Question

Suppose there are 2 commodities (good x and good y) and the consumer faces the following prices. The price of commodity x is $1 each. The price of commodity y is $2 each if strictly less than 2 units are purchased. If 2 or more units are purchased, it is $1.50 each. If the consumer has an income of $10, show that the budget set faced by the consumer is not a convex set.

Answer 1

Answer: In consideration of the bundle of 10 units of x and 0 unit of y, total cost will be $10 ( = $1*10 + $2*0) and thus affordable.

Now in consideration of the bundle of 7 units of x and 2 unit of y, total cost will be $10 ( = $1*7 + $1.5*2) and thus it is also affordable.

On an average the bundle includes 8.5 units of x [computed as (10+7) / 2] and 1 units of y [computed as (0+2) / 2]. Thus the total cost will be $10.5 (= 1*8.5 + 2 *1). Thus the bundle would not be affordable and therefore, the budget set is not convex