Cardinal

Utility
Theory
 Consumer

The one who takes decisions about what to buy for the satisfaction of wants,
both as an individual and as a member of the household, is called a consumer.

Rational Consumer

A consumer who seeks to maximize utility or satisfaction in spending his

income is called a rational consumer.

Consumer’s Equilibrium
Consumer’s Equilibrium refers to the situation when a consumer is
having maximum satisfaction with limited income and has no tendency
to change his way of existing expenditure

Cardinal Utility theory

Assumptions:
(i) Consumer is rational as he wants to maximize his total utility.
(ii) Utility is cardinally measured as one, two, three, and so on.
(iii) Marginal utility of money is constant. and
(iv) As more and more units of a commodity are consumed, the
utility from each additional unit falls.
Consumer’s equilibrium can be discussed under two different
situations:
1. Consumer spends his entire income on a single commodity.
2. Consumer spends his entire income on two commodities.

Equilibrium Condition for a Single Commodity

A consumer purchasing a single commodity will be at equilibrium,
when he is buying such a quantity of that commodity, which gives him
maximum satisfaction.

The number of units to be consumed will depend on:

1. Price of the given commodity

2. Expected utility (MU) from each successive unit.

To determine the equilibrium point, consumer compares the price (or

cost) of the given commodity with its) u.tility (satisfaction
Being a rational consumer, he will be at equilibrium when
marginal utility is equal to the price of the commodity.
 Marginal utility is expressed in utils and price is expressed in terms of
money. However, MU and price can be effectively compared only when
both are stated in same units. Therefore, MU in utils is expressed in
terms of money.

MU inutils
MU in terms of money, that is, MUx(money) = MU of one rupee (MUm)

Equilibrium condition can be written as:

MU × (Utils) = Price of commodity “X”

MU of a rupee
OR MUx = Px

Case 1: MUx (money) > Px

If MUx (money) > Px, consumer keeps on consuming more units. When
he consumes more unit, the additional utility derived from consuming
X keeps on falling. He keeps on consuming till MUx (money) = Px.

Case 2: MUx (money) < Px

If MUx (money) < Px, he will decrease the consumption of X. When he

decreases the consumption of X, the marginal utility of X will increase.
He will keep on decreasing consumption of X till MUx (money) = Px.
Thus, MUx (money) = Px is the condition for consumer’s equilibrium in a single
commodity case.

Let’s understand the equilibrium through an illustration.

Taking MUm = 2 utils.( 1 rs =2 utils)

Oranges MU MU in Price(Rs.) Gain Direction of change
consumed (Utils) terms of
money
0 0 0 1 -
1 8 8/2 = 4 1 3  Consumption
2 6 6/2 = 3 1 2  Consumption
3 4 4/2 = 2 1 1  consumption
4 2 2/2 = 1 1 0 ATTAINS
EQUILIBRIUM
5 0 0/2 = 0 1 -1  Consumption
6 -2 -2/2 = -1 1 -2  Consumption

Consumer equilibrium is attained when the consumer is consuming 4

units of oranges.

Consumer’s Equilibrium for Two Commodities

In such a situation, Law of Equi-Marginal Utility helps in optimum allocation of

his income.

According to Law of Equi-Marginal utility, a consumer gets maximum

satisfaction, when ratios of MU of two commodities and their
respective prices are equal and MU falls as consumption increases.

Or

It states that the last rupee (spent) gives him equal marginal utility
whether he spends it on Good X or Good Y.
Thus, the conditions are:

1. Per rupee MU from consumption of each good is same, ie.

MUx (Utils) = MUy (Utils) or (Mux = MUy)

Px Py
2. MU falls as consumption rises.
If MU does not fall, the consumer will end up buying only one good
which is unrealistic and consumer will never reach the equilibrium
position.

Case 1

MUx/Px > MUy/Py

a. MU from the last rupee spent on X > MU from the last rupee spent on Y.
b. Consumer buys more of X and less of Y.
c. MU derived from consuming X decreases due to law of DMU.
d. He keeps on consuming X till:
MUx/Px = MUy/Py

Case 2

MUx/Px < MUy/Py

a. MU from the last rupee spent on X < MU from the last rupee spent on Y.
b. Consumer buys more of Y and less of X.
c. MU derived from consuming Y decreases due to law of DMU.
d. He keeps on consuming Y till:
MUx/Px = MUy/Py
Limitations of Utility Analysis

1. Cardinal Measurement is arguable: Utility cannot be measured, for utility

is a subjective concept, it exists only in the mind of man.
2. Diminishing MU of money: Critics point out that MU of money never
remains constant, because MU does fall when its stock increases and vice-
versa.
3. Unrealistic comparison of marginal utility: This law assumes that it is
possible for a consumer to compare the MU from every successive unit of
a commodity. But actually, such comparison is not at all possible.
Ordinal
Utility
Theory
Ordinal Utility Analysis
This approach it makes use of ordinal numbers like 1st, 2nd, 4th, etc. which be
used only for ranking.

Meaning of Indifference Curve

Indifference curve refers to the graphical representation of various
alternative combinations of the goods, which provide same level of
satisfaction to the consumer.

Combination Good X Good Y

A 1 8
B 2 4
C 3 2
D 4 1

Consumer is indifferent between four combinations of good X and Y.

