Problem 1
The typical firm in a perfectly competitive market has a cost structure described by the equation C=25+q2. The market's demand curve is estimated by the equation QD=400-20P
a. Calculate the typical firm's output decision given that the market is perfectly competitive (Hint: firms will have to produce at their minimum average cost). What will the market price be? How much will consumer demand at that price level be? How many firms will the market be able to support?
b. Calculate the typical firm's profit. Next, derive the market supply curve and calculate producer surplus at the market equilibrium. Is this the same as (economic) profit? Why or why not?
c. The economic recession hit the market very hard, making consumers less able to afford Q at any given price. Their demand function shifts to QD=320-20P.
Derive the new short-run equilibrium, producer surplus, and economic profits when there continue to be 40 firms active in the market. What will happen in the long run, given there are no market entry/exit barriers?
Problem 2
Firm Z, operating in a perfectly competitive market, can sell as much or as little as it wants of a good at a price of $16 per unit. Its cost function is C = 50 + 4Q + 2Q2. The point of minimum average cost is Qmin = 5 (verify this).
a) Determine the firm's profit-maximizing level of output. Compute its profit.
b) The industry demand curve is Q = 200 - 5P. What is the total market demand at the current $16 price? If all firms in the industry have cost structures identical to that of firm Z, how many firms will supply the market?
c) The outcomes in part (a) and (b) cannot persist in the long run. Explain why.
Find the market's price, total output, number of firms, and output per firm in the long run.
d) Comparing the short-run and long-run results, explain the changes in the price and in the number of firms