explain how an indifference curve with constant marginal rate of substitution (e.i. good x and good...

explain how an indifference curve with constant marginal rate of substitution (e.i. good x and good y are perfect substitutes) will lead to the consumer purchasing only good x and good y. under what practical condition would the consumer only purchasing good x good y. draw a diagram and solution

Solutions

Expert Solution

Perfect substitute goods are those where MRS is constant.

Utility function of good x and y is U= aX+bY

So indifference curve will be a straight line.

Also tangency condition cannot be applied here since both BL and IC are straight lines. But the optimal point will be where the two lines meet at the highest IC.

Since the consumer considers these two goods as perfect substitutes, consumer would prefer to consume only that good which is cheaper.

MRS=MUx/MUy=Px/Py

There are 3 possibilities-

Case 1. Py<Px

Slope of budget line is more than slope of indifference curve

Good y is cheaper. So conaumer will only buy good y. And no good x.

Optimal point A.

Case 2. Px<Py

Slope of budget line is less than sloep of indifference curve.

Good X is cheaper. So only good X will be brought. Optimal point B.

Case 3. Px=Py

Slope of budget line is equal to the sloep of indifference curve.

Consumer can purchase at any point on the indifference curve.

Optimal line is AB.

AB is the budget line.

Rahul Sunny answered 3 hours ago

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