Answer to Question #268801 in Microeconomics for william

Question #268801

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.



1
Expert's answer
2021-11-29T15:13:20-0500

"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.

"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 of x by one units.

"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"

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