CONSUMER EQUILIBRIUM

Concept of utility:
The power of satisfaction of a consumer is termed as utility. Utility is the want
satisfying power of a commodity.
How is utility measured: According to some economists, utils can be taken as the
unit of measurement for utility on the other hand, some says that utility can directly be
expressed in terms of money.
Forms of Utility:
Total utility: Total utility is defined as the psychological satisfaction a consumer
obtains from consuming a given amount of a particular good. It is the sum total of
utility derived from the consumption of all the unit of a commodity. In other
words, it is the sum of the marginal utilities associated with the consumption of
successive units, symbolically:
TUn=MU1+MU2+MU3......MUn
When TUn is the total utility of n units and MU1, MU2, MU3, MUn are marginal
utilities from the 1st, 2nd, 3rd and nth unity of a commodity.

Marginal utility: marginal utility is the derived from the additional unit of a
commodity consumed. It is an increase in Total Utility, which results from an
increase in consumption. Symbolically:
MUn = TUn - TUn-1
(or)

In TU
In units of
commodity
Where, MU=Marginal Utility; TUn = Total Utility of n units of a commodity
TUn-1 = Total Utility of n-1 units of a commodity.

Utility schedule: Total and Marginal Utility curves:

Page 1 of 17
 CONSUMER EQUILIBRIUM

Units of
TU MU
Commodity
0 0 ---
1 8 8-0=8
2 14 14-8=6
3 18 18-14=4
4 20 20-18=2
5 20 20-20=0
6 18 18-20=-2

Consumer equilibrium:
Consumer equilibrium refers to a situation of maximum satisfaction while he is
spending his given income across different goods. In other words,” A consumer is in
equilibrium when he regards his actual behavior as the best possible under the
circumstances and feels no necessary to change his behavior as long as circumstances
remain unchanged”.

Methods of measuring consumer’s equilibrium:

Cardinal utility analysis (or) Marshall’s Utility analysis; and
Ordinal utility analysis (or) Hick’s Indifference curve approach.

CONSUMER’S EQUILIBRIUM THROUGH MARSHALL UTILITY APPROACH (OR)

CARDINAL UTILITY ANALYSIS:
Assumptions:
1. The consumer is rational; he aims at the maximization of his utility or
satisfaction.
2. Cardinal measurement of utility is possible.
3. Utility can be measured n terms of money, and marginal utility of money remains
constant.

Page 2 of 17
 CONSUMER EQUILIBRIUM

4. The law of Diminishing Marginal Utility operates.

5. Prices of the commodities remain constant.
In the utility approach the laws have been developed to explain the consumer’s
behavior and consumer’s equilibrium:
 The Law of Diminishing Marginal Utility;
 The Law of Equi-Marginal utility.
With the help of these two laws, we will explain the determination of consumer’s
equilibrium in the following situations:
 Case of a single commodity free good;
 Case of a single commodity price to be paid;
 Case of two or more goods.

The Law of Diminishing Marginal Utility:

The law states that as a consumer consumes successive units of a commodity, the
marginal utility goes on a diminishing. In words of Marshall- “the additional benefit a
person derives from a given increase of his stock of a thing diminishes with every increase
in the stock that he already has”.
In simple words, the law states that as the amount consumed of a commodity
increases, the utility derived by the consumer from the additional unit, i.e., marginal
utility goes on diminishing.
Assumptions of the law:
1. The units of consumption must be in standard units e.g., a cup of tea, a bottle f
cool drink etc.
2. All the units of the commodity must be identical in all aspects like taste, quality,
colour and size.
3. The law holds good only when the process of consumption continuous without
any time gap.
4. The consumer’s taste, habit or preference must remain the same during the
process of consumption.
5. The income of the consumer remains constant.
6. The prices of the commodity consumed and its substitutes are constant.
7. The consumer is assumed to be a rational economic man. As a rational consumer,
he wants to maximize the total utility.
8. Utility is measureable.
Suppose a consumer wants to consume mangoes he may get utility from the
different units of mangoes.
Unit of MU in
Mangoes price
1 3.0
2 2.5
3 2.0
4 1.5
5 1.0
6 0.5
7 00 Page 3 of 17
8 -0.5
 CONSUMER EQUILIBRIUM

