UNIT 3: INDIFFERENCE CURVE ANALYSIS

Contents
3.0 Aims and Objectives
3.1 Introduction to Ordinal Utility Approaches
3.2 What are Indifference Curves?
3.3 Assumptions Behind Indifference Curve Analysis
4.4 Properties of Indifference Curves
4.5 Consumer’s Equilibrium
4.6 Income, Substitution and Price Effects
3.7 Derivation of Demand Curve from Indifference Curve
3.8 Summary
3.9 Answers to Check Your Progress
3.10 Model Examination Questions
3.11 References

3.0 AIMS AND OBJECTIVES

The purpose of this unit is to explain the ordinal utility approach.

After reading this unit, you will be able to:

 recognize the importance of ordinal utility analysis;
 list out the properties of indifference curves;
 explain consumer equation.

3.1 INTRODUCTION TO ORDINAL UTILITY APPROACH

In the study of marginal utility analysis, we have assumed that utility is measurable in the
cardinal sense. To overcome this difficulty the modern economists have developed an
alternative approach of indifference curve analysis based on ordinal measurement of
utility. This is in recognition of the fact that exact measurement of utility is not possible
and that the economists can at best give a ranking to consumer’s satisfaction instead of
measuring it in units. The N-M index is also ordinal in its approach even though it seems

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to be using the cardinal approach. In the ordinal approach, the consumer need not assign
specific amounts to the utility, which he derives from the consumption of a good or
combination of goods. He will simply compare the different utilities or satisfaction in the
sense whether one level of satisfaction is equal to, lower than, or higher than another. For
example, if the various combinations are X, Y, Z etc., the consumer can tell whether he
prefers X to Y or Y to Z or is indifferent to the comparing of them. The concept of
ordinal utility implies that the consumer cannot go beyond stating his preference or
indifference. In other words, if a consumer happens to prefer X to Y he cannot precisely
tell by how much he prefers X to Y or he cannot tell the quantitative differences between
various levels of satisfaction. At the most he can merely judge whether one level of
satisfaction is higher than or lower than or equal to another or alternatively rank his
preferences as 1st, 2nd, 3rd and so on. For example, suppose the individual consumer is
consuming rice and clothing. The indifference curve analysis indicates that he would be
consuming both in such a manner that his level of satisfaction would be the same if he
consumes less of rice and more of clothing or more of rice and less of clothing as long as
remains on the same indifference curve.

Check Your Progress –1

1. What ordinal utility analysis?
__________________________________________________________________
___________________________.

3.2 WHAT ARE INDIFFERENCE CURVES?

To understand indifference curves, it is better to start with an indifference schedule.

Table 3.1: Indifference Schedule

Schedule –I Schedule –Ii

Goods ‘X’ Goods ‘Y’ Goods ‘X’ Goods ‘Y’
1 15 1 17
2 11 2 14
3 8 3 11
4 6 4 8
5 5 5 6

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In the above schedules the consumer has to start with 1 unit of X and 15 units of Y. Now
the consumer is asked to tell how much of goods he will be willing to give up for the gain
of an additional unit of X so that his level of satisfaction remains the same. If the gain of
one unit compensates him fully for the loss of 4 units of Y, then the next combination of
2 units of X and 11 units of Y(2X + 11y) will give him as much satisfaction as the initial
combination (1X + 15Y). Similarly by asking the consumer further how much of Y he
will be prepared to fore-go for successive increments in the stock of X so that his level of
satisfaction remains unaltered. We get combinations of 3X + 8Y, 4X + 6Y and 5X + 5Y
each of which provides the same satisfaction as combination 1X + 15Y or 2X + 11Y.
Since satisfaction is the same whichever combination of goods in the schedule is offered
to him, the consumer will be indifferent among the combinations included in a schedule.
Similarly the consumer may have another schedule representing more of both the goods
than the initial combination Schedule-II. Once again the consumer is indifferent among
the various combinations in Schedule-II, but however, it should be borne in mind that the
consumer will prefer any combination is preferred to less of it and hence any combination
in Schedule-II will give him more satisfaction than any combination in Schedule-I.

The indifference schedule can be converted into indifference curve by plotting the
various combinations on a graph paper.

