Page 53 - DECO401_MICROECONOMIC_THEORY_ENGLISH

Microeconomic Theory

Notes 4.5 Constant Marginal Rate of Substitution

One learns from the study of indifference curve that when a consumer gets one more unit of X
commodity, his satisfaction increases. If the consumer wants his level of satisfaction to be the
same, means if he wants to remain on the same
indifference curve, he will have to give up some units The marginal rate of substitution decides the slope
of commodity Y. In other words, in exchange of the of indifference curve. The stable marginal rate
satisfaction obtained from the additional apple, he means stability of sloping or marginal rate is a line
will have to give up that quantity of oranges whose of indifference curve. The decrease marginal rate
of substitution means falling of slope or convex
satisfaction is equal to the additional satisfaction indifference curve means convex to the main point.
obtained from an additional apple.

Satisfaction Gained of Apples = Satisfaction Lost from Oranges

In order to get one more unit of apple, a consumer gives up three units of oranges, it means, he
substitutes one apple for 3 oranges, then it will be said that satisfaction derived from one apple is equal
to the satisfaction of 3 oranges. So the marginal rate of substitution for apple to oranges is 1:3. In this
way, it can be said that the marginal rate of substitution of apple for orange is the number of oranges
that will be given up for obtaining each additional unit of apple, so that the satisfaction of the consumer
remains the same. In other words, marginal rate of substitution (MRS) is the rate at which the consumer
can substitute one product for another without changing the level of satisfaction. It indicates the slope
of indifference curves.
According to Bilas, “The marginal rate of substitution of product X for product Y (MRS ) is defined as
xy
the amount of Y, the consumer is just willing to give up to get one more unit of product X and maintain
the same level of satisfaction.”

Loss of Y ∆Y
MRS = Gain of X = (–) ∆X
xy
Where MRS is marginal rate of substitution of X for Y; = DY, changes in commodity, DX = changes in
xy
commodity –X.
In other words, if consumer wants to maintain same level of satisfaction, then marginal rate of
substitution is that ratio of quantities of commodity Y and commodity X which have to necessarily
be given up for getting one more unit of commodity X. This ratio is normally negative as change in
commodity Y with the increase in commodity X is negative.

(i) Constant Marginal Rate of Substitution
Marginal Rate of substitution is constant when in order to get one more unit of commodity X only one
unit of commodity Y has to be sacrificed so that level of satisfaction remains the same. In other words,
rate of substitution is equal. Marginal rate of substitution of perfect substitute goods is equal.

Constant Marginal Rate of Substitution is only a Theoretical Possibility

When commodity X is substituted for commodity Y at an increasing rate, then quantity of Y reduces and quantity of
X increases with the consumer. When the quantity of commodity X increases with the consumer, then every additional
unit gives more satisfaction from the previous units. In contrast, as a result of reduction in the units of commodity Y and
because of sacrificing on additional unit of Y, there is additional loss in satisfaction. When as a result of sacrificing one
additional unit of Y, the loss in satisfaction is more than the satisfaction yielded by the additional unit of X then how can
there be exchange at constant rate between X and Y.

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