Suppose that the market for auto detailing in a city is perfectly competitive. The auto detailing firms are identical and have long-run cost functions given by TC(Q) = 10Q3 - 100Q2 + 300Q. Market demand is QD = 5,000 - 90P.
a. Derive the marginal and average cost curves for a firm in this industry.
b. Find the quantity at which average total cost is minimized for each firm.
c. Find the long-run equilibrium price in this industry.
d. Use market demand to find the equilibrium total industry output.
e. Find the equilibrium number of firms.