It could be seen from the table that the consumer gets marginal utility equal to RS.3
from the 1st unit of mango. As he consumes additional units of mangoes, he MU goes on
diminishing from the 7th unit the consumer doesn’t get any utility i.e., MU falls to zero, it
is called the point of satiety or saturation. If he continuous the consumption of mangoes
beyond 7th unit, he gets negative marginal utility. In the diagram, ab is the Marginal
Utility curve, the downward slope of the marginal utility curve indicates that

the law of diminishing marginal utility

operates on the consumption of mangoes. Point of saturation is reached when 7 units of
mangoes are consumed at this point marginal utility falls to zero.
Consumer’s equilibrium in case of a single free good:
A consumer will consume a commodity till the point of satiety if he does not have to
pay any price of the commodity. At this point his total utility will be maximum he will be
said to be in equilibrium. The condition for consumer’s equilibrium can be stated as:
MUX=PX. Since the price f the commodity is assumed to be zero, the consumer would be
in equilibrium at the level of consumption where MUX=Zero. In our above example the
consumer will consume 7 units of mangoes and get total utility equal to
(3.0+2.5+2.0+1.5+1.0+.05+0) =10.5 with 7 units the consumer has reached the point of
satiety. Beyond this consumption of mangoes would yield negative utility. In the
diagram point of saturation itself becomes consumers equilibrium since at this level of
consumption is MUX=PX =Zero.
Consumer’s equilibrium in case of a single good for which price has to be paid:
In this case also, consumer’s equilibrium condition will remain the same as before i.e.,
MUX=PX suppose, the price of mangoes is rupees 1.5 per unit, now since the consumer
has to pay a price, he will restrict his consumption of mangoes to a level where marginal
utility of mangoes in the schedule this equality occurs when he consumes 4 units of
mangoes at this level of consumption, consumer will get the maximum total utility that
equals.(3.0+2.5+2.0+1.5)=9.0.He spends a total of rupees 6 (1.5x4) and gets total utility
equal to Rs.9-Rs.6=Rs.3. this is also called consumer’s surplus if he consumes the 5 th
unity of mango he will get additional utility equal to Rs.10, where as he would have to
pay Rs.1.5 he would not like to do this he will not consume the 5 th unit and he gets a
Page 4 of 17
 CONSUMER EQUILIBRIUM

total utility equal to Rs.10 and pays Rs.7.5 (Rs.1.5x5) his surplus of satisfaction falls to
RS.10-7.50=Rs.2.50 he will not like it conversely, suppose he restricts his consumption
to 2 units. He gets a total utility of (3+2.5)=Rs.-5.5 and pays a total of Rs.3 (Rs.1.5x2). His
surplus of satisfaction is Rs.5.5-Rs.3=2.5. He can increase his surplus of satisfaction till
he reaches the point where MUx =Px.

Limitations of the law:

1. Marginal utility in certain cases may increase rather than decrease.
2. Utility is not quantitative.
3. Consumer does not consume only one commodity in real life. He has to attain
large no of goods and services.
4. Consumption is not always continuous.

The Law of Equi-Marginal Utility:

The idea of Equi-marginal principle was first mentioned by H.H. Goshen. It is also
called as Goshen’s second law. Alfred Marshall made significant refinements of this law
in his principles of economics. The law of equi-marginal utility explains the behavior of
a consumer when he consumes more than one commodity. Wants are unlimited but the
income which is available to the consumer to satisfy all his wants is limited. This law
explains how the consumer spends his limited income on carious commodities to get
maximum satisfaction. The law of equi-marginal utility is also known as the law off
substitution or the law of maximum satisfaction or the principle of proportionality
between prices and marginal utility.
Definition : In words of marshal “ if a person has a thing which can be put to second use,
he will distribute it among those uses in such a way that it has the same marginal utility in
all”,
Assumptions:
1. The consumer is rational so he wants to get maximum satisfaction.
2. The utility of each commodity is measurable.
3. The marginal utility of money remains constant.
4. The income of the consumer is given

