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Consider a competitive firm, which takes prices as given. There are two factors used to produce a product. The amount of capital is fixed at 10 units. Suppose that the marginal product of labor (while capital is held fixed) is given by MPL = 50 - L, where L is the labor input. Suppose that the wage rate is equal to 40 while the rental rate is 50. The output price is equal to 1.
(a) What is the fixed cost?
(b) What is the relationship between marginal cost and marginal product of labor when labor is the only variable input? Determine the marginal cost in terms of the labor input.
(c) What is the amount of labor the firm wants to hire?
(d) What is the resulting total cost? (e) What is the total revenue? What is the short-term profit?
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