Aishwarya has preferences represented by the utility function U(x,y) = 20x+5y

Economics Dec 17, 2020

Aishwarya has preferences represented by the utility function U(x,y) = 20x+5y. She consumes 20 units of good x and 4 units of good y. If her consumption of good x is lowered to 13, how many units of y must she have in order to be exactly as well off as before?

A. 37 units of good y

B. 22 units of good y

C. 32 units of good y

D. 4 units of good y

E. None of the above

Expert Solution

For an individual to have to have the same well being the utility functions have to be set equal to each other.

U(x,y) = 20x + 5y. Initially she consumes 20 units of good x and 4 units of good y. Then,

U(x,y) = 20(20) + 5(4)

= 400 + 20

= 420

If consumption of x decreases from 20 to 13, then

420 = U(x,y) = 20(13) + 5(y)

420 = 260 + 5y

160 = 5y

32 = y

This means that the answer is C. Aishwarya has to consume 32 units of good y to have the same utility.

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