Question

1. Ginger’s utility function is U(x, y) = x2y, with associated marginal utility functions MUx = 2xy and MUy = x2. She has income I = 240 and faces prices Px = $8 andPy = $2.
a) Determine Ginger’s optimal basket given these prices and her income.
b) If the price of y increases to $8 and Ginger’s income is unchanged, what must the price of x fall to in order for her to be exactly as well off as before the changein Py?

Answer 1

a) When utility is maximized, MUx/Px=MUy/Py, and we have a budget constraint of 8x+2y=240, so you simply plug in numbers and solve.

Thus:

2xy/8=x^2/2
=> 2xy=4x^2
2y=4x
y=2x

I=PxX+PyY
240=8x+2(2x)
240=12x
x=20
y=40

Answer 2

Maximise utility

Equate utility functions

2xy/8=x²/2
2xy=4x²
2y=4x
y=2x

Income

I=PxX+PyY
240=8x+2(2x)
240=12x
x=20
y=40

Answer 3

1. Ginger’s utility function is U(x, y) = x2y, with associated marginal utility functions MUx = 2xy and MUy = x2. She has income I = 240 and faces prices Px = $8 and Py = $2.
a) Determine Ginger’s optimal basket given these prices and her income.

8X +2Y=240

2Y/X = 8/2= 4

(X,Y)=(20,40)

20^2 X 40= 16000