------ ------------------------------------

d1 d2 MD

O 2 6 10 O 2 4 6 O 4 10 16

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Thus, the market demand fort a commodity shows the various quantities of the
commodity demanded in the market per unit of time at various alternative price of the
commodity while holding every thin else constant. The market demand for a commodity
is negatively sloped (just as an individual demand curve), indicating that price and
quantity are inversely related. That is, the quantity demanded of the commodity increases
when its price falls and decreases when its price rises.

DETERMINANTS OF DEMAND

Determinants of demand are factors that cause the consumer to increase or decrease its
demand for a particular commodity. Demand is a multi-variety function in a sense that
it‘s determined by many factors/variables. The most important determinants of market
demand are considered to be the price of the commodity in question, the price of other
related commodities, the consumer income and testes. The result of change in the price of
the commodity is shown by a movement from one point to another on the same demand
curve, while the effect of changes in other determinants is shown by a shift of demand
curve and these factors are called shift factors.
Px

P2----------- B

P ------------------------------

P1--------------------------- A

D D‘ D‘‘
D
Qx Qx
O X2 X1 O X1 X2 X3

Movement along the demand curve Shifts of the demand curve as, for exam-
as the price of X changes. ple income increases

Apart from the above determinants, demand is affected by numerous other factors, such
as the distribution of income, total population and its consumption, wealth, credit
availability, change in expectation about the future price of the commodity, etc.

ELASTICITY OF DEMAND
The concept of elasticity is used to measure the amount by which the quantity demanded
changes when its determinants change. There are as many elasticities of demand as there
are its determinants. The most important of these elasticities are:

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(A) The price elasticity of demand

(B) The income elasticity of demand
(C) The cross-elasticity of demanded.

THE PRICE ELASTICITY OF DEMAND

The price elasticity is a measure of the responsiveness of demand to changes in the
commodity‘s own price. If the changes in price are very small we use as a measure of the
responsiveness of demand the point elasticity of demand. If the changes in price are not
small we use the arc elasticity of demand as a relevant measure.
The point elasticity of demand is defined as the proportionate change in the quantity
demanded resulting from a very small proportionate change in price. Symbolically, we
may write as:
ep = dQ/Q dQ P
OR ep = x
dP/P dP Q
If the demand is linear
Q = bo – b1P, its slope is dQ/dP = -b1. Substituting in the formula we obtain,
ep = -b1.P/Q.

Graphically, the point elasticity of a linear demand curve is shown by the ratio of the
segments of the line to the right and to the left of the particular point. For example, in the
figure below the elasticity at point F is the ratio:

Given this graphical measurement of point elasticity it is obvious that at the mid-point of
a linear demand curve ep = 1 (point M). At any point to the right of M the point elasticity
is less than unity (ep < 1); finally at any point to the left of M, ep > 1. At point D, the
ep  , while at point D‘ the ep = O. The price elasticity is always negative because of
the inverse relationship between Q and P implied by the law of demand. However, the
negative sign is omitted when writing the formula of the elasticity.

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The range of values of the elasticity is O  ep  .

(1) If ep = O, then the demand is perfectly inelastic
(2) If ep = 1, then the demand is unitary elastic
(3) If ep = , then the demand is perfectly elastic
(4) If O< ep < 1, then the demand is inelastic
(5) If 1 < ep < , then the demand is elastic.
Px
D ep

ep>1

M ep = 1

ep<1

o ep = O
P P P

P D

Q o Q Q
ep = o ep = 1 ep = 

The above formula for the price elasticity is applicable only for infinitesimal changes in
the price. If the price changes appreciably we use the following formula, which measures
the arc elasticity of demand:
Q P1 + P 2 Q P1 + P2
ep = x 2 x
P = P Q1 + Q2
Q1 + Q2

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Microeconomics I

The arc elasticity is a measure of the average elasticity, i.e. the elasticity at the mid-point
of the two points A and B on the demand curve defined by the initial and the new price
levels.
P

P1---------- A

P2--------------------------------B

D
Q
O Q1 Q2

DETERMINANTS OF PRICE ELASTICITY OF DEMAND

The basic determinants of the elasticity of demand of a commodity with respect to its
own price are:
(1) The availability of substitute; the demand for a commodity is more elastic if there
are close substitute for it.
(2) The nature of the need that the commodity satisfies. In general, luxury good are
price elastic, while the necessity is price inelastic.
(3) The time period; demand is more elastic in the long run.
(4) The number of uses to which a commodity can be put. The more the possible uses
of a commodity, the greater its price elasticity will be.
(5) The proportion of income spent on the particular commodity.

INCOME ELASTICITY OF DEMAND

The income elasticity is defined as the proportionate change in the quantity demanded
resulting from a proportionate change in income.
ey = dQ/Q dQ Y
= x
dY/Y dY Q

If ey > o, then the commodity is normal.

If ey < o, ― ― ― inferior.
If ey > 1, ― ― ― luxury.
If o < ey < 1, ― ― necessity.

The main determinants of income elasticity are

(1) The nature of the need that the commodity covers: the percentage of income spent
on food declines as income increases.

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(2) The initial level of income of a country. For example, a TV set is a luxury in
underdeveloped countries while it is a necessity in a country with high per capital
income.
(3) The time period, because consumption patterns adjust with a time lag to changes
in income.
THE CROSS- ELASTICITY OF DEAMADN
The cross elasticity of demand is defined as the proportionate change in quantity demand
of X resulting from a proportionate change in the price of Y.
dQx/Qx dQx Py
exy = = x
dPy/Py dPy Qx
If exy < o, then X & Y are complementary goods.
If exy > o, ― ― substitute goods.

The main determinants of the cross elasticity is the nature of the commodities relative to
their use. If two commodities can satisfy equally well the same need, cross elasticity is
high and vice versa.

PRICE ELASTICITY AND TOTAL EXPENDITURE

An important relationship exists between the price elasticity of demand and the total
expenditure of consumers on the commodity (total revenue of producers). It postulates
that a decline in the commodity price results in an increase in total expenditures if
demand is elastic leaves total expenditure unchanged if demand is unitary elastic, and
results in a decline in total expenditure if demand is inelastic.
Specifically when the price of the commodity falls, total expenditure (price times
quantity) increase if demand is elastic because the percentage increase in quantity (which
by itself tends to increase total expenditure) exceeds the percentage decline in price
(which by itself tends to decline total expenditure). Total expenditures are maximum
when /ep/ = 1and decline thereafter. That is, when /ep/ < 1, a reduction in the commodity
price leads to a percentage increase in the quantity demanded of the commodity that is
smaller than the percentage reduction in price, and so total expenditure on the commodity
decline. This can be shown by the following table.

point Price of X (Px) Quantity (Qx) Total Absolute value

expenditure(TE) of ep /ep/
A 2.00 0 0 
C 1.50 3 4.50 3
E 1.00 6 6.00 1
F 0.50 9 4.50 1/3
H 0 12 0 0

From the above table we see that between points A and E, /ep/>1 and total expenditure on
the commodity increases as the commodity price declines. The opposite is true between
points E and F over which /ep/<1. Total expenditures are maximum at point E (the
geometric mid-point of the demand curve). The general rule summarizing the relationship

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among total expenditures, price and the price elasticity of demand is that total
expenditures and price move in opposite directions if demand is elastic and in the same
direction if demand is inelastic.

MARKET DEMAND, TR AND MR

From the market demand curve we can derive the total expenditure of the consumer,
which forms the total revenue of firms selling the particular product. The total revenue is
the product of the quantity sold and the price.
TR = P.Q
If the market demand is linear the TR curve will be a curve which initially slopes
upwards, reaches a maximum and then starts declining. We can proof this from our
previous discussion of the relationship between elasticity and TR/TE.
P TR
D
Rmax
P1 A
B
P* ep = 1
C
P2
D‘ TR
O Q1 Q* Q2 Q O Q* Q

Another important point in the theory of firm is the MR. the marginal revenue is the
change in total revenue resulting from selling an additional unit of the commodity.
Graphically, MR is the slope of total revenue curve at any one point. If the demand curve
is linear, the MR curve is twice as steep as the demand curve.
P
D

D‘
O Q

MR
This can be proved mathematically as follows:
MR is the derivative of TR function:
MR = d(TR)
dQ

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Microeconomics I

= d(PQ)
dQ
= P + Q.dP
dQ
if the demand curve is linear its equation in terms of price is:
P = ao – a1Q
Substituting P in the TR function we find
TR = PQ = aoQ – a1Q2

The MR is then MR = d(TR)

dQ
= ao – 2a1Q
This proves that the MR curve starts from the same point (ao) as the demand curve, and
that the MR is a straight line with a negative slope twice as steep as the slope of the
demand curve.

