Question

1. You are the manager of a monopolistically competitive firm and your demand and cost functions are Q = 36 – 4P and C(Q) = 4 + 4Q + 4Q².
   1. Determine the profit maximizing price and level of production
   2. Calculate your firm’s maximum profits
   3. What long-run adjustments should you expect? Explain.

Answer 1

a) Q = 36 - 4P

4P = 36 - Q

P = 9 - 0.25Q

TR = P * Q = 9Q - 0.25Q²

MR = 9 - 0.5Q

TC = 4 + 4Q + 4Q²

MC = 4 + 8Q

The profit maximization condition is

MR = MC

9 - 0.5Q = 4 + 8Q

8.5Q = 5

Q = 5 / 8.5 = 0.59          (profit maximizing quantity)

P = 9 - 0.25(0.59) = $8.85    (profit maximizing price)

b) TR = P * Q = 8.85 * 0.59 = $5.22

TC = 4 + 4Q + 4Q² = 4 + 4(0.59) + 4(0.59)² = 4 + 2.36 + 1.39 = $7.75

Profit = TR - TC = 5.22 - 7.75 = -$2.53   (it is a loss)

c) Since in the short run, firm is making loss, some firms will exit the industry in the long run. This exit will continue until every firm in the industry earns zero economic profit