Useful Concepts of Indifference Curve Analysis
Meaning of Indifference Set
The combinations A, B, C and D give equal satisfaction to the consumer and
therefore he is indifferent among them. These combinations are together
known as ‘Indifference Set’.

Meaning of Indifference Map

Indifference Map refers to the family of indifference curves that represent
consumer preference over all the bundles of the two goods.

Marginal Rate of Substitution

MRS is defined as the amount of one good the consumer is willing to give up
to consume an additional unit of the other good.
MRSxy = Quantity of goods sacrificed = ΔY
Quantity of goods obtained ΔX
Combination Good X Good Y MRS
A 1 8
B 2 4 4Y:1X
C 3 2 2Y:1X
 D 4 1 1Y:1X
MRS decreases with greater quantities of one good.

Assumptions of Indifference Curve

1. Two commodities
It is assumed that the consumer will spend his fixed amount of money
on two goods, given constant prices of both the goods.
2. Ordinal Utility
The consumer can rank his preferences.
3.Non-satiety
The consumer always prefers more of both commodities, that is, he always tries to move
towards a higher indifference curve to get higher satisfaction.
4. Diminishing MRS
Due to this assumption, the indifference curve is convex to the origin.
5.Rational consumer.

Properties of Indifference Curve

1. The indifference curve slopes downwards from left to right i.e. it is
negatively sloped.
This is because when consumer increases consumption of X, he must
reduce consumption of Y to keep the utility level unchanged.
 [IC doesn’t touch either axis because the assumption of IC curve is that
he consumes both the goods].
2. The indifference curve is strictly convex to the origin. This is because
MRS declines as he moves downwards al along the indifference curve.

MRSxy = slope of indifference curve

Combinations Good X Good Y MRS
A 1 8 -
B 2 4 4Y:1X
C 3 2 2Y:1X
D 4 1 1Y:1X

• This rate keeps on decreasing due to law of diminishing marginal

utility.

• He is willing to sacrifice less units of Y to obtain additional units of

X. [Initially he is willing to sacrifice 4 units of X, then 2 units and so
on].

3. Higher Indifference Curve represents Higher Utility.

A set of indifference curves representing various levels of satisfaction is

known as indifference map.
4. Indifference curve can never intersect each other.

As two indifference curves cannot represent the same level of satisfaction,

they cannot intersect each other.

➢ Point A and B on IC1 give the same level of satisfaction.

➢ Point A and C on IC2 give the same level of satisfaction.

➢ However, B and C lie on different indifference curves and therefore

cannot give the same level of satisfaction.

➢ Therefore, IC1 and IC2 can’t intersect each other.

Budget Constraint

The consumer can buy combination of two goods within his income constraint
i.e.
Px X + Py. Y < M
where, Px and Py are price of X and Y goods
X and Y are the amount of X and Y goods purchased
M – money income of the consumer.
Budget Line
Budget line is a graphical representation of all possible combination of two
goods which can be purchased with given income and prices, such that the
cost of each of these combinations is equal to the money income of consumer
i.e.
PxX + PyY = M
It is also known as price line.

Slope of Budget Line

The market rate of exchange is the rate at which the two goods can be
exchanged in the market or it is the rate at which the market requires
sacrifice of one good to obtain extra unit of the other good.
Slope of budget line = Market Rate of Exchange (MRE)
Thus,
MRE = Price of good obtained = ΔY
Price of good sacrificed ΔX
MRE = Px/Py
➢ Price ratio is the price of the good on the horizontal or X-axis divided by
the price of the good on the vertical or Y-axis.

Properties of Budget Line

1. Budget line is downward sloping from left to right.
The market requires consumer to sacrifice one good to obtain extra unit
of the other good.
2. Budget line is downward sloping straight line.
Slope of budget line is equal to MRE i.e. ‘Price Ratio’ of two goods which
remains constant.
Consumer Equilibrium conditions:
Condition 1: MRSxy = MRE = Px / Py (Necessary Condition)
CASE I : MRSxy > Px/Py.

➢ The consumer is willing to pay more for X than the price prevailing in the
market.
➢ Consumer will buy more of x.

➢ When he buys more of x, utility derived from X falls and he is willing to

sacrifice less of Y.

➢ Thus MRSxy starts declining.

➢ He continues to consume more of X, till MRSxy = MRE = Px/Py.

CASE II: MRSxy < Px /P y.

➢ The consumer is willing to pay less for X than the price prevailing in the
market.
➢ It induces the consumer to buy less of X and more of Y.

➢ MRSxy began to rise.

➢ He continues to decrease the consumption of X, till MRSxy = Px/Py.

Condition 2: MRSxy is Declining. (Sufficient Condition)

The indifference curve must be convex to the origin at the point of
equilibrium. Unless MRS continuously falls, the equilibrium cannot be
established.
“A consumer is in equilibrium at a point where budget line is tangent to
indifference curve”.
In the above diagram,
➢ Equilibrium is at point E, (Budget line touches the highest indifference
curve IC2) where the consumer purchases OX1 quantity of commodity ‘X’
and OY1 quantity of commodity ‘Y’

➢ MRS = Ratio of prices or Px/Py at tangency point E. The absolute values

of the slope of the indifference curve and of the budget line are same.