Answer to Question #314702 in Microeconomics for Cheu Soeur Lonh

Question

Unique Motor Inc. manufactures motorcycles that are sold in a monopolistically competitive market. The firm’s demand curve is                      

                               P = 5,000 – 2Q

               Where P is price and Q is quantity and the average cost (AC) function is

                               AC = 6,000 – 4Q + 0.001Q²

               All firms in the industry have the same demand and average cost functions. If the entry or exit of firms in the industry results in the demand curve shifting in a parallel manner, what is the long-run equilibrium price and quantity produced for Unique( and, of course, for each of the other firms in the industry)?

Answer 1

In the long run equilibrium the firm still produces where marginal cost and marginal revenue are equal.

Marginal cost is MC=TC'=(AC×Q)'=((6,000-4Q+0.001Q²)×Q)'=6,000-8Q+0.003Q²

Marginal revenue is MR=(P×Q)'=((5,000-2Q)×Q)'=5,000-4Q

So, 6,000-8Q+0.003Q²=5,000-4Q; 0.003Q²-4Q+1,000=0; Q1=333.33; Q2=1000. Respectively, P1=5,000-2×333.33=4333,34

P2=5,000-2×1000=3000

In the long run the demand curve has shifted as other firms entered the market and increased competition. The firm no longer sells its goods at the price above AC. If Q1=333.33, then AC=6,000- 4×333.33+0.001×333.33²=4777.79; => 4333.34<4777.79 (P<AC)

If Q2=1000, then AC=6,000-4×1000+0.001×1000²=3000; P=AC.

So, it is reasonable for the firm to sell at the price of 3000, quantity is 1000.