Application of indifference curve analysis

Application of Indifference
Curve Analysis

Application of Indifference Curve Analysis
• The indifference curve analysis has also been used to explain
producer’s equilibrium, the problems of exchange, rationing, taxation,
supply of labour, welfare economics and a host of other problems.
Some of the important problems are explained below with the help of
this technique.
(1) The Problem of Exchange:
With the help of indifference curve technique the problem of exchange
between two individuals can be discussed. We take two consumers A
and В who possess two goods X and Y in fixed quantities respectively.
The problem is how can they exchange the goods possessed by each
other. This can be solved by constructing an Edgeworth-Bowley box
diagram on the basis of their preference maps and the given supplies of
goods.

Оa is the origin for firm A and Ob the origin for
В (turn the diagram upside down for
understanding). The vertical sides of the two
axes, Оa and Ob, represent good Y and the
horizontal sides, good X. The preference map
of A is represented by the indifference curves
I1a, I2a and I3a and B’s map by I1b, I2b and
I3b indifference curves. Suppose that in the
beginning A possesses Oa Ya units of good Y
and Oa Xa units of good X. В is thus left with
Ob Yb of Y and Ob Xb of X. This position is
represented by point E where the curve I1a
intersects I1b curve.

Suppose A would like to have more of X and B more of Y. Both will be
better off, if they exchange each other’s unwanted quantity of the good,
i.e. if each is in a position to move to a higher indifference curve. But at
what level will exchange take place? Both will exchange each other’s
good at a point where the marginal rate of substitution between the two
goods equals their price ratios.
This condition of exchange will be satisfied at a point where the
indifference curves of both the exchangers touch each other. In the
above figure P, Q and R are the three conceivable points of exchange. A
line CC passing through these points is the “contract curve” or the
“conflict curve”, which shows the various positions of exchange of X
and Y that equalise the marginal rates of substitution of the two
exchangers.

(2) Effects of Subsidy on Consumers:
The indifference curve technique can be used to measure the effects of
government subsidy on low income groups. We take a situation when the
subsidy is not paid in money but the consumers are supplied cereals at
concessional rates, the price-difference being paid by the government. This is
actually being done by the various state governments in India. Income is
measured on the vertical axis and cereals on the horizontal axis.

• Suppose the consumer’s income is OM and his price-income line
without subsidy is MN. When he is given subsidy by supplying cereals
at a lower price, his price-income line is MP (it is equivalent to a fall
in the price of cereals). At this price-income line, he is in equilibrium
at point E on curve I1 where he buys OB of cereals by spending MS
amount of money. The full market price of OB cereals is MD on the
line MN where the curve lo touches.
• The government, therefore, pays SD amount of subsidy. But the
consumer receives cereals at a lower price. He does not receive SD
amount of subsidy in cash.

(3) The Problem of Rationing:
The indifference curve technique is used to explain the problem arising
from various systems of rationing. Usually rationing consists of giving
specific and equal quantities of goods to each individual (we ignore
families because equal quantities are not possible in their case).
The other, rather liberal, scheme is to allow an individual more or less
quantities of the rationed goods according to his taste. It can be shown
with the help of indifference curve analysis that the latter scheme is
definitely better and beneficial than the former.
Let us suppose that there are two goods rice and wheat that are rationed,
the prices of the two goods are equal and that each consumer has the
same money income. Thus, given the income and price-ratios of the two
goods, MN is the price-income line. Rice is taken on vertical axis and
wheat on the horizontal axis .

• According to the first system of rationing, both
consumers A and В are given equal specific
quantities of rice and wheat, OR + OW. Consumer
A is on indifference curve Ia and В is on lb. With the
introduction of the liberal scheme each can have
more or less of rice or wheat according to his taste.
In this situation, A will move from P to Q on a
higher indifference curve Ia1. Now he can have
ORb of rice + OWa of wheat. Similarly, В will move
from P to R on a higher indifference curve Ib1 and
can buy ORb of rice + OWb of wheat. With the
introduction of the liberal scheme of rationing both
the consumers derive greater satisfaction. The total
quantity of goods sold is the same.
For when В buys more quantity of wheat WWb, he purchases less quantity of rice RRb and
when A buys RRb more of rice, he purchases WW less of wheat. Thus, the governmental aim of
controlled distribution of goods is not disturbed at all rather there has been a better distribution
of goods in accordance with individual tastes.