Page 5 of 17
 CONSUMER EQUILIBRIUM

5. The price of the commodities are given

6. The law is based on the laws of diminished marginal utility

Explanation of the law:

Suppose there are two goods X and Y on which a consumer has to spend a given
income. The consumer being rational, he will try to spend his limited income on good X
and Y to maximize his total utility or satisfaction, only at that point the consumer will be
in equilibrium. According to the law of equi-marginal utility, the consumer will be in
equilibrium at the point where the utility derived from the last rupee spent on each is
equal. Symbolically the consumer will be in equilibrium when
Mux MuY
= =MuM
PX PY

MuX = marginal utility of commodity X; Mu Y= marginal utility of commodity Y ; PX =

price of commodity X; PY= price of commodity Y; MuM= marginal utility of money.
MuX
∧MuY
PX
are know as marginal utilityof money expenditure .
PY
They explain that marginal utility of one rupee spent on commodity X and the
marginal utility of one rupee spent on commodity Y.

Marginal utility of Good X and Good Y Marginal utility of money expenditure

MuX MuY
units
PX PY
1 10 9
2 9 8
3 8 7
4 7 6
5 6 5
6 5 4
7 4 3
8 3 2

Page 6 of 17
 CONSUMER EQUILIBRIUM

Units MuX MuY

1 50 36
2 45 32
3 40 28
4 35 24
5 30 20
6 25 16
7 20 12
8 15 8

Consumer’s equilibrium is graphically explained, since marginal utility curves of goods

slop downwards, curve depicting
MuX
∧MuY
PX
will alsobe sloping downwards .
PY
Taking the income of a consumer as given, het his marginal utility of money be constant
MuX
at OM utils in the diagram. is equal to OM, when OH amounts of good X is
PX
MuY
purchased; is equal to OM when OK quantity of good Y is purchased. Thus when
PY
the consumer is buying OH of X and OK of Y, then
Mux MuY
= =MuM
PX PY
Therefore the consumer will be in equilibrium when buys OH of X and OK of Y. no other
allocating of money expenditure will yield greater utility than when he buys OH of X and
OK of Y. suppose the money income of the consumer falls, then the new marginal utility
of money will be equal to OM, then the consumer will increase the purchase of good X
and Y for OH and OK respectively.

CONSUMER’S EQUILIBRIUM THROUGH HICK’S INDIFFERENCE CURVE APPROACH

(OR) ORDINAL UTILITY ANALYSIS:

What is an Indifference curve?

The basic tool of Hicks-Allen ordinal utility analysis of demand is the
indifference curve which represents all those combinations of goods which give same
satisfaction to the consumer. Since all the combinations on an indifference curve give

Page 7 of 17
 CONSUMER EQUILIBRIUM

equal satisfaction to the consumer, he will be indifferent between them, that is, it will
not matter to him which one he gets. In other words, all combinations of two goods
lying on a consumer’s indifference curve are equally desirable to or equally preferred by
him.
Definition: An Indifference curve is the locus of different combination of two commodities
giving the same level of satisfaction.
Assumptions of indifference curve analysis:
1. More of a commodity is better than less: it is assumed that the consumer will
always prefer a larger amount of a good to a smaller amount of that good,
provided that the other goods at his disposal remain unchanged. This is a
reasonable and a realistic assumption. This assumption implies that the
consumer is not over-supplied with any good.
2. Preferences or indifference of a consumer are transitive: suppose there are three
combinations of two goods A, B and C. if the consumer is indifferent between A
and B and condition implies that consumer’s tastes are quite consistent. This
assumption is known as assumption of transitivity.
3. Diminishing marginal rate of substitution: Indifference curve analysis the
principle of diminishing marginal rate of substitution is assumed. In other words,
it is assumed that as more and more units of X are substituted for Y, the
consumer will be willing to give up fewer and fewer units of Y for each additional
unit of X, or when more and more of Y is substituted for X, he will be willing to
give up successively fewer and fewer units of X for each additional unit of Y this
rule about consumer’s behavior is described as the principle of diminishing
marginal rate of substitution.
The Indifference schedule:
An indifference schedule may be defined as a schedule of various bundles of goods
that give equal level of satisfaction to the consumer.

