Doreen has preferences represented by the utility function U(x, y)= 10x + 5y.She consumes 10 units of good x and 9 units of good y.If her consumption of good x is lowered to 1, how many units of y must she have in order to be exactly as well off as before?
A)20
B)30
C)27
D)18
E)None of the above.

Question

Quizplus · Accepted Answer

To find out how many units of good y Doreen needs to have in order to be as well off as before, we need to find the utility she derives from (1, y) and then solve for y.

U(1, y) = 10(1) + 10(5y) 
U(1, y) = 50y + 10

We want to find y such that the utility from (1, y) is the same as the utility from (10, 9).

U(10, 9) = 10(10) + 10(5(9)) 
U(10, 9) = 460

So we want to solve for y in the equation:

50y + 10 = 460

50y = 450

y = 9

Therefore, Doreen must have 9 units of good y when her consumption of good x is lowered to 1 in order to be as well off as before.

Doreen Has Preferences Represented by the Utility Function U(x, Y)=