Thus when there are two difference curves (I & II), combinations on indifference curve I
will be of equal value and similarly combination on the indifference curve II will be of
equal value. But combinations on the higher indifference curve will have greater value
than combinations on the lower indifference curve. The higher the indifference curve or
the farther it is from the origin ‘O’, the higher the level of satisfaction from the
combination of two commodities.

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3.3 ASSUMPTIONS BEHIND INDIFFERENCE CURVE ANALYSIS

Before we discuss the properties of indifference curve it will be useful if we mention the
assumption about the psychology of the consumer, which one generally makes in
indifference curve analysis.

Assumption-I
It is assumed that a consumer will also prefer more of a piece of goods to less of another,
that is, if he is over supplied or over satiated with one of them he will prefer a smaller
quantity, of that one to the larger quantity. It is thus assumed that the consumer has not
yet reached the point of satiety in the consumption of any of the goods. This assumption
is therefore known as non-satiety assumption.

Assumption-II (Transitivity)
By transitivity let us suppose there are three combinations of two goods, X, y and Z. If
the consumer is indifferent between combination X and Y and also between X and Z, it is
obvious that by law of transitivity he will be indifferent between combination of Y and Z,
which implies that consumer’s tastes are quite consistent.

Assumption-III (Diminishing Marginal Rate of Substitution)

According to the principles of diminishing marginal rate of substitution, it is assumed that
the consumer will be prepared to give up less and less of goods. Y for each additional
unit of X. In the indifference schedule given earlier we have seen that in the beginning
the consumer gives up 4 units of Y for the gain in one additional unit of X but the level of
satisfaction remains the same. It follows that he gives up 3 units of Y for an additional
unit of X and later on 2Y for 1X and so on. Thus the marginal rate of substitution of X
for Y (MRS xy) diminishes as more and more of goods X is substituted for goods Y.

3.4 PROPERTIES OF INDIFFERENCE CURVES

Based on the above assumptions we can proceed to deduce the properties of indifference
curves namely:
a) Indifference curves slope downwards form left to right.
b) Indifference curves are convex to the origin.

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 c) Indifference curves cannot intersect each other.
d) A higher indifference curve represents higher level of satisfaction than the
indifference curve at the lower level.

Indifference curves slope downwards from left to right

This property implies that an indifference curve has a negative slope which means that
when the amount of one piece of goods in the combination is increased, the amount of the
other good is reduced so that the loss of satisfaction by giving up the first good is
compensated for the gain the satisfaction by additional unit of the other good. (see figure
3.1). If the indifference curves do not slope down wards form left to right, they can be
horizontal or they must slope upwards from left to right. Let us examine the horizontal
indifference curve in the outline given below.
If the indifference curve had the shape of
Y
horizontal straight line as given above it would
mean that all combinations along the curve are
Goods ‘Y’

of equal value i.e., 4X + 1Y, 4X+2Y, 4X+3Y

and so on. But this cannot be so if our first
A B C D E F IC
assumption is to hold good, i.e., a consumer
always prefers a larger amount of a good to a
smaller one. Hence each succeeding
O 1 2 3 4 5
6 X combination is better than the previous one, so
Fig. 3.2 Goods ‘X’ much so the consumer cannot be indifferent
He would definitely prefer a combination including a larger
between the amount
various of one commodity
combinations.
with the same amount of the other to a combination including a smaller amount of one
commodity with the same amount of other. Therefore, an indifference curve cannot be
horizontal since different combinations on the curve will differ in importance and
If the indifference curve were upward sloping
satisfaction.
to the right, it would mean that combination
The other alternative to a downward sloping indifference
which combines curve would
more of both be
thean upward
goods could
sloping indifference curve as shown below: give the same satisfaction to the consumer as

Y the combinations which had smaller amounts

of both the goods. This is clearly invalid
6 IC
because the consumer would always prefer the
combination containing more of both 30the
goods to a combination containing less.
Goods ‘Y’

5 E
4 D
3 C
2 B
1 A
O X
1 2 3 4 5 6
Fig. 3.3 Goods ‘X’

Therefore; the consumer prefers the same combination to the other. He cannot be
indifferent between them. It follows therefore that indifference curve cannot slope
upwards to the right because in such a case the combinations on the curve will be of
different significance and not of equal significance which is quite contradictory to the
property of an indifference curve. Hence the indifference curve must necessarily slope
downwards from left to right as given below in figure 3.4 A.