The relationship between MR and price elasticity

The MR is related to the price elasticity of demand with the formula

MR = P(1 – 1/e)
Proof:
Assume that the demand function is P = f(Q)
The total revenue is TR = PQ = [f(Q)]Q

The MR is
MR = d(PQ)
dQ
= P.dQ + Q.dP
dQ dQ
= P + Q.dP
dQ
The price elasticity of demand is defined as
e = - dQ .P
dP Q
Rearranging we obtain
-eQ = dQ
P dP
-P = dP
eQ dQ
Substituting dP/dQ in the expression of the MR we find
MR = P + QdP
dQ
= P – Q.P
eQ
=P–P

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Microeconomics I

e
MR = P(1 – 1/e)

Total revenue, marginal revenue and price elasticity

We said that if the demand curve is falling the TR curve initially increases, reaches a
maximum, and then starts declining. We can use the earlier derived relationship between
MR, P and e to establish the shape of the total revenue curve.
The total revenue curve reaches its maximum at the point where e = 1, because at this
point its slope, the MR, is equal to zero:
MR = P(1 – 1/1) = 0
If e>1 the TR curve has a positive slope, that is, it is still increasing and hence has not
reached its maximum point given that
P > 0 and (1 – 1/e) >0; hence MR > 0
If e<1 the TR curve has a negative slope, that is, it is falling given
P > 0 and (1 – 1/e) < 0; hence MR < 0
We may summarize these results as follows:
- If the demand is inelastic (e<1), an increase in price leads to an increase in TR,
and a decrease in price leads to a fall in TR.
- If the demand is elastic (e>1), an increase in price will result in a decrease of TR,
while a decrease in price will result in an increase in TR.
- If the demand is unitary elastic, TR is not affected by change in price since e=1
and MR=0.

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CHAPTER TWO
THE THEORY OF PRODUCTION
3.1 THE PRODUCTION FUNCTION

In the production process/ activity, firms turn inputs into output. This transformation of
inputs (factor of productions) into output at a particular time period and at a given
technology (state of knowledge about the various methods that might be used to
transform inputs into outputs) is described by a production function.
The production function is a function that shows the highest output that a firm can
produce for every specified combination of inputs. It is a purely technical relation which
connects factor inputs to outputs. Assuming labor (L) and capital (K) as the only inputs,
the production function can be written as: Q = f(L,K).
The production function allows inputs to be combined in varying proportions so that
output can be produced in many ways (using either more capital or less labor or vise
versa). For example, a unit of commodity X may be produced by the following processes:

Process P1 Process P2 Process P3

Labor units 2 3 1
Capital units 3 2 4

Activities or these methods of productions can be shown by a line from the origin to the
point determined by the labor and capital inputs combination.
K

3 p1
2 p2

1 p3

0 2 3 4 L

The production function (a purely technical relationship which connects factor inputs and
outputs) includes all the technically efficient methods of production. The technically
inefficient methods are not included in the production functions. A method of production
A is technically efficient than any other method B if A uses less of at least one input and
no more of the other factors as compared with B. For example, commodity Y can be
produced by two methods, A and B as follows:
A B
Labor 2 3
Capital 3 3
Method A is considered as technically efficient method as compared with B. The basic
theory of production concentrates only on efficient methods and thus inefficient methods
will not be used by rational producer.

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If a process A uses less of some factor(s) and more of some other(s) as compared with B,
then A and B cannot be directly compared on the criterion of technical efficiency. For
example, the activities
A B
Labor 2 1
Capital 3 4
are not directly compared. Both processes are considered as technically efficient and are
included in the production function. Which one of them will be chosen at any particular
time depends on the price of factors (inputs).The choice of any particular technique
among the set of technically efficient processes is an economic one, which is based on the
price of factors of production. Note that a technically efficient method is not necessarily
economically efficient.
ISOQUANTS
Assuming that labor and capital are the only two inputs used to produce an item, the
output achievable for various combinations of inputs can be shown by using isoquants.
An isoquant is the locus of all the technically efficient methods (or all the combinations
of factors of production) for producing a given level of output. It is a curve showing all
possible combinations of inputs that yield the same output. The production isoquant may
assume different shapes depending on the degree of substitutability of factors. These are:
(1) Linear isoquant: this type assumes perfect substitutability of factors: a given
output may be produced by only labor, or only capital, or by an infinite
combinations of K and L. See figure A below.
(2) Input-output isoquant: this assumes strict complementarily (i.e. zero
substitutability) of the factors of production. There is only one method of
production for any one commodity. The isoquant takes the shape of right angle
triangle. This type of isoquant is called ―Liontief isoquant‖ after the name
Leontief who invented the input output analysis. See figure B below.
(3) Kinked isoquant: this assumes limited substitutability of K and L. there are only
few processes for producing a particular commodity. Substitutability of the
factors is possible only at the kinks. See figure C below.
(4) Smooth or convex isoquant: this form assumes continuous substitutability of K
and L only over a certain range, beyond which factors can not substitute each
other. The isoquant is a smooth curve which is convex to the origin. Consider
figure D below.

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Microeconomics I

K K

O L O L
A. Linear isoquant B. Input-output isoquant
K K
P1
P2
X
P3

P4 X

O L O L
C. Kinked isoquant D. Convex isoquant

Even though the kinked isoquant is more realistic, most of the time the smooth or convex
isoquant is used in the tradition economic theory because it is mathematically simpler to
handle by the simple rules of calculus.
Isoquant map: is a graph combining several or a set of isoquants. An isoquant map is
another way of describing a production function, just as an indifference map is a way of
describing a utility function. The level of output increases as we move upward to the right
where as it remains constant along an isoquant (see points A, B & C in the figure below).
K

*A
*C

Q=100
*B
Q=50

O L

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Microeconomics I

SHORT RUN PRODUCTION FUNCTION AND STAGES OF PRODUCTION

The production function in the traditional theory assumes the form:
X = f(L, K, r, y)
Where L is labor, K is capital, r is returns to scale which refers to the long run analysis of
the laws of production since it assumes change in the plant, and y is the efficiency
parameter related to the organizational and entrepreneurial aspect of the production.
Graphically, the production function can be shown as follows:
X Panel A X Panel B

X=f(L)k3,r3,y3 X=f(K)L3,r3,y3

X=f(L)k1,r1,y1
X=f(K)L1,r1,y1

O L O K
In panel A, as labor increases, ceteris paribus, output increases: we move along the curve
depicting the production function. If K and/or r, and/or y increase, the production
function shifts upwards. The same is true for panel B.
The slope of the production function is the marginal products of the factors of production.
The MP of a factor is defined as the change in output resulting from the change in the
factor, keeping all other factors constant. That is
MPL = X and MPK = X
L K

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Graphically, the MPL is shown by the slope of the production function X=f(L) and the
MPK is shown by the slope of the production function X=f(K). The slope of a curve at
any one point is the slope of a tangent line at that point.

X MPL=X = 0 MPK=X = 0
L K
X=f(L) X=f(K)

O A‘ B‘ L O C‘ D‘ K
MPL MPK

Stage I Stage II Stage III Stage I Stage II Stage III

APL APK
O A B L O C D
MPL MPK

From the above graph we can understand that as the labor units used in the production
processes goes on increasing, the output initially increases at an increasing rate, then
starts rising at a decreasing rate, reaches a maximum and then starts falling. As a result
the MP initially increases, reaches a maximum, and then starts declining since it is the
slope of the TP curve. The MP is even negative when the TP declines. On the other hand,
the AP is given by the slope of the line drawn from the origin to the corresponding point
on the TP curve. Thus, the AP initially increases, reaches a maximum at A‘ level of input
and then starts declining. AP and MP are equal at the maximum of the AP. Accordingly
we can divide this production function into three stages as stage I (from zero TP, MP, &
AP up to the maximum of AP), stage II (from the maximum of AP to zero MP), and stage
III (from zero MP onwards).
At stage I, MP>AP and both of them are rising initially and MP falls latter on. Since each
additional unit of labor (on panel A) is coming up with contribution larger than the
average, it is rational to hire more labor and produce more. Thus, it is not reasonable to
produce at this stage.

