Question

A competitive industry consists of n firms that have different production costs but are
producing an identical product. Individual firms in this industry are numbered i from 1, 2, 3,
… n. Each firm i can produce up to two units of output qi at a constant marginal cost of 2i
but cannot produce more than that (i.e. each firm has a capacity constraint of 2 units of
output). Accordingly, firm #1 can produce up to 2 units of output at a constant marginal
cost of 2, firm #2 can produce up to 2 units of output at a constant marginal of 4, and so
forth. Assume there are no fixed costs.
a. Graph the industry supply function for this product.
b. Suppose the inverse industry demand function is P = 20 – Q where Q = q1 + q2 +… + qn.
Solve for the long run competitive equilibrium in this industry. At what price will this
product be sold, how much will be sold in total, and how many firms will be in the industry
in the long run equilibrium.
c. Compute each firm’s long-run equilibrium profits.

Answer 1