Showing work for all parts please. 1. A perfectly competitive, constant cost ind

Question

Showing work for all parts please. 1. A perfectly competitive, constant cost industry faces a demand curve given by Q-800-8P Each firm has identical long-run total costs given by: TC-200- 10q+247, where q is firm output a. What is the long-run equilibrium output, price and number of firms? b. Now suppose that product q has been identified by the Food and Drug Administration as a potential cancer causing agent, resulting in a shift in demand to Q = 600-8. What is the resulting equilibrium output, price and number of firms?

Explanation / Answer

A) Long run price level is the price that is equal to LMC = LAC

LAC = 200/q - 10 + 2q and LMC = 4q - 10

Find the long run price

200/q - 10 + 2q = 4q - 10

200/q = 2q

q* =10 units and so each firm produces 10 units. Price = 4*10 - 10 = $30. Demand = 800 - 8*30 = $560. There are 560/10 = 56 firms in the long run

b) See that AVC = 2q - 10. Minimum quantity that makes AVC minimum is q = 5. Hence supply curve of firm is P = 4q - 10, q > 5

Or

4q = P + 10.

q = P/4 + 10/4

Market supply is Q = 56q = 56(P/4 + 10/4) = 14P + 140

Hence supply curve is Q = 14P + 140

New quantity and price are

600 - 8P = 14P + 140

460 = 22P

Short run price is 460/22 = $20.9 and so each firm produces MC = P

20.9 = 4q - 10

q* = 7.73. Number of firms will not change in the short run.

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