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At the third stage where both APL and MPL are declining and MPL<APL, it is not
rational to produce at all because each additional unit of labor added makes the total
product to decline (i.e. its contribution is negative).
Thus, it is in the second stage that a rational firm operates. Here each additional labor
contributes positively to the production but less than the average. At this stage as the use
of a variable input (labor) increases with other inputs (capital) being fixed, the resulting
additions to output (MPL) will eventually decrease. This principle is known as the law of
variable proportion or the law of diminishing marginal returns.
In summary, the production theories concentrate only on the efficient part of the
production function, that is, on the ranges of output over which the MP‘s are positive. No
rational firm would employ labor beyond OB or capital beyond OD since an increase in
the factors beyond these levels would result in the reduction of the TP of the firm. Thus,
the basic theory of production concentrates on the range of output over which the MPs
are although positive, decreases (i.e. A‘B‘ and C‘D‘). This means over the range where
MPL > 0 but (MPL) < 0 and MPK > 0 but (MPK) < 0
L K
This condition implies that the tradition theory of production concentrates on the range of
the isoquants over which their slope is negative and convex to the origin. In the figure
below, the production function is depicted by a set of isoquants. Similar to the case of
indifference curves, the further away from the origin an isoquant lies, the higher the level
of output it represents and isoquants do not intersect.
The locus of points of isoquants where the marginal products of the factors are zero
forms the ridge line. At points A, B, &C the MPK is zero and hence forms the upper
ridge line. The lower ridge line shows that the MPL is zero. Thus, production techniques
are only efficient inside the ridge lines. Outside the ridge lines the marginal product of
the factors is negative and the methods of productions are inefficient, since they require
more quantities of both factors for producing a given level of output.
K
Upper ridge line (MPK = 0)
A B C
Lower ridge line (MPL = 0)

F X3
X2
E
X1
D
O L
The slope of the isoquant (dK/dL) defines the degree of substitutability of the factors of
production. This slope decreases (in absolute terms) as we move downwards along the
isoquant, showing the increasing difficulty in substituting L for K. The slope of the
isoquant is called the rate of technical substitution, or the marginal rate of technical
substitution (MRTS) of factors:
MRTSL,K = -K = slope of an isoquant.
L

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MRTSL,K is defined as the amount of K that the firm must sacrifice in order to obtain one
more unit of L so that it produces the same level of output. It is the slope of an isoquant.
It can be proved that the MRTS is equal to the ratio of the marginal products of the
factors. That is,
MRSL,K = -K = X/L = MPL
L X/K MPK
Proof:
The production function can be written as X = f(K,L)= C. It is equal to C because along
an isoquant the TP is constant.
The slope of a curve is the slope of a tangent line at that point. The slope of a tangent line
is defined by the total differential. The total differential (dX) is zero along an isoquant
since the TP is constant. Thus,
dX = (X/K)K + (X/L)L = 0
 (MPK)K + (MPL)L = 0
 -(MPK)K = (MPL)L
 -K/L = MPL/MPK
Along the upper ridge line we have
MRTSL,K = MPL/MPK = ∞ => MPK = 0
And along the lower ridge line
MRTSL,K = MPL/MPK = 0 => MPL = 0
The MRTS as a measure of the degree of substitutability of factors has a serious defect
since it depends on the units of measurement of the factors. A better measure of factor
substitutability is provided by the elasticity of substitution. It is given by:
 = percentage change in K/L
Percentage change in MRS
 = d(K/L)/(K/L)
d(MRTS)/(MRTS)
The elasticity of substitution is a pure number independent of the unit of measurement of
K and L since both the numerator and the denominator are measured in the same units.

FACTOR INTENCITY

Factor intensity refers to a measure of the intensity of a method of production in the sense
that a measure of whether a given method of production is labor intensive (uses more
labor than capital) or capital intensive (uses more capital than labor). It can be measured
by the slope of the line from the origin to a particular point on the isoquant representing a
particular process. Factor intensity can also be measured by the capital labor ratio. In the
figure below process P1 is more capital intensive than process P2 because the slope of the
line OP1 is higher than the slope of OP2 or the ratio K1/L1 is greater than K2/L2. This

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implies that the upper part of the isoquant includes more capital intensive techniques
where as the lower part includes more labor intensive techniques.

K1 P1

P2
K2 X

O L
L1 L2

EXAMPLE:
Let us illustrate the above concepts with a specific form of production function, namely
the Cobb-Douglas production function. This form is the most popular in applied research,
because it is easier to handle mathematically. It is of the form:
X = bo.Lb1.Kb2
1. The marginal product of factors
MPL = X/L = b1.bo.Lb1-1.Kb2
= b1(boLb1Kb2)L-1
= b1.X/L = b1(APL) since X = bo.Lb1.Kb2
and APL = X/L
MPK = b2.X/K = b2(APK)
2. The marginal rate of substitution
MRSL,K = X/L = b1(X/L) = b1 . K
X/k b2(X/K) b2 L`
3. The elasticity of substitution
 = d(K/L)/(K/L) = 1
d(MRS)/(MRS)
Proof:
Substitute the MRS in to the elasticity formula and obtain
 =d(K/L)
(K/L)
d(b1/b2.K/L)
(b1/b2.K/L)

= d(K/L) . (b1/b2)(K/L)
(K/L) d(K/L)(b1/b2)

= d(K/L)(b1/b2) = 1
d(K/L)(b1/b2)

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4. Factor intensity. In a Cobb-Douglas function factor intensity is measured by the ratio

b1/b2. The higher the ratio the more labor intensive the technique is and vise versa.
3. The efficiency of production. The efficiency in the organization of factors of
production is measured by the coefficient bo. It is clear that if two firms have the same K,
L, b1, and b2 and still produce different quantities of output, the difference can be due to
the superior organization and entrepreneurship of one firm which resulted in production
difference. The more efficient firms will have a higher bo than the less efficient one.
4. The returns to scale. In the Cobb-Douglas production function, the returns to scale are
measured by the sum of the coefficients b1+b2. It will be discussed latter on.

LAWS OF PRODUCTION
The laws of production describe the technically possible ways of increasing the level of
production. This can be in various ways. Output can be increased by changing all factors
of production which is possible in the long run. This is called the law of returns to scale.
On the other hand output can be increased by changing only the variable input while
keeping the fixed inputs constant, which is possible in the short run. The MP of the
variable factor will decline eventually as more and more quantities of this factor are
combined with the other constant factors. This is known as the law of variable proportion.
Let us see these laws one by one.

1. THE LAW OF VARIABLE PROPORTION

This is a law for the case of short run where there is at least one fixed inputs. In our
earlier discussion of the short run production function and stages of production, we have
assumed labor as a variable input and capital as a fixed input. From that graph, what we
can understand is that as the use of a variable input (labor) increases with other inputs
(capital) fixed, the resulting addition to output will eventually decreases. This is shown
by a downward sloping MPL curve after its maximum point. This principle is known as
the law of variable proportion or the law of Diminishing returns.

2. LAWS OF RETURNS TO SCALE

The law of returns to scale refers to the long run analysis of production. In the long run,
where all inputs are variable output can be increased by changing all factors by the same
proportion. The rate at which output increases as inputs are increased by the same
proportion is called returns to scale. We have three cases of returns to scale: increasing,
constant and decreasing returns to scale.
I) Increase returns to scale: this is the case where increasing all factors by the
same proportion, m, leads to an increase in output by more than m scale.
II) Constant returns to scale: if we increase input by some factor, m and output is
increased by the same proportion as inputs, m, then it is called constant
returns to scale. In this case the size of the firm‘s operation doesn‘t affect the
productivity of its factors.
III) Decreasing returns to scale: if scaling up all inputs by m scales output up by
less than m, it is called decreasing returns to scale. This is because, may be

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difficulties in organizing and running a large scale operation may lead to

decreased production of both labor and capital.

Examples

1. If Q = 2K + 3L. We will increase both K and L by m and create a new production

function Q*. Then we will compare Q* to Q.

Q* = 2(Km) + 3(Lm) = 2Km + 3Lm = m(2K + 3L) = mQ

After factoring, we can replace (2K + 3L) with Q, as we were given that from the start.
Since Q* = mQ, we note that by increasing all of our inputs by the multiplier m we have
increased production by exactly m. So we have constant returns to scale.

2. Q=.5KL Again we put in our multipliers and create our new production function.

Q* = .5(Km)(Lm) = .5KLm2 = Qm2. Since m > 1, then m2 > m. this implies our new
production has increased by more than m.. so we have increasing returns to scale.

3. Q=K0.3L0.2 Again we put in our multipliers and create our new production function.
Q* = (Km)0.3(Lm)0.2 = K0.3L0.2m0.5 = Q m0.5. Since m > 1, then m0.5 < m. Our new
production has increased by less than m. so we have decreasing returns to scale.

RETURNS TO SCALE AND HOMOGENIETY OF THE PRODUCTION

FUNCTION

Suppose we increase both factors of production function X=f(L, K) by the same

proportion m, and we observe the resulting new level of output X* as X* = f(mK, mL). If
m can be factored out (that is, can be taken out of the bracket as a common factor), then
the new level of output can be expressed as a function of m (to the power n) and the
initial level of output as follows: X* = mnf(L, K) or X* = mnX. If so, the function is
called homogeneous. If m cannot be factored out, the production function is called non-
homogeneous. The above three examples are a homogeneous functions since m can be
factored out. Thus, a homogeneous function a function such that if each of the inputs is
multiplied by m, the m can be completely factored out of the function. The power n of m
is called the degree of homogeneity and is a measure of the returns to scale.
If n=1, we have a CRS.
If n <1, ― DRS.
If n >1, ― IRS.

