Sheila has preferences represented by the utility function U (x, y)= 8x + 4y. She consumes 12 units of good x and 3 units of good y. If her consumption of good x is lowered to 10, how many units of y must she have in order to be exactly as well off as before?
A)10 units of good y
B)5 units of good y
C)12 units of good y
D)7 units of good y

Question

Quizplus · Accepted Answer

To keep Sheila's utility the same after reducing her consumption of good x from 12 to 10 units, we first calculate her initial utility: U(12, 3) = 8(12) + 4(3) = 96 + 12 = 108. After reducing x to 10, we set her utility equal to 108 and solve for y: 8(10) + 4y = 108, which simplifies to 80 + 4y = 108. Solving for y gives 4y = 28, so y = 7. Therefore, Sheila must have 7 units of good y to be as well off as before.

Sheila Has Preferences Represented by the Utility Function U (X