Consider a firm that produces output from capital and labor according to the production function q = 10LK. The price of capital (r) is $120 per unit. The price of labor (w) is $40 per unit.

a. If capital is fixed at 10 in the short run, how much labor must be employed to produce 500 units of output in the short run?

b. What is the total cost of producing 500 units of output in the short run? What is the short run marginal cost when 500 units of output are produced?

c. If the price of labor increases from $40 per unit to $60 per unit, what happens to the total cost of producing 500 units of output in the short run (up or down, and by how much)? What happens to the short run marginal cost (up or down, and by how much)?

d. At the initial prices, which bundle of inputs (L, K) would enable the firm to produce 500 units of output at the lowest cost in the long run?

e. What is the total cost of producing 500 units of output in the long run at the initial prices? What is the long run marginal cost when 500 units are produced?

f. If the price of labor increases from $40 per unit to $60 per unit, what happens to the total cost of producing 500 units of output in the long run (up or down, and by how much)? What happens to the long run marginal cost?