Given a Cobb-Douglas production function Q=boLb1Kb2, returns to scale is measured by

the sum of the powers of the factors. That is,
If b1 + b2 =1, then there is a CRS
If b1 + b2 >1, ― ― IRS
If b1 + b2 <1, ― ― DRS
Proof

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Let L and K increases by m. The new level of output is

X*=bo(mL)b1(mK)b2
= bomb1Lb1mb2Kb2
X* =mb1+b2(boLb1Kb2)
X*= mb1+b2X
This implies the function is homogeneous of degree b1+b2 and the returns to scale
depend on the sum.

PRODUCT LINE: It shows a physical movement from one isoquant to another as we

change either both factors or a single factor. It describes the technically possible
alternative paths of expanding output. What path will actually chosen by the firm will
depend on the prices of factors. The product curve passes through the origin if both
factors are variable. But if only one factor variable (the other being kept constant), the
product line is a straight line parallel to the axis of the variable factor.
K K K

PL (Isoclines) PL
(Points with constant PL
MRTSL,K are joined)
PL
K PL

O L O L O L
Product line for homogen Non-homogeneous function Product line where K is fixed.
eous function. (Here, the K/L ratio diminishes)

A special type of product line which is the locus of points of different isoquants at which
the MRS of factors is constant is called an isocline. For homogeneous production
functions the isoclines are straight lines through the origin. In such case, the K/L ratio is
constant along any isocline (refer to the first graph).

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GRAPHICAL PRESENTATION OF RETURNS TO SCALE FOR

HOMOGENEOUS PRODUCTION FUNCTION
Constant returns to scale: Along any isocline, the distance between successive isoquants
is constant. Doubling the factor inputs double the level of output, tripling inputs results in
triple output, and so on.
K
In this case, there is a constant
C PL returns to scale because OA=AB=BC.
3K
2K B 3Q1

K A 2Q1

Q1
O L
L 2L 3L
Decreasing returns to scale: the distance between consecutive isoquant increases. By
doubling inputs, output increases by less than twice its original level.
K
In this case, there is a decreasing
PL returns to scale because doubling
Inputs will bring an output which is l
3K C 3Q1 less than double.

2K B <3Q1
2Q1
K A
Q1 <2Q1
O L
L 2L 3L

Increasing returns to scale: the distance between consecutive isoquant decreases. By

doubling inputs, output is more than doubled.
K
PL In this case there is an increasing return
To scale because doubling inputs results
3K in an output which is more than double.

C >3Q1
2K
B >2Q1 3Q1
K A 2Q1

Q1
O L 2L 3L L

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Microeconomics I

TECHNICAL PROGRESS AND THE PRODUCTION FUNCTION

As knowledge of new and more efficient methods of production become available,

technology changes. Furthermore new inventions may result in increase of the efficiency
of all methods of production. These changes in technology constitute technical progress.
Graphically, the effect of technical progress is shown with an upward shift of the
production function or a downward movement of the isoquant. This shift shows that the
same output may be produced by less factor inputs, or more output may be produced with
the same inputs.

X K

X‘ X‘=f(L)
X=f(L)
X

Xo

Xo
O L O L
L*

Technical progress may also change the shape (as well as produce a shift) of the isquant.
Hicks has distinguished three types of technical progress, depending on its effect on the
rate of substitution of the factors of production.
Capital deepening technical progress: a technical progress which increases the MPK by
more than the MPL. For this kind of technical progress, along a line on which the K/L
ratio is constant, the MRTSL,K decreases in absolute terms (the slope of an isoquant
declines). The slope of the shifting isoquants becomes less steep along any given radius.
This type of technical progress is also called capital saving or labor using technical
progress.
K
Isocline

A‘
A‘‘

O L

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Labor deepening technical progress: a technical progress which increases the MPL by
more than the MPK. Along a line on which the K/L ratio is constant, the MRTSL,K
increases(the slope of an isoquant increases in absolute value). It is also called labor
saving or capital using technical progress.
K
Isocline

A‘
A‘‘

Neutral technical progress: a technical progress that increases the MPL and MPK by the
same percentage, so that the MRTSL, K (along any radius) remains constant. The
isoquant shifts downwards parallel to itself.
K
Isoline

A
A‘

A‘‘
O L

EQUILIBRIUM OF THE FIRM: CHOICE OF OPTIMAL COMBINATION OF

FACTORS OF PRODUCTION

A firm is said to be in equilibrium when it employs those levels of inputs that will
maximize its profit. This means the goal of the firm is profit maximization (maximizing
the difference between revenue and cost). Thus the problem facing the firm is that of
constrained profit maximization, which may take one of the following forms:
a) Maximizing profit subject to a cost constraint. In this case total cost and prices are
given and the problem may be stated as follows
Max П = R – C
П = PxX – C
Clearly maximization of П is achieved in this case if X is maximized, since C and Px are
constants.
b) Maximize profit for a given level of output.
Max П = R- C
П = PxX –C

Department of economics 39
Microeconomics I

Clearly in this case maximization of profit is achieved by minimizing cost, since X and
Px are given.

To derive graphically the equilibrium point of the firm, we will use the isoquant map and
the isocost line. An isoquant is a curve that shows the various combinations of K and L
that will give the same level of output. It is convex to the origin whose slope is defined
as:
- ∂K/∂L = MRSL,K = MPL/MPK = ∂X/∂L
∂X/∂K
The isocost line is defined by the cost equation
C = rK + wL
Where w=wage rate, and r=price of capital services.
The isocost line is the locus of all combinations of factors that the firm can purchase with
a given monetary cost outlay. The slope of the isocost line is equal to the ratio of the
prices of the factors of production, w/r.
K the isocost equation is given by C=wL + rK
C/r => rK = C - wL
=> K = C/r – w/r L
From this the slope is –w/r or it is the
vertical change over the horizontal change.
=> Slope = C/r
C/w
=> Slope = C/r.w/C
=> Slope = w/r.
O C/w L
Case 1: Maximization of output subject to a cost constraint.
Given the level of cost and the price of the factors and output, the firm will be in
equilibrium when it maximizes its output. This is at the point of tangency of the isocost
line to the highest possible isoquant curve. In the following graph, it is at point e where
the firm produces X2 with K1 and L1 units of the two inputs. Higher levels of output to
the right of e are desirable but not attainable due to the cost constraint. Other points
below the isocost line lie on a lower isoquant than X2. Hence X2 is the maximum output
that can be achieved given the above assumptions (C, w, r, & Px being constant).
K
A

K1 e X3

X2
X1

O B L
L1
At the point of tangency:
a. slope of isoquant = slope of isocost

Department of economics 40
Microeconomics I

w/r = MPL/MPK = MRSL,K. this is a necessary condition.

b. the isoquant is convex to the origin. This is the sufficient condition.

NOTE: If the isoquant is concave to the origin, the point of tangency does not define the
equilibrium position.
K

e1
e

X2

O e2 L

Output X2 depicted by the concave isoquant can be produced with lower cost at e2 which
lies on a lower isocost curve than e (corner solution).

Mathematical derivation of the equilibrium of the firm.

A rational producer seeks the maximization of its output, given total cost outlay and the
prices of factors. That means:
Maximize X = f (K, L)
Subject to C = wL + rK

This is a constrained optimization which can be solved by using the lagrangean method.
The steps are:
a. rewrite the constraint in the form
wL + rK – C = 0
b. multiply the constraint by a constant which is the lagrangian multiplier
(wL + rK – C) = 0
c. form the composite function
Z = X - (wL + rK – C)
d. partially derivate the function and then equate to zero
∂Z = ∂X - w = 0
∂L ∂L
 MPL = w
  = MPL----------------------------------------------------------------------- (1)
w
∂Z = ∂X - r = 0
∂K ∂K
 MPK = r
  = MPK----------------------------------------------(2)
r
∂Z = rL + rK – C = 0------------------------------------------- (3)

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Microeconomics I

∂
From equation (1) and (2) we understand that
MPL = MPK
w r
=> MPL = w
MPK r
This shows that the firm is in equilibrium when it equates the ratio of the marginal
productivities of factors to the ratio of their prices. It can be shown that the second order
conditions for the equilibrium of the firm require that the marginal product curves of the
two factors have a negative slope.
Slope of MPL = ∂2X
∂L2
Slope of MPK = ∂2X
∂K2

=> ∂2X < 0 and ∂2X < 0

∂L2 ∂K2
2
And ∂2X . ∂2X > ∂2X
∂L2 ∂K2 ∂L∂K

Case 2: minimization of cost for a given level of output

The condition for the equilibrium of the firm is formally the same as in case 1. That is,
there must be tangency of the given isoquant and the lowest possible isocost line, and the
isoquant must be convex. However, in this case we have a single isoquant which denotes
the desired level of output, but we have a set of isocost lines. Curves closer to the origin
show a lower total cost outlay. Since isocosts are drawn on the assumption of constant
prices of factors, they are parallel to each other and their slopes (w/r) are equal. Thus the
firm minimizes its cost by employing the combination of K and L determined by the
point of tangency of X isoquant with the lowest possible isocost line. Points below e are
desirable because they show lower cost but are unattainable for output X. points above e
show higher costs. Hence point e is the least cost point.