The down ward sloping indifference curve would mean that all combinations on the
curve are of equal significance and he is the therefore indifferent between them for every
increase in the amount of X, there is corresponding decrease in the amount of Y.

Indifference curves are convex to the origin

The property of indifference curve being convex to the origin follows from the
assumption of diminishing marginal rate of substitution. This may be illustrated below
(see figure 3.4 B)

Along OX we have made AB = BC = CD representing three equal units of commodity X.

In order to get more Y, the consumer will exchange X for Y. It will be clear form the

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above figure that as more and more of X is acquired, for each extra unit of X the
consumer is willing to part with less and less of Y i.e., MRS xy diminishes as more and
more of X is substituted for Y. Thus the convex indifference curves are consistent with
the principle of diminishing MRS xy. We therefore conclude that indifference curves are
convex to the origin.

If the indifference curve is concave to the origin it goes contrary to the law of
diminishing marginal utility. A concave indifference curve will imply that the MRS xy
increases as more and more of X is substituted for Y as shown below.

It can be seen from the figure 3.5 that as

more and more of X is acquired for each
extra unit of X, the consumer is willing
to part with more and more of Y. i.e,
MRS xy increases as more and more of X
is substituted for Y. Thus if the principle
of diminishing marginal rate of
substitution is valid, then indifference
curves cannot be concave to the origin.

Indifference curves cannot intersect each other

Another important property of indifference curves is that they cannot intersect each other.
If they should intersect we arrive at self-contradictory or absurd conclusions. In the figure
3.6 two indifference curves are shown cutting each other at point C.

Taking IC2 No.1 first

OM of X + OS of Y = ON of X + OR of Y

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 Taking IC1 No.2
OM of X + OS of Y = ON of X + OQ of Y
Therefore OR of Y = OQ of Y

Hence, On of X + OR of Y = ON of X + OQ of Y, but conclusion that OR of Y = OQ of

Y is absurd

Two indifference curves cannot intersect and can also be shown by the law of transitivity.
Take point A on IC2 and point B on IC1 vertically below A. Combination A & C will give
the consumer equal satisfaction because they lie on the same indifference curve IC 2.
Likewise between combinations B & C on IC 1 the consumer is different because they
give him same level of satisfaction. If combination A is equal to combination C in terms
of satisfaction, and combination B is equal to combination C, it follows that the
combination A will be equivalent to B in terms of satisfactions. But a glance at the figure
will show that this is absurd since combination A contains more of commodity than
combination B, while the amount of commodity is the same in both the combinations.
Thus the consumer will definitely prefer A to B, i.e., A will give more satisfaction to the
consumer than combination B. We therefore conclude that the indifference curves cannot
cut each other.

A higher indifference curve represents higher level of satisfaction than the indifference
curve at the lower level.
The combinations which lie on a higher
Y
indifference curve will be preferred to the
Goods ‘Y’

combinations which lie on a lower indifference

A curve because combination A contains more of
B both the goods than the combination B. Hence,
IC2
combination A on a higher indifference curve
IC1
0 X will give him more satisfaction than the
Goods ‘X’
combination B on lower indifference curve.
Fig. 3.7
3.5 CONSUMERS’ EQUILIBRIUM

Price Line or Budget Line

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In order to explain consumers, equilibrium there is also the need for introducing the price
line into the indifference curve diagram, which represents the prices of the goods and
consumers’ income.
Suppose our consumer has got Br. 100/- to
spend on X and Y. Let the price of
commodity X in the market be Br. 20/-per
unit and that of Y Br. 10/-. If he spends the
whole of his income on X he would buy 5
units of X and if the entire amount is spent
on Y, he would buy 10 units of Y. These
two, therefore represent the two extreme
alternatives open to the consumer.

In other words he can buy any combination that lies in the price line with his given
income combination outside the price line AB will be beyond the reach of the consumer
with his given income and price of goods and any point within the reach of the consumer
but on such combinations he will not be spending all his income. He will not be at point
G inside AB since by assumption he spends all his income on X or Y. Therefore, the
consumer with given income under given market conditions will have different
opportunities of consumption along path AB.

