A manufacturing firm produces output using a single plant. The relevant cost function is C = 500 + 5Q2. The firm’s demand curve is P = 600 - 5Q.
a. Find the level of output at which average cost is minimized. Set AC equal to MC. What is the minimum level of average cost?
b. Find the firm’s profit-maximizing output and price. Find its profit.
c. Suppose the firm has in place a second plant identical to the first. Argue that the firm should divide production equally between the plants.
Check that the firm maximizes profit at total output Q* such that
MR(Q*) = MC1(Q*/2) = MC2(Q*/2).
Find Q*. Explain why total output is greater than in part (b).
d. In the long run, the firm can produce using as many or as few plants as it wishes (each with the preceding cost function). In this case, what kind of returns to scale hold? What are the firm’s optimal output and price in the long run? How many plants will the firm use to produce the good? Refer to the value of minimum AC you found in part (a).