Question

The consumer's utility is given by u(x,y)=16x-3√√x+y. The price of good 2 is normalized to 1. Find the change in consumer's surplus if the price of good 1 changed from 10 to 5.

Answer: 18.35

Answer 1

$u(x,y)=16x-3\sqrt {\sqrt (x+y)}$

Assume that the consumer initially consumes 10 units of x and 0 units of y at the prices of x being 10 and y being p.

Therefore:

$u(x,y)_{1}=16\times10-3\sqrt {\sqrt10}= 155.59$

When price of x declines to 5 (by half), the consumer can increase his consumption of y by an additional 50 units while reducing their consumption ofx by one units.

Therefore:

$u(x,y)_2=16\times9-3\sqrt {\sqrt69}= 137.24$

$Change in utility surplus =u(x,y)_1-u(x,y)_2$

$Change in utility surplus=155.59-137.24=18.35$