e
K1
X

O L

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Microeconomics I

L1

In this case also the lagrangian method can be followed to derive the equilibrium point
mathematically. But the problem is different. That is,
Minimize C = wL + rK
Subject to X = f(K,L)
The lagrangian function will be:
Z = (wL + rK) + [X-f(K,L)]
Partially derivate Z w.r.t L, K, &  and equate to zero.
∂Z = w -  ∂f(K,L) = 0
∂L ∂L
=> w -  ∂X = 0
∂L
=> w =  MPL
=>  = MPL ----------------------------------------- (1)
w
∂Z = r -  ∂f(K,L) = 0
∂K ∂K
=> r -  ∂X = 0
∂K
=> r =  MPK
=>  = MPK --------------------------------------- (2)
r
∂Z = X – f(K,L) = 0 ------------------------------------(3)
∂
From equation (1) and (2):
MPL = MPK
w r
=> w = MPL = MRSL,K
r MPK
This is the same as the condition in case one. In a similar way, the second condition will
be:

=> ∂2X < 0 and ∂2X < 0

∂L2 ∂K2
2
2 2 2
And ∂ X.∂ X> ∂ X
∂L2 ∂K2 ∂L∂K

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CHAPTER-THREE
THEORY OF COST
Cost functions are derived functions (derived from production function).Economic theory
distinguishes between short-run and long-run costs. Both in the short-run and in the long-
run, total cost is a multi variable function, i.e. total cost is determined by many factors
such as output, technology, prices of factors and fixed factors. To simplify the analysis
we consider cost as a function of output [c= f(x)] on a ceteris paribus assumption. Thus,
determinants of costs, other than output, are called shift factors.

4.1 Short-Run Costs

Short-run costs are costs over a period during which some factors of production 9usually
capital equipment and management) are fixed. Short-run total costs are split into two
groups: total fixed costs and total variable costs: TC = TFC+TVC.Total variable cost is a
cost that varies as output varies whereas total fixed cost is a cost that does not vary with
the level of output. The fixed costs include:
 Salaries of administrative staff
 Expenses for building depreciation and repairs
 Expenses for land maintenances
 Depreciation of machinery.
The variable costs include:-
 The raw materials cost
 The cost of direct labor
 The running expenses of fixed capital, such as fuel, ordinary repairs and
routine maintenance.
As the total fixed cost (TFC) does not depend on the level of output, it is represented by a
horizontal line.
TC
Cost

TVC

TFC

O
Output (X)

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The total variable cost has usually an inverse-S shape which reflects the law of variable
proportions. According to this law, at the initial stage of production with a given plant, as
more of the variable factors is employed, its productivity increases and thus total variable
cost(TVC) increases at a decreasing rate = AVC declines. When the productivity of the
variable input falls, larger and larger units of the variable input will be needed to increase
output by the same unit and thus TVC and TC increase at increasing rates. By adding the
TFC and TVC we obtain the TC of the firm.
From the total-cost curves we obtain average cost curves.
 AFC is the total fixed cost divided by the amount of output, i.e., AFC= TFC.
X
Since TFC is constant, increase in X reduces the ratio and thus the AFC approaches
the quantity (output) axis as output rises.
 AVC= TVC.
X
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. For example in the figure below, the AVC at X1 is the slope of the ray oa, the
AVC at X2 is the slope of a ray ob, and so on. It is clear from the figure that the slope of
a ray through the origin declines continuously until the ray becomes tangent to the TVC
curve at c. to the right of this point the slope of rays through the origin starts increasing.
Thus the AVC curve falls initially as the productivity of the variable factor increases,
reaches a maximum when the plant is operated optimally and rises beyond that point.

C C AVC

TVC

d a

c b d
B
a c

o x1 x2 x3 x4 X o x1 x2 x3 x4 X

 ATC or AC = TC = TFC+TVC = AFC + AVC.

X X

Graphically the ATC curve is derived in the same way as the AVC. The ATC at any one
point is the slope of a line from the origin to the point on the TC curve.

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C C ATC

TC

d a

c b d
b
a c

o x1 x2 x3 x4 X o x1 x2 x3 x4 X

 MC = ∆TC = ∆ (TFC+TVC) = ∆TVC.

∆X ∆X ∆X
Graphically the marginal cost is the slope of the TC curve (which of courseis the same at
any point as the slope of the TVC). The slope of the TC curve at any one point is the
slope of a tangent line at that point. As we can see from the following graph, the tangent
line is initially becoming flatter up to X4 level of output and then become steeper as the
output goes on increasing. This implies the slope of the TC curve (MC) is initially
decreasing, reaches a minimum and then starts increasing.

C C
TC

MC

O X4 O X4 X

In summary the traditional theory of cost postulates that in the short run the cost
curves (AVC, ATC and MC) are U-shaped, reflecting the law of variable
proportions. In the short run with a fixed plant there is a phase of increasing
productivity (falling unit costs) and a phase of decreasing productivity (increasing
unit costs) of variable factor. Between these two phases of plant operation there is a
single point at which unit costs are at a minimum. In general, the short run cost
curves can be shown as follows.

Department of economics 46
Microeconomics I

Costs MC
ATC

AVC

AFC
O output (X)

The relationship between ATC and AVC

The AVC is a part of the ATC, given ATC = AFC + AVC. Both AVC and ATC are U-
shaped, reflecting the law of variable proportions. However, the minimum point of the
ATC occurs to the right of the minimum point of the AVC. This is due to the fact that
ATC includes AFC which falls continuously with increase in output. Initially the fall in
the AFC offsets the rise in the AVC and thus the ATC declines. But later on the rise in
the AVC more than offsets the fall in the AFC and thus the ATC will start rising
continuously. The AVC approaches the ATC asymptotically as X increases since the
AFC declines continuously.

The Relationship between MC and ATC

The MC cuts the ATC and the AVC at their minimum points. We said that MC is the
change in the TC for producing an extra unit of output. Assume that we start from a level
of n units of output. If we increase the output by one unit the MC is the change in TC
resulting from the production of the (n+1)th unit.
The AC at each level of output is found by dividing TC by X. Thus the ATC at the level
of Xn is
ATCn = TCn
Xn
And at the level of n+1
ATCn+1 = TCn+1
Xn+1
Clearly TCn+1 = TCn + MC
Thus,
a) if the MC of the (n+1)th unit is less than ATCn ( the ATC of the previous n units)
the ATCn+1will be smaller than the ATCn.
b) If the MC of the (n+1)th unit is higher than ATCn (the ATC of the previous units)
the ATCn+1 will be higher than the ATCn.

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As far as the MC is below the ATC, it pulls the ATC downwards and if the MC is above
the ATC, it pulls the latter upwards. From this it follows that the MC curve intersects the
ATC at the minimum point of the ATC. This can also be proofed by using a simple
calculus.
From ATC = TC => TC= (ATC).X
X
MC = d(TC) by definition.
dX

=> MC = d(ATC.X)
dX
=> MC = ATC.dX + X.d(ATC)
dX dX
=> MC = ATC + (X)(slope of the ATC)

Given that X and ATC are Positive,

 MC<ATC if slope of ATC is negative.
 MC=ATC if slope of ATC=0, (at the minimum of the ATC).
 MC>ATC if slope of ATC>0.

The relationship between MC and AVC

From AVC = TVC , => TVC = (AVC).X

X
MC = d(TC) = d(TFC+TVC) = d(TFC) + d(TVC)
dX dX dX dX

=> MC = d(TVC) , since there is no change in the TFC.

dX
=> MC = d(AVC.X) = AVC.dX + X.d(AVC)
dX dX dX
=> MC = AVC + (X) (slope of AVC)

Given that AVC and X are Positive,

 MC<AVC if slope of AVC<0
 MC =AVC if slope of AVC=0 (at the minimum point of the AVC).
 MC >AVC if slope of AVC>0.

Relationship between Product Curves and Cost Curves

Unit products and unit cost curves are mirror images of each other, i.e.
o when AP(MP) is ring AC(MC) is falling;
o when AP(MP) is falling AC(MC) is rising; and
o when AP(MP) is maximum AC(MC) is minimum

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See below for illustration of these relations.

Let TVC =wL, where w= given wage rate &L =labor input
Thus, AVC= TV = (wL) /Q = w (L /Q) = w
Q (Q/L)
But Q/L=APL, so AVC= w/ APL

Similarly, MC=TVC/Q, since TVC=wL

MC = wL = w (L) = w
Q (Q) (Q/L)
but Q/L =MPL
Thus, MC=w/MPL

Graphically:
AP/MP

APL

AC/MC MPL
MC

AVC

4.2 Long-run costs

The long-run is a period of time of such length that all inputs are variable. It is a
planning horizon in the sense that economic agents can plan ahead and choose many
aspects of the ―short-run‖ in which they will operate in the future. Thus, the long-run
consists of all possible short-run situations among which an economic agent may
choose.

