Question: Suppose a firm manufacturing clock-radios could be represented by the production function:

a. Explain why a production function is considered a flow concept.

b. Assume the firm’s price of labor, w, is $9 per labor hour and its capital cost, r, is $4 per hour. Derive the short run total cost function assuming capital K₀=81.

c. Derive the firm’s short run marginal cost function.

d. Is the firm’s short run marginal cost curve upward sloping? Explain why the short run marginal cost curve must at some point always begin to slope upward. Explain why such a strong statement cannot be made for the long run marginal cost function.