Question

Consider an individual making choices over two goods, x and y with prices px and py, with income I , and the utility function u(x,y) = xy1/2.You already know that this yields the demand functions x∗ = 2I 3px and y∗ = I 3py (no need to calculate).
(a) Find the indirect utility function, expenditure function and the compensated (Hicksian) demands for x and y. Show your work.
(b) Use your expenditure function to find the compensating variation for a price increase from $2 to $3 for good x, given income I = 60, and py = 1.
(c) Use your answer from part (a) to determine which of these options is best for this consumer: (i) px = 1, py = 3, I = 100; (ii) px = 2, py = 2, I = 90;(iii) px = 3, py = 1, I = 120; (iv) px = 2, py = 1, I = 110.
1

Answer 1

Answer:

Given that:

Consider an individual making choices over two goods x and y with prices px and py with income I , and the utility function u(x,y) = xy^1/2

a)

Substitute it into the utility function

Where v is indirect utility function

Separate I from the above equation

Compound demand for x

for y

  

b)

  

Substitute P_x = 3 , P_y = 1 , I = 60

CV = 60-103.43

= -43.43

CV= -$43.43

c)

i) P_x = 1 ,P_y = 3 , I =100

ii)

P_x = 2 ,P_y = 2 , I =90

x = 30 , y = 15

iii)  P_x = 3 ,P_y = 1 , I =120

x=26.6 , y=40

iv) P_x = 2 ,P_y = 1 , I =110

x=36.6 , y= 36.6

Highest is in case i).