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If a production technology is characterized by constant return to scale (CRS),

doubling output requires doubling of input, which implies doubling of total output
(cost) for given factor prices. Hence, the long-run total cost curve in this case is a
straight line through the origin. This implies that the long-run average and marginal
costs are horizontal lines and equal (LAC = LMC).
TC LAC
LMC
TC(Q)

LAC=LMC

O Q O Q

If we consider the case where total cost first increase at a deceasing rate due to
increasing returns to scale (which implies economies of scale). And then at an
increasing rate attributed to decreasing returns to scale after the optimum size, the
long-run total cost curve will look like the following. The LAC and LMC curves will
be U-shaped. LAC
TC TC(Q) LMC LMC
LAC

O Q O Q

The range from the minimum point of LAC to the left is called the economies of scale
range, which means output can be doubled for less than doubling of cost. The range
from the minimum of LAC to the right is called diseconomies of scale, because a
doubling of output requires more than a doubling of cost. The traditional theory of the
firm assumes that economies of scale exist only up to a certain plant, which is known
as the optimum plant size. With this plant all possible economies of scale are fully
exploited. If the firm increases further than this optimum size there are diseconomies
of scale arising from managerial inefficiencies. It is argued that management becomes
highly complex, managers are overworked and the decision making process become
less efficient.

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When a firm is producing at an output at which the LAC is falling, the LMC is less
than LAC. Conversely, when LAC is rising (increasing), LMC is greater than LAC.
The two curves intersect at a point where the LAC curve achieves its minimum. Like
the short run average cost (SAC) and SMC curves, the LAC and LMC curves are U-
shaped, but for different reasons. In the long-run, the source of the U-shape is
increasing and decreasing returns to scale, rather than diminishing returns to a factor
of production.

The Relationship between Short-run and long-run Average and Marginal costs

Assume that a firm is uncertain about the future demand for its product and is
considering three alternatives plant sizes: Small, Medium and Large. The short-run
average cost curves are SAC1, SAC2 and SAC3 in the figure below.
Cost

SAC1
SAC3
C1 SAC2
C3
C2
C4

O
Q1 Q1* Q2 Q2*

If the firm expects that the demand will expand further than Q1, it will install the
medium plant, because with this plant outputs larger than Q1 are produced with a
lower cost (for instance C2<C1 for output equal to Q*1). Similar considerations hold
for the decision of the firm when it reaches the level Q2.
If we relax the assumption of the existence of only three plants and assume that
there is a very large number (infinite number) of plants, we obtain a continuous curve,
which is the planning LAC curve of the firm. LAC curve is the locus of points
denoting the least cost of producing the corresponding output. It is a planning curve
because on the basis of this curve the firm decides what plant to set up in order to
produce optimally (at minimum cost) the expected level of output. The LAC curve is
U-shaped and it is often called the envelop curve because it envelopes the short run
curves.

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Microeconomics I

C
LAC
SAC1 SAC6
SAC2
SAC3 SAC5
SAC4

O Q
M
Because there are economies of scale and diseconomies of scale in the long-run, the
points of minimum average cost of the smaller and larger plant (plants 1 up to 4 and 5 up
to 7) do not lie on the long-run average cost curve. For example, a plant size 2 operating
at minimum average cost is not efficient because a larger plant can take advantage of
increasing returns to scale to produce at a lower average cost.
Each point of the LAC curve is a point of tangency with the corresponding SAC curve.
The point of tangency occurs to the falling part of the SAC curves for points lying to the
left of M. since the slope of the LAC is negative up to M, the slope of the SAC cures
must also be negative, because at the point of tangency the two curves have the same
slope. By the same logic, the point of tangency for outputs larger than Q occurs to the
rising part of the SAC curves.
Only at the minimum point M of the LAC is the corresponding SAC also at a minimum.
At the falling part of the Lac curve the plants are not worked to full capacity. To the
rising part of the LAC curve the plants are overworked. Only at the minimum point M is
the plant optimally employed.

The LMC is derived from the SMC curves but does not envelop them. The LMC is
formed from points of intersections of the SMC curves with vertical lines drawn from the
points of tangency of the corresponding SAC and the LAC curve.

C LMC
SMC1 SMC3 SAC3
LAC
a

SMC2

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To the left of a, SAC1 is greater than LAC so that SAC1 declines at a faster rate than the
LAC. So they are equal at a. this implies LMC >SMC1 to the left of a. At a, LMC=SMC1
(the same additional costs accrue to both the short-run and the long-run costs so that
SAC1=LAC). To the right of a, LMC<SMC1 (more incremental cost is added to the
short-run cost than to the log-run cost). At the minimum point of the LAC, the LMC
intersects the LAC. At this point, SAC=SMC=LAC=LMC.

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CHAPTER FOUR
PERFECT COMPETITION

Perfect, unlike everyday usage of the word, is characterized by a complete absence of

rivalry (competition) among firms.

Assumptions
- Large number of buyers and sellers: because of the very large number of buyers
and sellers an individual buyer or seller is too small to affect the market price.
- Identical commodities are produced by all firms in an industry in terms of its
technical characteristics and services associated with its sale and delivery ruling
out non-price competition.
- There is free entry to and exit from the industry.

These assumptions will imply that the firms are price takers so they are faced with
perfectly elastic demand curve.
Px

DDx

O Qx

- Profit maximization is the sole objective of firms in the industry (no other
objectives like welfare, etc.)
- No government intervention
- Perfect mobility of productive resources between or among firms.(Skills can be
learned and no factor monopolization and labor unionization.)
- Perfect (complete) knowledge of market condition in the part of sellers and buyers
both of the present and the future, and information is free and costless.
These assumptions rule out any uncertainty.

Short-run Equilibrium of the Firm and the Industry

The equilibrium output of the firm is the output that maximizes its total profit. Total
profits equal the difference between total revenues and total costs, i.e.
∏= TR – TC
∏= PQ – ATC (Q)
∏= Q (P –ATC)

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In a perfectly competitive market structure, price is given (firms are price takers). Thus
firms decide on the level of output (Q) they produce to attain their equilibrium points.
Two approaches are used in determining a firm‘s equilibrium.

1. The total approach: total profits are maximized when the positive difference between
total revenues and costs is largest.
TR/TC STC TR

Qe Q

To the left of point B and to the right of C, STC>TR so that the firm is in a loss (negative
∏). Between B and C, however, the firm is enjoying a positive profit and it is maximized
at the point where the vertical difference between the TR and STC is largest (at Qe).
Point B is the break-even point where the firm just covers its cost of production and
operates at zero economic profit.

2. The marginal approach: the perfectly competitive firm is a price taker and faces a
perfectly elastic demand curve. Since marginal revenue (MR) is dTR/dQ and price(P)
is constant, then P = MR.

MR = dTR = d(PQ) = p dQ = P
dQ dQ dQ
Total profit is maximum when the slope of the TR and total cost curves are equal.
That is, when MR (P) = MC

The firm is at equilibrium at quantity level Qe (where MR = P = MC at point E). To

the left of E, MR > MC (i.e., benefits > costs) and it should increase production. To
the right of E, MC>MR and the firm should cut back its production. This particular
figure represents the case where the firm operates at a loss (= area of rectangle
EFGH).

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∏ = Q(P – ATC)
∏ = Qe ( - EF)
∏ = - (EH) (EF)
= - area of EFGH
P/MR MC
MC ATC
AC

AVC

F
G M

H I E P=MR

O Q
Qe
It can be the case that competitive firms may operate at losses, at positive profits, or
at a normal (zero) profit. For instance, a firm operates at a positive profit if the
demand curves (MR) lies above point M. On the other hand, a firm gets only a normal
(zero) profit if the demand curve passes through M. In general,

If Then
P > AC Positive ( economic) profit
P = AC Normal ( zero ) profit, i.e., break-even point
AVC < P < AC Loss, but the firm continues to produce
P = AVC Shut-down point
P < AVC Loss or no operation

N.B.: in the figure above, P(MR) = MC at two points, E and I. But the profit
maximizing level of output is that level of output which corresponds to E. Condition
for profit maximization is
1. MR = MC this implies d∏ = 0
dQ
2. MC is rising => d2∏ < 0 or dM∏ < 0
dQ2 dQ
The firm operates at different points at the marginal cost curve depending on the level
of price it faces. Thus, its supply curve is its MC curve but above the shut-down
point. The industry supply curve is the simple horizontal summation of the supply
curves of the individual firms. Thus, the industry is at equilibrium when the industry
demand curve intersects the industry supply curve.

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S
$ $
S

Pe E P = MR Pe E*

O Qe Q O Qe Q

Panel A – short-run equilibrium Panel B – Equilibrium of the

the firm. Industry.

