Ordinal Utility Theory
INDIFFERENCE CURVE
• An indifference curve is a curve that
represents all the combinations of goods
that give the same satisfaction to the
consumer. Since all the combinations give
the same amount of satisfaction, the
consumer prefers them equally. Hence the
name indifference curve.
• Here is an example to understand the indifference curve
better. Peter has 1 unit of food and 12 units of clothing.
Now, we ask Peter how many units of clothing is he
willing to give up in exchange for an additional unit of
food so that his level of satisfaction remains unchanged.
• Peter agrees to give up 6 units of clothing for an
additional unit of food. Hence, we have two combinations
of food and clothing giving equal satisfaction to Peter as
follows:
• 1 unit of food and 12 units of clothing
• 2 units of food and 6 units of clothing
• By asking him similar questions, we get various
combinations as follows:
Indifference Map
• An Indifference Map is a set of Indifference
Curves. It depicts the complete picture of a
consumer’s preferences. The following
diagram shows an indifference map
consisting of three curves:
• We know that a consumer is indifferent among the
combinations lying on the same indifference
curve. However, it is important to note that he
prefers the combinations on the higher
indifference curves to those on the lower ones.
• This is because a higher indifference curve implies
a higher level of satisfaction. Therefore, all
combinations on IC1 offer the same satisfaction,
but all combinations on IC2 give greater
satisfaction than those on IC1.
Properties of an Indifference Curve
• An IC slopes downwards to the right
This slope signifies that when the quantity of
one commodity in combination is increased,
the amount of the other commodity reduces.
This is essential for the level of satisfaction
to remain the same on an indifference
curve.
• An IC is always convex to the origin
From our discussion above, we understand that as Peter substitutes clothing
for food, he is willing to part with less and less clothing. This is the
diminishing marginal rate of substitution. The rate gives a convex shape
to the indifference curve. However, there are two extreme scenarios:
• Two commodities are perfect substitutes for each other – In this case, the
indifference curve is a straight line, where MRS is constant.
• Two goods are perfect complementary goods – An example of such goods
would be gasoline and water in a car. In such cases, the IC will be L-
shaped and convex to the origin.
• Indifference curves never intersect each
other
• Two ICs will never intersect each other.
Also, they need not be parallel to each other
either. Look at the following diagram:
• Fig 3 shows two ICs intersecting each other
at point A. Since points A and B lie on IC1,
they give the same satisfaction level to an
individual. Similarly, points A and C give
the same satisfaction level, as they lie on
IC2. Therefore, we can imply that B and C
offer the same level of satisfaction, which is
logically absurd. Hence, no two ICs can
touch or intersect each other.
• A higher IC indicates a higher level of satisfaction as
compared to a lower IC
A higher IC means that a consumer prefers more goods
than not.
• An IC does not touch the axis
This is not possible because of our assumption that a
consumer considers different combinations of two
commodities and wants both of them. If the curve
touches either of the axes, then it means that he is
satisfied with only one commodity and does not want the
other, which is contrary to our assumption.
Indifference Curve Analysis
• Indifference curves are based on a number of
assumptions, such as that each indifference curve is
convex to the origin and that no two indifference curves
ever overlap. When obtaining bundles of commodities on
indifference curves that are farther from the origin,
consumers are supposed to be more satisfied.
• The majority of the time, indifference curve analysis
assumes that all other variables are stable or constant.
• The slope of the indifference curve is referred to by the
MRS. The MRS measures how eager a consumer is to
trade one product for another. If a customer values a
banana, for example, the rate of substitution for
watermelon will be slower, and the slope will reflect this
rate of substitution.
• Marginal Rate of Substitution
This is the rate at which a consumer is
prepared to exchange a good X for Y. If we
go back to Peter’s example above, we have
the following table:
• In this example, Peter initially gives up 6 units of clothing to
get an extra unit of food. Hence, the MRS is 6. Similarly, for
subsequent exchanges, the MRS is 2 and 1 respectively.
Therefore, the MRS of X for Y is the amount of Y whose loss
can be compensated by a unit gain of X, keeping the
satisfaction the same.
• Interestingly, as Peter accumulates more units of food, the
MRS starts falling – meaning he is prepared to give up fewer
units of clothing for food. There are two reasons for this:
• 1. As Peter gets more units of food, his intensity of desire for
additional units of food decreases.
• 2. Most of the goods are imperfect substitutes for one
another. If they could substitute one another perfectly, then
MRS would remain constant.
Budget Line
• Since a higher indifference curve represents a
higher level of satisfaction, a consumer will try
to reach the highest possible IC to maximize his
satisfaction. In order to do so, he has to buy
more goods and has to work under the
following two constraints:
• He has to pay the price for the goods and
• He has limited income, restricting the
availability of money for purchasing these
goods
• As can be seen above, a budget line shows all
possible combinations of two goods that a consumer
can buy within the funds available to him at the
given prices of the goods. All combinations that are
within his reach lie on the budget line.
• A point outside the line (point H) represents a
combination beyond the financial reach of the
consumer. On the other hand, a point inside the line
(point K) represents under-spending by the
consumer.
