Suppose That an Economy Has 1,500 Units of Capital and 1,000

Essay

Suppose that an economy has 1,500 units of capital and 1,000 workers. This economy produces computers and shoes. Computer production requires four units of capital per worker and shirt production requires one unit of capital per worker.
I. Solve for the amount of labor and capital used in each industry.
Given that:
(1) K_C + K_S = the total capital stock, and L_C + L_S = the total labor force; and
(2) K_C = 4 · L_C, and K_S = 1 · L_S.
II. Suppose that the number of workers increases to 1,250 due to immigration, keeping total capital fixed at 1,500. Solve for the distribution of labor and capital between the two sectors.