LONG RUN EQUILIBRIUM OF THE FIRM AND INDUSTRY

When long-run equilibrium is achieved, product prices will be exactly equal to, and
production will occur at each firm‘s point of minimum ATC. This is illustrated below for
a constant cost industry (the case where the expansion of the industry through entry of
new firms will have no effect up on resource prices and, therefore, up on production
costs) and a respective firm.

S0
LMC
ATC
$ S1

P1
P1
P1 = MR1

Po Po= MRo Po D1

D0

Firm Industry

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Suppose that a change in consumer tastes increase and thus product demand from D0 to
D1. This favorable shift in demand obviously makes production profitable; the new price
(P1) exceeds ATC. This economic profit will lure new firms into the industry. As the
firms enter, the industry supply of the product will increase causing product price to
gravitate downward towards the original level. The economic profits caused by the boost
in demand have been completed away to zero and as a result the previous incentive for
more firms to enter the industry has disappeared.
Therefore, in the long-run, all firms operate at a point where
(1) P = MR = LMC = LAC = SMC = SAC for the firm and
(2) Supply curve crosses demand for the industry.
In the long-run, all firms in a perfectly competitive industry (market) enjoy only normal
profit (zero profit) or at the break-even where TR = TC.

EXERCISE

Suppose you are the manager of a watch-making firm operating in a competitive market.
Your cost of production is given by C = 100 + Q2, where Q is the level of output and C is
total cost.
a) If the price of watches is birr 60, how many watches should you produce to
maximize profit?
b) What will your profit level be?
c) At what minimum price will you produce a positive output?

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CHAPTER ONE
PURE MONOPOLY
1.1. Characteristics and source of monopoly
Characteristics of Monopoly
The following are some of the characteristics or features of this market structure of pure
monopoly
I. Single Seller: It is a market structure in which the entire supply is controlled by one
firm, which implies that the firm and industry are same.
II. No clear substitutes:there are no close substitutes for the goods produced.
III. The monopolist is the price maker: It does not take a price which is determined by
the interaction of market demand and market supply. In order to expand its sale, it
decreases the price of the commodity.
IV. Entry Barrier: Entry is blocked in such market structure. The barriers may be legal,
financial, and natural.
V. No Collusion and Competition: Because there is only one firm there is no
competition exists and no collusion among firms also.

Sources of Monopoly
The rise and existence of monopoly is related to the factors, which prevents the entry of
new firms. The different barriers to entry that are the causes of monopoly are described
below.
The main causes to monopoly are:
i. Ownership of strategic raw materials:- some firms may get monopoly power if
they posses certain scarce & key raw materials that are essential for the
production of certain goods or if the supply of a commodity is localized in a
single place. For example, India possesses manganese mines; the extraction of
diamonds is controlled by South Africa.
This type monopoly is known as raw material monopoly.
ii. Patent rights for a product or for a production process: A firm may acquire a
monopoly over the production of a good by having patents on the product or on
certain basic processes that are used in its production. The patent laws permit an
inventor to get the exclusive right to make a certain product or to use a particular

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process (usually for 17 years) as an incentive to inventors. Patents can be very

important in keeping competitors out. Examples of monopolies based on patents
are the Xerox Corporation for copying machines, Polaroid for instant cameras and
Mr Biellgates in the computer Microsoft ware area. Such monopolies are called
patent monopolies
iii. Government Licensing or the imposition of foreign trade barriers to exclude
foreign competitors. A monopoly, which are created for the interest of the public. For
example, the public utility sectors such as water supply, postal, telegraph and telephone
services, radio and TV services, generation and distribution of electricity. Such
monopolies are known as public monopolies.
iv. Economies of Scale: - A primary and technical reason for growth of monopolies
is Economies of scale. The size of the market may be such as not to support more
than one plant of optimal size. Technology may be such as to exhibit substantial
economies of scale, which require only a single plant, if they are to be fully
reaped. For example, in transport, electricity, communications there are
substantial economies which can be Realized only at large scales of output (the
average cost of producing the product reaches
a minimum at an output rate that is big enough to satisfy the entire market at the price
that is profitable). The size of the market may not allow the existence of more than a
single large plant. If there is more than one firm producing the product, each must be
producing at a higher-than-minimum level of average cost. In these conditions it is said
that the market creates a "national' monopoly, such monopolies are known as national
monopoly. It is usually the case that the government undertakes the production of the
commodity or of the service so as to avoid exploitation of consumers.
v. Limit-pricing policy: The existing firm adopts a limit pricing policy, that is, a
pricing policy aiming at the prevention of new entry. Such a pricing policy may
be combined with other polices such as heavy advertising or continuous product
differentiation, which render entry unattractive. This is the case of monopoly
established by creating barriers to new competition (Coca-Cola Comp. ) or
Colgate-tooth paste.

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vi. Entry Lags: Some enterprises lack the power to enter a certain production for some
temporary periods and those that are able to enter for some temporary periods and
those that are able to enter will have temporary monopoly power over the production
fill the others enter to it.

Demand, Marginal Revenue And Cost Curves Under Monopoly

In the analysis of consumer behavior you have seen that the demand curve is generally
down ward sloping showing inverse relation ship between price and quantity demanded.
In perfectly competitive market the industry faces down ward sloping demand curve;
firms face a horizontal demand curve because of the existence of large number of
producers and homogeneity of the product, the firm can not exert power on the total
industry supply.

The monopoly industry on the other hand is a single firm industry. A monopoly firm
there fore faces a down ward sloping demand curve. It implies given the demand curve, a
monopoly firm has the option to choose between prices to be charged or out put to be
sold. But he cannot simultaneously control both the price and the level of out put. He can
either decide the level of out put, and leave the price of the out put to be determined by
consumer demand or he can fix the price and leave the level of out put to be decided by
the demand for the product at that price. One of the fundamental differences between a
monopolist and a competitor is there fore the demand (AR) and marginal revenue curves
they face. In the case of perfectly competitive market MR = AR=P=D. But in the case of
down ward sloping demand curve of monopoly marginal revenue curve falls twice as
much as the fall of average revenue curves i.e. the slope of MR is twice as steep as the
average revenue curve. The following figure illustrates this relationship.
AR and RM curves for Monopoly

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This can be shown mathematically as follows assuming linear demand function

1. The demand function
P = a - bx where a = constant, x=quantity demanded
2. The total revenue is
R = Px = (a - bx)x = ( substituting P = a -bx) = ax -bx2
3. The Average revenue

R
P x AR =
—=—= P
= a -
b x x x
Thus the demand curve is also the AR curve of the monopolist with
slope = -b 4. The marginal revenue (the first derivative of R)
dR d(ax- bx2)
—= =a-2bx
dx dx
That is the MR is a straight line with the same intercept (a) as the demand curve,
but twice as steep ( i.e slope = -2b) Note: - the general relation between P and MR is
found as follows
R = Px
dx( P) d ( p) x (Product rule of differentiation, you have learned in your
quantitative for economists I course)
MR = -------- \ --------
dx dx
dp dx
xd( p) MR = P + x (But — is negative due to the inverse relation between
demand & price)
MR = P + ^ dx dp
P- X dp ^ P =
MR = dp
MR+x dx dx
Thus, the marginal revenue is smaller than price at all levels
of out put.
The Monopolist's Costs
As in the case of perfect competition in the traditional theory of monopoly the shapes of
the average cost curves are the U-shaped (AVC, MC and ATC are U-shaped, while the
AFC is a rectangular hyperbola). One point to be stressed here is that the MC curve is not
the SS-curve of the monopolist, as is the case in pure competition. In monopoly there is
no unique relationship between price and the quantity supplied (no unique ss curve for
the monopolist derived from its MC) given his MC, the same quantity may be offered at
different prices depending on the price elasticity of demand.
1.2. Short Run and Long-Run Equilibrium

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1.2.1. Short Run Equilibrium of the monopolist.

The monopolist maximizes his short run profit if the following two conditions are
fulfilled.
1. The marginal cost is equal to the marginal revenue.
2. The slope of marginal cost is greater than the slope of the marginal revenue at the
point of the intersection.
Proof: The monopolist aims at the maximization of his profit (Π = R – C)
(a) The first – order condition for maximum profit Π

0
Q
 R C
  0
Q Q Q
or
R C
 , That is MR = MC
Q Q
The second – order condition for maximum profit
 
2
0
Q 2
 2   2 R  2C
  0
Q 2 Q 2 Q 2

 2 R  2C
or  , that is [Slope of MR] < [Slope of MC]
Q 2 Q 2
E.g Given the demand curve of the monopolist
Q = 50 – 0.5P……….. solving for p
P = 100 – 2Q
Given the cost function of the monopolist as C = 50 + 40Q
The goal of the monopolist is to maximize profit Π = R – C
(i) We first find the MR
R = QP = Q (100-2Q)
R = 100Q – 2Q2
R
MR = = 100 – 4Q
X
(ii) Next find the MC
TC = 50 + 40Q
TC
MC =  40
X
(iii) Equate MR = MC
100 – 4Q = 40
100 – 40 = 4Q
60 = 4Q
⇒ Q = 15

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(iv) The monopolist‘s price is found by substituting Q = 15 into the demand-price

equation
P =100 – 2Q = 70
(v) The profit is Π = TR – TC
= PQ –TC = 70(15) – [50 + 40 (15)]
= 1050 – 650 = 400
This profit is the maximum possible profit, since the second-order condition is satisfied:
 2 R  2C
(a) When 
Q 2 Q 2
MC  (40)
 0
Q Q

MR  (100  4Q) 2R

(b) From  =-4 we have  4 ..
Q Q X
Clearly -4 < 0.
So we can say output level 15 maximizes profit; and hence it is optimal. Therefore, we
can see that the classical condition for equilibrium of equating the marginal revenue and
marginal cost remained intact, except that price is different from marginal revenue
(unlike the case of perfect competition).
Graphically: The decision for the maximization of the monopolists profit is the equality
of his MC and MR, provided that the marginal cost cuts the marginal revenue curve from
below.