By superimposing the indifference curve on the price or budget line, the equilibrium
position of the consumer is determined. A consumer is said to be in equilibrium when he
is buying such a combination of goods, which leaves him with no tendency to rearrange
his purchases of goods.

Assumptions
The following assumptions are made to explain the consumers’ equilibrium.
a) He has a given amount of money to spend on the two goods.
b) Prices of all the goods are fixed in the market so that no individual consumer can
alter the price.
c) Goods are homogeneous and divisible.

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 d) The consumer is rational, i.e., the consumer will maximize his satisfaction with
given income and prices of goods.

Conditions
The consumer is in equilibrium when he maximizes his utility, given his income and the
market prices. Two conditions must be fulfilled for the consumer to be in equilibrium.

The first condition is that the marginal rate of substitution be equal to the ratio of
commodity prices.

MRS xy =

This is a necessary but not a sufficient condition for equilibrium. The second condition is
that the indifference curves be convex to the origin. This condition is fulfilled by the
axiom of diminishing MRS.

Graphical Presentation
Given the indifference map of the consumer and his budget line, the equilibrium is
defined by the point of tangency of the budget line with the highest possible indifference
curve. At the point of tangency the slope of the price line Px/Py and of the indifference
curves (MRSxy = MUx/My) are equal.

Thus the first order condition is denoted

graphically by the point of tangency of the
two relevant curves. The second order
condition is implied by the convex shape of
the indifference curves. The consumer
maximizes his utility by buying OX and OY
of the two commodities. Any other possible
combination of the two goods either would
lie on a lower indifference curve and thus
Yield less satisfaction or would be unattainable. Take point E which also lies on the same
price line AB but E lies on lower indifference curve IC1 and therefore will yield less
satisfaction than P. Likewise points F, G, H are also rejected in favor of P, since they lie

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on lower indifference curve. It is thus clear that of all combinations lying on AB
combination, P lies on the highest possible indifference curve and yield maximum
possible satisfaction and therefore the consumer will be in the equilibrium position at
point P.

Only at the tangency point of P, the slopes of the price line and indifference curve are
equal. The slope of the indifference curve, while the slope of the price shows the MRS xy
line, indicates the ratio between the prices of the two goods. At points EF, the marginal
rate of substitution (MRSxy) is greater than the given price ratio; hence he will buy more
of X than Y and come down along the price line. He will continue to do so to till
MRSxy = Px/Py. On the contrary at points GH, MRS xy is less than the given price ratio.
Therefore it will be to the advantage of the consumer to substitute good y for good x and
thereby move up the price line AB until the MRS xy = Px/Py. Therefore only at point P, the
consumer is in equilibrium because at that point the price line is tangent to the
indifference curve or in other words the marginal rate of substitution of good x for good y
must be equal to the ratio between the prices of the two goods.

3.6 INCOME, SUBSTITUTION AND PRICE EFFECTS

Income Effect
Another concept associated with indifference curves is the income effect. So far we have
assumed a consumer with a given income buying two different commodities at given
prices. We must also consider how the consumer will react in regard to his purchases of
the commodity when his commodity income changes while prices of the goods and his
tastes and preferences remain unchanged. Thus the income effect means the change in
consumer’s purchases of the goods as a result of change in his income. The income effect
is illustrated in the figure 3.10.

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With given price and a given money incomes as indicated by price line P 1L1 the consumer
is in equilibrium at point Q (see fig. 3.10). If the income of the consumer increases, with
increased income, he would be able to purchases larger quantities of both the goods. As a
result of a change in his income, the price line will shift upwards to the right and will be
parallel to the price line P 2L2. With further rise in income, the price line shifts to P 3L3 and
the consumer is at equilibrium at S. if the various points of Q, R & S showing consumer’s
equilibrium at various levels of income are connected, we will get the income
consumption curve. Income consumption curve is thus the locus of equilibrium points at
various levels of consumer’s incomes.