Bundles Good X Good Y

A 1 12
B 2 8
C 3 5
D 4 3
E 5 2

The consumer has to start with 1 unit of X and 12 units of Y. now, the consumer is
asked to tell how much o good Y he will be willing to give up for the gain of an additional
of unit of X so that his level of satisfaction remains the same. If the gain of one unit o X
compensates him fully for the loss of 4 units of Y, then the next combination of 2 units of
X and 8 units of Y (2X+8Y) will give him as much satisfaction as the initial combination
(1X+12Y). similarly, by asking the consumer further how much of Y he will be prepared
to forgo for successive increments in his stocks of X so that his level of satisfaction
remains unaltered, we get combinations 3X+5Y, 4X+3Y, and 5X+2Y. Each of which

Page 8 of 17
 CONSUMER EQUILIBRIUM

provides him same satisfaction as combinations 1X+12Y or 2X+8Y , since his satisfaction
is the same whichever combinations of goods in the schedule s offered to him, he will be
indifferent among the combinations of two goods included in the schedule.
Indifference curve:
An Indifference curve is the locus of different combination of two commodities giving
the same level of satisfaction.

Indifference map:
A complete description of consumer’s tastes and preferences can be represented by
an indifference map which consists of a set of indifference curves. Because the field in a
two dimensional diagram contains an infinite number of points, each representing a
combinations of goods X and Y, there will be an infinite number of the indifference
curves each passing through combinations of goods that are equally desirable to the
consumers.

Properties of Indifference curves:

Property 1: Indifference curves slope downward to the right: an indifference curve always
slopes downwards from left to the right, ie., it has a negative slope. It is because of the

Page 9 of 17
 CONSUMER EQUILIBRIUM

simple reason that if the consumer wants to have more units of one good, he will have to
reduce the number of units of another good, if his level of satisfaction is to remain
unchanged. In other words, an indifference curve slopes downwards because of
monotonic preferences.

Property 2: Indifference cures are convex to the origin: as the quantity of one good
increase, its marginal rate of substitution or slope of the indifference curve goes on
diminishing. The only curve which is convex to the origin can indicate declining slope or
diminishing marginal rate of substitution. Hence, indifference curves are always convex
to the origin.

Property 3: Two indifference curves never intersect each other: only one indifference
curve will pass through a point in the indifference map. This property can be easily
proved by first making the two indifference curves cut each other and then showing the
absurdity or self-contradictory. In the below diagram two indifference curves are shown
cutting each other at point C. Now take point A on indifference curve IC2 and point B on
indifference curve IC1 vertically below A. Since indifference curve represents those
combinations of two commodities which give equal satisfaction to the consumer, the
combinations represented by points A and C will give equal satisfaction to the consumer
because both lie on the same indifference curve IC2.

Likewise, the combinations B and C will give equal satisfaction to the consumer; both
being on the same indifference curve IC1. If combination A is equal to combination C, it
follows that the combination A will be equivalent to B in terms of satisfaction. But in the
diagram since the combination A contains more of good Y than combination B, while the
amount of good X is the same in both the combinations. Thus, the consumer will
definitely prefer A to B, that is, A will give more satisfaction to the consumer than B. But
the two indifference curves cutting each other lead us to an absurd conclusion of A
being equal to B in terms of satisfaction. WE therefore conclude that indifference curves
cannot cut each other.

Page 10 of 17
 CONSUMER EQUILIBRIUM

Property 4: A higher Indifference curve represents a higher level of satisfaction than a

lower Indifference curve:
This is because of the assumption that preferences are monotonic and more quantity
consumed means more utility. Higher indifference curve represents more quantity of
goods.

