Question

In: Economics

Suppose that the utility function is U(c, l) = c^(a) l^(1−a) where < a < 1....

Suppose that the utility function is U(c, l) = c^(a) l^(1−a) where < a < 1. Calculate the slope of an indifference curve for this utility function. What happens to the slope of the indifference curve when c decreases and l increases? Explain.

Solutions

Expert Solution

Utility function is;

U(c,I) = ca I(1-a)

Marginal rate of substitution

MRS is the rate at which consumer is willing to give up some units of one good in order to gain 1 more unit of other good. It represents the slope of the indifference curve and is calculated as;

MRS = MUc / MUI
= aca-1I(1-a) / (1-a)ca I-a
= aIa I1-a / (1-a)ca c1-a
= aI / (1-a) c
MRS = aI / c - ac

When c decreases it means that MRS will increase, i.e slope of the indifference curve will increase and at the same time when I increases, MRS will increase i.e slope of the indifference curve will increase.

Rahul Sunny answered 2 years ago
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