Answer

Solution

1. 1

   With $U = \min\{x,y\}$, demand satisfies $x = y$ and expenditure is $(p_x + p_y) x = M$,

2. 2

   giving utility $u = M/(p_x + p_y)$.

3. 3

   Old utility: $u_0 = 200/4 = 50$. \

4. 4

   New utility (at new prices, old income): $u_1 = 200/5 = 40$.

5. 5

   Equivalent Variation $A$ (money taken at old prices to leave consumer at new utility):

6. 6
   $$A = M - (p_x^{\text{old}} + p_y^{\text{old}})\, u_1 = 200 - 4(40) = 40.$$
7. 7

   Compensating Variation $B$ (extra money at new prices to restore old utility):

8. 8
   $$B = (p_x^{\text{new}} + p_y^{\text{new}})\, u_0 - M = 5(50) - 200 = 50.$$
9. 9

   So $(A, B) = (40, 50)$.

Answer structure / marking notes

Content note