Monotonic preferences refer to those preferences in which consumer always prefer the
bundle having either more of both goods and more of at least one good and no les of the
other good compared to another bundle.
Marginal rate of substitution: When a consumer increases the quantity of a commodity,
he has to sacrifice some quantity of another commodity so that the level of satisfaction
should remain the same. Here one commodity is substituted in place of the other. The
marginal rate of substitution (MRS) of good1 for good2 is the number of units of good2
that the consumer is willing to give up for an additional unit of good1, so as to maintain
the same level of satisfaction. The marginal rate of substitution is explained with the
help of following table:

Bundles Good X Good Y MRS

A 1 12 --

B 2 8 4:1

C 3 5 3:1

D 4 3 2:1

E 5 2 1:1

Page 11 of 17
 CONSUMER EQUILIBRIUM

The example shows the different combinations of good1 and good2 which give equal
satisfaction to the consumer. In the beginning, consumer has 1 unit of good 1+12 units
of good2. Now in order to get an additional unit of good1, he is prepared to give up 4
units of good2 hence MRS will be 4:1. It implies that the consumer gets the same
satisfaction from 2 units of good 1+8 units of good 2 as he gets from 1 unit of good 1+12
units of good2. Thus, the marginal rate of substitution between two goods can be
estimated with the help of the following formula:

∆ Good 2
MRS X1X2 = ---------------
∆ Good 1

It is shown in the diagram that the MRS is equal to the deep vertical line divided by the

∆ Good 2
---------------
deep horizontal line in the diagram. The ratio of
∆ Good 1 shows the slope of
the indifference curves. The absolute value of the slope of an indifference curve
indicates the marginal rate of substitution. Thus, MRS=slope of the indifference curve.
Budget line or Budget constraint:
The concept of budget line is also called budget constraint which is essential for
understanding the theory of consumer’s equilibrium.
Meaning of Budget line: Budget line shows ass those combinations of two goods which
the consumer can buy by spending his given money income on the two goods at their
given prices.
Definition of Budget line: “a set of combinations of two commodities of that can be
purchased if whole of the given income is spent on them”.

Page 12 of 17
 CONSUMER EQUILIBRIUM

Budget set: The budget set refers to all those bundles that that the consumer can
purchase with his money-income at the prices of the goods.
Budget set depends upon two factors:
1. Consumer’s money income;
2. Prices of the two goods.
Example:
Income of the consumer M = Rs=50
Price of Good X Px = Rs=10 per unit
Price of Good Y Py = Rs=5 per unit

MRE
Bundles Good X Good Y Px/Py
It is A 0 10 2y:1x assumed that consumer
spends 2y:1x his entire income. One
B 1 8
possible way is to buy only X.
C 2 6 2y:1x
The maximum of X he can buy is 5
units D 3 4 2y:1x (50/10). Another possible way
is t E 4 2 2y:1x spend only on Y. he can buy a
F 5 0 2y:1x maximum of 10y (50/5). Still
another way is to spend 50% of
income on X and 50% on Y. he can buy 2.5X and 5Y. Like these, there can be many other
possibilities if we avoid fractions, all these possibilities areas given in the above
schedule. If the consumer wants one more unit of X, which costs Rs.10. since his income
is limited, in order to obtain an extra unit of X he must give up his plan to purchase
Rs.10 worth of Y. he can get 2 units of Y from Rs.10. it amounts to that to obtain one unit
of X he must give up 2 units of Y. the rate at which the market requires sacrifice of one
good to obtain extra unit of the other good is called Market Rate of Exchange (MRE).
In the above schedule the consumer sacrifices commodity Y to obtain X, therefore

MRE can also be expressed as ratio of prices it is expressed as:

Page 13 of 17
 CONSUMER EQUILIBRIUM

Price of the good obtained

------------------------------------
MRE =
Price of the good sacrificed

Px 10
MRE =------ = ------- = 2
Py 5
MRE is constant throughout because
Y Px and Py is constant throughout. Points
below the Budget line and points
A
above the budget line.
The points below the budget line,
we know that a point below the
budget line indicates a bundle which
costs less than the consumer’s
GO
OD
Y

income. It implies that if a consumer

purchases this bundle, he will have
some money left over. He can spend
0 B X this extra money on either of the two
GO goods. If he does so, he can buy a
OD bundle which consists of more
quantity of, at least, one of the foods
X and the same quantity of the other as
compared to the bundle lying below the budget line. This bundle will lie on the budget
line. Thus, a bundle on the budget line indicates a bundle which costs exactly equal to
the consumer’s income. It also indicates that there is always some bundle on the budget
line which contains more quantity of at least one of the goods and no less of the budget
line.
 A point on the budget line may have more of good x and the same amount of
good y compared to a point below the budget line.
 A point on the budget line may have more of good y and the same amount of
good x compared to a point below the budget line.
 A point on the budget line may have more of both the goods compared to a point
below the budget line.
Changes or Shifts in the budget line:
Changes in the income and the budget line: Change in income can take two
directions; there may be increase in income or decrease in income. If there is
increase in income, the vertical intercept increases and the budget line shifts
outward parallel to the original budget line. On the other hand, if there is