If the income effect is positive for both the

goods X and Y, the consumption curve will
slope upwards to the right as given below
by ICC1 in fig. 3.11. If the income effect is
negative for good X, ICC will slope
backward to the left as ICC2 and will slope
downwards to the right as ICC3 if
commodity Y happens to be an inferior
one.
Substitution Effect
Yet another factor responsible for the changes in the consumption of commodity is the
substitution effect. Under this effect we assume change in prices for a corresponding
change in money income with the result that the consumer is neither better off nor worse
off than before, i.e., the real income of the consumer remains the same. However, when
prices change, commodities, which are cheaper, would be substituted for commodities,
which are dearer. This result is known as substitution effect.

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Thus substitution effect is illustrated below:

With the given income and prices, the

consumer is at equilibrium at point Q on the
indifference curve, purchasing ON of
commodity of Y and OM of commodity X.
Suppose the price of commodity X falls, the
price line shift to PL1. With this fall in price
the consumer’s real income or purchasing
power would increase. In order to find out the
substitution effect, the gain in real income
should be wiped out by reducing the money
income of the consumer that forces him to stay
on the same indifference curve. When some money income is taken away, the price line
is shifted to a new position PL 1 parallel to AB which means that the reduction of
consumer’s income by the amount PA (in terms of Y) or L1B (in terms of X) has been
made to keep him on the same indifference curve. The consumer would therefore
rearrange his purchases of X and Y and will substitute X for Y since X is now relatively
cheaper and Y is now relatively dearer. Thus in order to buy more of X he moves on the
same indifference curve from point Q to point T. Thus, increase in the purchase of
commodity x by MM1 and the decrease in the purchase of commodity Y by NN 1 is due to
the change only in the relative prices of commodity x and y, since the effect due to the
gain in real income has been wiped out by making a simultaneous reduction in
consumer’s income. Therefore movement form Q to T represents the substitution effect.
Substitution effect on commodity X, is the increase in its quantity purchased by MM 1 and
substitution effect on Y is the fall in This effect shows
the quantity the reaction
purchased by NNof1the
. Inconsumer
short, the
andthemeasures
substitution effect implies that a change on the of
real income fulla consumer
effect of the
due change in
to a change
the price ofchange
in the price is compensated by a corresponding the commodity
in moneyonincome
the quantity
but the
purchased
relatively cheaper commodity is bought in the placewith given
of the money
dearer one. income.
Price Effect To begin with, the consumer is at equilibrium
at point Q on budget line AB. With the fall in
the price of X, the budget line shifts to the
right BA1 and the consumer can now buy OA1
of X of OB of Y. A further fall in price of X38
will shift the budget line to BA2 and so on.
By joining Q, Q1 and Q2 we got a curve called the price consumption curve. The price
consumption curve shows the price effect.

3.7 DERIVATION OF DEMAND CURVE FORM INDIFFERENCE CURVE

The demand curve can be derived from indifference curves. This is done by measuring
money on Y-axis and units of X commodity on X-axis. As the price of commodity X
falls, the consumer will be moving to a higher indifference curve. With the help of unit
price of X, the demand curve for commodity X can be drawn, where it will be downward
sloping indicating that more and more of X will be bought as price of X falls.

3.7.1 Graphic Presentation

Money is measured along Y-axis and commodity X along X-axis. To begin with, the
consumer is at equilibrium position at A, where the price line RA 2 is tangential to
indifference curve IC1. If there is a fall in the price, the price line shifts to RB 2 and the
consumer has a new equilibrium position at B. With every fall in the price of X, the
consumer moves from one position of equilibrium.

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3.8 SUMMARY

Indifference curve analysis is based on ordinal measurement of utility. By consuming a

combination of commodities, consumer can compare the different utilities. Indifference
curve is the line of those combinations of two commodities, Say X and Y goods, which
yield equal satisfies to the consumer. A consumer gets equilibrium when the ratio of
marginal utilities from two commodities is equal to the ratio of commodity price and
when the indifference curves are convex to the origin. The ratio of commodity prices is
explained through price time.

3.9 ANSWERS TO CHECK YOUR PAR OGRESS

1. The ordinal utility says that the exact measurement of utility is not possible and at
bests a given ranking to customers’ satisfaction instead of measuring in units.

3.10 MODEL EXAMINATION QUESTIONS

1. What are indifference curves?

2. Can two indifference curves interest each other?
3. What is price line?
4. What are meant by income and substitution effects?
5. Why do indifference curves slope downward?
6. Explain the properties of indifference curves.

3.11 REFERENCES

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