Qe
Fig. 1.1equilibrium of monopolist firm in short- run
The profit maximizing (equilibrium) out put is Qe and price is 0P1. At OQe level of
out put, the average cost is OP2 (or QeB). Thus the monopolist's per unit abnormal
profit is equal to AB, which is the difference between the price OP1, and the
corresponding average cost of production (OP2). The shaded area; P1ABP2 represents
the total monopoly profit. Total revenue = AR x Output sold Total Cost = AC x
Output produced

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= OP1 x OQe = OP2 x OQe

= Area OP1AQe = Area OP2 BQe
\ Profits = TR-TC
= Area OP1 AQe - Area OP2 BQe = Area P1AB P2
Monopolist supply curve in the short – run
There is no unique supply curve for the monopolist derived from his MC. Given his MC
the same quantity may be offered at different prices depending on the price elasticity of
demand. Graphically this is shown by the following diagram,

Qe is sold at P1 for some consumers and

at P2 for others.

Fig 1.2
Similarly, given the MC of the monopolist, various quantities may be supplied at any one
price, depending on the market demand and the corresponding marginal revenue curve.
Such a situation is depicted in the following figure.

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Fig.1.3
Since the monopolist can sell the same quantity of output at different prices and can sell
different quantities at the same price, depending on elasticity of demand, there is no
distinct relationship between price and quantity supplied by a monopolist. To conclude
we must say that ―the supply curve is not clearly defined.
1.2.2. Long run Equilibrium of Monopolist
In the long run the monopolist has the time to expand his plant or to use his existing plant
at any level which will maximize his profit. But given entry impossibility into a
monopolist market the firm may not necessarily build the optimal plant size. (That is to
build up his plant until he reaches the minimum point of the LAC).
Given entry barrier, the monopolist will most probably continue to earn super normal
profits even in the long run. However, the size of his plant and the degree of utilization
of any given plant size depend entirely on the market demand. The monopolist may reach
the optimal scale (minimum point of LAC) or remain at suboptimal scale (falling parts of
his LAC) or operate beyond the optimal scale (expand beyond the minimum LAC)
depending on the market condition.
(i) For instance if market is limited/small the firm will maintain a sub-optimal plant and
may under utilize the plant.

Fig.1.4. Monopolist with suboptimal plant and excess capacity.

The firm is employing plant size smaller than the optimum and it is under utilizing the
plant (excess capacity).
(ii) If the market is so large relative to the expansion path, the firm may build a
production plant larger than the optimal and may over-utilize the plant.
When the market is larger, the optimum occurs to the right of the minimum point of Long
run average cost as at point e.

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Fig.1.5 Monopolist operating in a large market: his plant is

large than the optimal and it is being over-utilized (at e|).
(iii) If the market size is just large enough to permit the monopolist to build the optimal
plant, the firm will be operating at minimum point of LAC.

Fig: 1.6 Monopolist operating at his optimal plant size (Full capacity
utilization)
If the monopolist is at his optimal plant size SMC = LMC = SAC =MR at minimum of
LAC.
Note: The firm still earns supernormal profit because price is greater than the marginal
revenue k(profits in the shaded area).
Price Discrimination
A producer, mostly likely a monopolist need not always charge a single price to his
customers since he is the only producer in the market, he has a control over the supply of

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the product. He can charge different prices to different consumers or in different markets.
Thus when the same product is sold at different price to different consumers, it is called
price discrimination. The two most important points to note about the definition of
price discrimination are: first, exactly the same products must have different prices. A
trip from Bahir Dar to Gondar is not the same as a trip from Bahir Dar to Dessie because
transportation costs are different and this difference raises the price of the trip. Second, in
order for price discrimination to exist, production costs must be equal. If costs are
different, a profit maximizing firm who sets MR=MC will usually charge different price
for a product. This price difference is also due tot cost difference not discrimination.

Consumers are discriminated in respect of price on the basis of their incomes,

geographical location, Age, sex, quantity they purchase, frequency of visits to the shop
etc. For instance, price discrimination on the basis of age in airways, railways, Cinema
shows, Musical concerts, charging lower price for teenagers. Doctors has charged
different price for rich and poor persons. But to implement price discrimination
effectively the following necessary conditions has to be full filled.
1. There must be separate markets, so that no reselling can take place from a low price
market to a high price market. It is most commonly effective for goods that can not
be easily traded (exchange of services for example, a poor receiving medical care at
relatively low price can not resell his or her operation to another patient, but a lower
price buyer of some raw material could resell it to some one in the higher price
market.
2. Existence of monopoly power.
3. Differences in the elasticity of demand. It is the difference in price elasticity that
provides opportunity for price discrimination. If price elasticity of demand in
different markets are the same, price discrimination would not be important (gain
full).
Degrees of price discrimination

The main objective of price discrimination is to maximize profit more than that the firm
could obtain by charging the same price defined by the equation of his MC and MR. The
degree of price discrimination, therefore, refers to the extent to which a seller can divide

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the market and can take advantage of it in extracting the consumers surplus. Accordingly
there are three degrees of price discrimination practiced by monopolists.

A. First degree price discrimination

The discriminatory pricing that attempts to take away the entire consumer surplus is
called first-degree discrimination. Under first price discrimination, the firm treats each
individual's demand separately and each consumer is assumed as a separate market.

B. Second -Degree price Discrimination.

First-degree price discrimination is expense to implement. Because dealing each

individual demand curve needs vast information and it is costly. Second degree price
discrimination is some what simpler because it requires the firm to consider groups of
consumers. This is discrimination on the basis of quantity purchased and intends to take
only the major part of consumer surplus rather than the entire.
C. Third degree Price discrimination
Selling the same product with different price in different markets having demand curves
with different elasticity is called third degree price discrimination. Profit in each market
would be maximum only when ‗his MR=MC in each market. The monopolist there for
divides his out put between the markets so that in all markets his MR=MC.
In this case suppose that the monopolist has to sell his product in only two markets A and
B. As
a result, the monopolist must allocate out put between the two markets in such proportion
that the necessary condition for profit maximization (i.e. MR = MC) is satisfied. The
equilibrium condition is satisfied i.e. MC=MRa =MRb (common MC equal individual
MR)

Numerical Example
⇒Given TC=5Q+20 and q1=55- p1 – The DD function in market 1
q2=70- 2p2 – The DD function in market 2
1. Determine q1, q2, p1, and p2 that maximises profit
2. Find the elasticity of DD in the two markets?
3. Calculate the total profit the monopolist will obtains from its sell in the two markets

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1.4 Social Costs of Monopoly

Price is higher and output is lower in the monopoly market model than the competitive
market model.Because of these monopoly is said to be socially inefficient in allocating
factors of production.
In Competitive Market P = MC
Monopoly Market P > MC
To calculate the degree of inefficiency due to monopoly we can use the concepts of
producer‘s surplus and consumer‘s surplus.

Fig1.7 social cost of monopoly

Under Competition the net welfare gained by the consumers and producers is as follows:
Net Welfare = aepc + Pcef

Consumer‘s Producer‘s
Surplus Surplus
Under Monopoly the net welfare gained by the consumers is (aPmb) which is less than net
welfare gained under competitive (aePc). PmbcPc is taken by producers. But the area bed
is totally lost. (This is not consumer surplus & Producers surplus). Area bed is
deadweight loss due to monopoly allocation as opposed to competitive market.
Example
Assume there is a tendency of moving from competitive to monopoly output. If the
demand
and total functions are Q=100-2P and TC=14Q+2Q2, respectively
A. Determine Pc, Qc, Pm, and Qm.
B. Show the equilibrium Q and P you obtained in A above graphically.
C. Calculate the CS and PS under competitive and monopolist firms.
D. Calculate part of CS transferred to the monopolist due to inefficiency of monopoly
E. Calculate the social cost (net loss or DWL) of monopoly

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