Page 14 of 17
 CONSUMER EQUILIBRIUM

decrease in income then the vertical intercept decrease and the budget line shifts
inward parallel to the original budget line. Now consumer can purchase smaller
quantity of goods at the given market prices.

YA1
A
A2
GO
OD
Y

0 B2 B B1 X
GO
OD
X
Changes in the price of good x and the budget line: If the price of good x falls then
the absolute value of the slope of the budget line becomes flatter on the x-axis. It
is shown in the diagram that the budget line shifts outward from AB to AB1. Now
with the lower price of good x the consumer will be able to purchase more
quantity of good x than before with his given income. On the other hand, if the
price of the good x rises then the absolute value of the slope of the budget line
increases and hence, the budget line becomes steeper on the x-axis. With higher
prices of good x the consumer will be able to purchase the smaller quantity of
good x than before. The budget line shifts inward from AB to AB2.

Y
A
GO
OD
Y

0 B2 B B1 X
GO
OD
X

Page 15 of 17
 CONSUMER EQUILIBRIUM

Thus, in short, when consumer’s income and the price of good y remains
unchanged but the price of good x changes, the budget line also undergoes a
change. In this situation, the budget line moves to the right or left on the x-axis
with the fall or rise in the price of good x.

Change in the price of good y and the budget line: If there is a fall in the price of
the good y, other things remaining unchanged, the consumer could buy more of
good x and therefore, budget line will become flatter on the y-axis and it will shift
from AB to A1B. Similarly, with the rise in price of good y, other things being
constant, the consumer could buy less of good Y and therefore, budget line will
become steeper on the y-axis and it will shift from AB to A2B. When the
consumer’s income and the price of good x remain unchanged but the price of
good y changes, the budget line also undergoes a change. In this situation, the
budget line moves to the right or left on the y-axis with the fall or rise in the rice
of good y.

Y
A1
A
A2
OD
O
G

0 B X
GO
OD
X
It is thus clear that the budget line will change if either the consumer’s income changes
or the prices of goods change. Thus, the two determinants of the budget line are:
1. Consumer’s income to be spent on the goods; and
2. The prices of the goods.

Consumer’s equilibrium:
A very important assumption is that the consumer is rational; he tries to maximize
his satisfaction. We also know that the budget set describes those bundles that are
available to the consumers and indifference map indicates the scale of preference of the
consumers. A consumer is said to be in equilibrium when he maximizes his satisfaction,
given his money-income and the prices of the commodities he consumes.

Page 16 of 17
 CONSUMER EQUILIBRIUM

Y
M
GO
OD

E
Y

IC
IC
IC3 4
IC 2
0 N1 X
GO
OD
X
In other words, a consumer is in equilibrium, when on the basis of a given budget line to
choose a point below the budget line because it represents inferior bundle compared to
a point on the budget line. On the other hand, points above the budget line are not
affordable by the consumer. Therefore, the optimum point of the consumer would be on
the budget line. In the above diagram MN is the budget line and IC 1, IC2, IC3 and IC4 are
indifference curves. Consumer’s equilibrium is determined at the point where budget
line touches the indifference curve. MN budget line touches the IC 2 at point E; hence it is
the point of the consumer’s equilibrium. It is clear from the diagram that any point on
the budget line other than the point at which it touches the indifference curve lies on a
lower indifference curve and hence, represents inferior bundle. On the other hand,
bundles represented by the points on the indifference curves which lie above the point
E on IC2 curve are not affordable. Hence, consumer’s equilibrium cannot be on any point
on IC3 and IC4 curve. Thus, the consumer gets the highest level of satisfaction only on
point E of IC2 curve given the MN budget line.

Page 17 of 17