Unit 7 homework key (Ch. 7)

1. Solution in text.

7. When the wage increases, the firm will use a more capital-intensive input mix. The expansion path becomes steeper. See Figure 7.5.

Figure 7.5

12. Solution in text.

14. Solution in text.

26. a. You must set dAC/dq = 0 for each firm. The minimum point of AC₁ is at q = 2. At plant 2, the minimum point is at q = 1.

b. The firm should produce 3 units in plant 1, and 1 unit in plant 2.

33. MP_L/MP_K = (1/2K^1/2/L^1/2)/(1/2L^1/2/K^1/2) = K/L = w/r

In U.S., w = r = 10 = > L = K;

In Mexico, w^* = 5; r^* = 10 = > L = 2K

C_us = wL + rK = 20K; C_mexico = 20K

q_us = (LK)^1/2 = K ; q_mexico = 2^1/2K

C_us = 20q_us; C_mexico = 14.1q_mexico

When q = 100, for U.S., C = 2000, L = K = 100;

for Mexico, C = 1410, K = 70.7, L = 141.