Question

Johnny B. Good is a retired economist based in Prague. His income is equal to 15,000 CZK, the market price of the two goods he consumes is p1 = 10 and p2 = 20 CZK and his utility function is U(x1, x2) = min{x1, x2}. Nevertheless, his daughter Maria wants him to move to her place in South Moravia so that she could take care of him. Due to the lower price of second good in Moravia (p2 = 10 CZK), the moving is equally good to for him as his pension would be increased by A CZK. Simultaneously, he would be indifferent between staying in Prague and moving if his pension in Moravia was decreased by B CZK. Calculate A and B, using the concept of equivalent and compensating variation.

Answer 1

Answer -

given :-

Johnny B. Good's income = 15,000 CZK

Market price of two goods he consumes is

p1 = 10 and p2 = 20 CZK

His utility function is -

U(x1,x2) = min{x1,x2}

Lower price of second good in Moravia => p2 =10CZK

In Prague =>

U = min(x1,x2)

Max utility x1 = x2

Plug with budget constraint-

x1 + 2x2 = 1500

x2 + 2x2 = 1500 ......... (x1=x2)

3x2 = 1500

x2 = 1500/3

x2 = 500

x1 = 500

U = 500

In South Moravia=>

500 = min(x1,x2)

Budget =>

x1 + x2 = M

x1 = x2 = 500

10x1 + 10x2 = M

10(x1 + x2) = M

10 (500 + 500) = M

10 x 1000 = M

M = 10,000

Compensating variation = 10,000 - 15,000

= - 5000

For equivalent variation =>

In South Moravia =>

U = min(x1,x2)

x1 = x2

10x1 + 10x2 = 15000

10 (x1 + x2) = 15000

(x1 + x2) = 15000/10

x1 + x2 = 1500

x1 + x1 = 1500........(x1 = x2)

2x1 = 1500

x1 = 1500/2

x1 = 750

x1 = x2 = 750

U = 750

In Prague =>

750 = min (x1,x2)

x1 = x2 = 750

10x1 + 20x2 = M

10 x 750 + 20 x 750 = M

7500 + 15000 = M

M = 22500

Equivalent variation = 15000 - 22500

= - 7500

So,

A = - 7500

B = - 5000