(4) Index Numbers: Measuring Cost of Living:
The indifferent curve analysis is used in measuring the cost of living or
standard of living in terms of index numbers. We come to know with the
help of index numbers whether the consumer is better off or worse off
by comparing two time periods when the income of the consumer and
prices of two goods change.
Suppose a consumer buys only two goods X and Y in two different time
periods 0 and 1 and he spends his entire income on them in the two
periods. It is also assumed that the consumer’s tastes and quality of the
two goods do not change.

Suppose the initial budget line is
AB in the base period 0 and the
consumer is in equilibrium at point
P on the indifference curve Io. The
new budget line in period 1 is CD
which passes through point P1 on
the new indifference curve I1. Both
the combinations P and P1 lie on
the original budget line AB.
Therefore, they have the same cost. But combination P is on the higher
indifference curve I0 than combination P1. However, the consumer cannot
have combination P at the new price (P1) in period 1. Thus he chooses
combination P1 on the lower indifference curve I1 and is worse off in period 1
than in the base period 0. This shows that his standard of living has decreased
in period 1 as compared with period 0.

(5) The Supply of Labour:
The supply curve of an individual worker can also be derived with the indifference curve
technique. His offer to supply labour depends on his preference between income and leisure
and on the wage rate. Hours of work and leisure are measured on the horizontal axis and
income or money wage on the vertical axis. W2L is the wage line or income-leisure line
whose slope indicates wage rate (w) per hour. When the wage rate increases, the new wage
line becomes W3L and the wage rate per hour-also increases and similarly for the wage line
W2 L.

• As the wage rate per hour increases,
the wage line becomes steeper. When
the worker is in equilibrium at the
tangency point E1 of wage line W1L
and indifference curve I1, he earns
E1L1 wage by working L1L hours
and enjoys OL1 of leisure. Similarly,
when his wage increases, to L2, he
works for longer hours L2 L and with
E3 L3 wage increase, he works for
still longer hours L3 L and enjoys
lesser and lesser leisure than before.
The line connecting the points E1E2
and E3 is called the wage-offer
curve.

(6) The Saving Plan of an Individual:
The indifference curve technique can also be used to study the saving
plan of an individual. An individual’s decision to save depends upon his
present and future income, his tastes and preferences for present and
future commodities, their expected prices, on the current and future rate
of interest, and on the stock of his savings.
As a matter of fact, his decision to save is influenced by the intensity of
his desire for present goods and future goods. It he wants to save more,
he spends less on present goods, other things being equal. Thus saving
is, in fact, a choice between present goods and future goods.

• Let PF1 be the original price-income line of
the individual where he is in equilibrium at
point S on the indifference curve I.
• Given the price of the present and future
goods, the income of the consumer, his tastes
and preferences for the present and the future,
and the rate of interest, he buys OA of the
present goods and plans to save so much as to
have OB of goods in the future.
Suppose there is a change in his preferences. What will be the effect of such a change on the
consumer’s saving plan? If his preference for the present goods increases, his price-income line will
move to P1F so that he is in equilibrium at point Q on I1 He now buys OA1 present goods and thus
saves less for the future goods. As a result, the purchase of the future goods will fall from OB to OB1.
On the other hand, if in his estimation the value of future consumption increases, his price-income line
will move to P2F where he will be in equilibrium at point R on L2 curve. He will, therefore, save more
and thus reduce his consumption of present goods to OA2 in order to have OB2 future goods.

Application of indifference curve analysis

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Application of indifference curve analysis