12.8 An enterprising entrepreneur purchases two firms to produce widgets. Each firm produces identical products, and each has a production function given by The firms differ, however, in the amount of capital equipment each has. In particular, firm 1 has Kx = 25, whereas firm 2 has K> = 100. Rental rates for Kand L are given by w = v = $1.

a. If the entrepreneur wishes to minimize short-run total costs of widget production, how should output be allocated between the two firms?

b. Given that output is optimally allocated between the two firms, calculate the short-run total, average, and marginal cost curves. What is the marginal cost of the 100th widget?

The 125th widget? The 200th widget?

c. How should the entrepreneur allocate widget production between the two firms in the long run? Calculate the long-run total, average, and marginal cost curves for widget pro duction.

d. How would your answer to part

(c) change if both firms exhibited diminishing returns to scale?