4. Calculate the changes in wages and the rental price of capital. The initial output was Q = L0.5K0.5 = 1000.51000.5 = 100. The marginal product of labor was MPL = 12 Q/L = 12

(100/100) = 12

, so the real wage was w/p = 12

, given that p = 1. Similarly, the marginal product of capital was MPK = 12 Q/K = 12

, and the real price of capital was r/p = 12

. After the plague, the labor force fell to L* = 14

* 100 = 25, and output dropped to Q = 250.51000.5 = 50. Consequently, the marginal product of labor rose to MP*

L = 12

(50/25) = 1, so the real wage rose to w*/p = 1. Similarly, the marginal product of capital and the real price of capital fell to MP*

K = 12

(50/100) = 14

= r*/p. Thus, the real wage doubled and the real rental rate on capital dropped by half.