A perfectly competitive industry has a large number of potential entrants. Each ?rm has an identical cost
structure such that long-run average cost is minimized at an output of 20 units (qi (qi) = 20). The minimum average cost is $10 per unit. Total market demand is given by
Q = 1,500 - 50P.
a. What is the industry's long-run supply schedule?
b. What is the long-run equilibrium price (P*)? The total industry output (Q*)? The output of each ?rm (q*)? The number of ?rms? The pro?ts of each ?rm?
c. The short-run total cost function associated with each ?rm's long-run equilibrium output is given by
C(q) = 0.5q2 - 10q + 200.
Calculate the short-run average and marginal cost function. At what output level does short-run average cost reach a minimum?
d. Calculate the short-run supply function for each ?rm and the industry short-run supply function.
e. Suppose now that the market demand function shifts upward to Q = 2,000 - 50P. Using this new demand curve, calculate equilibrium price and quantity (for the firm as well as the industry) for the very short run when ?rms cannot change their outputs.
f. In the short run, use the industry short-run supply function (from part (d)) and the new market demand function to recalculate equilibrium price, total industry output, firm output, firm profit.
g. What is the new long-run equilibrium for the industry with the new market demand curve?