Suppose the demand and inverse demand for nail guns is Q = 100P and P = 100 Q. Suppose it is a competitive market. Each nail gun maker has one plant (all the same size) and can make 5 nail guns at an average cost of 40, regardless of how many firms are producing. 40 is the minimum average cost. The cost function is C(q) = 50 + 20q + 2q ² . This implies the average total cost is u-shaped. The marginal cost function of each firm is mc(q) = 20 + 4q. There are currently 12 firms and each firm has one plant. (Note that 12 firms may not be enough for the perfect competition assumption to be reasonable, but small numbers are easier to work with.)

(a) What is the rule that determines the output decision of a profit maximizing firm that takes price as given.

(b) Using that rule, find the output of each firm as a function of price (this is just solving an equation for q.

(c) Suppose that demand unexpectedly increases to Q = 132 P and P = 132 Q. In the short run, firms must meet demand with their existing plants and existing marginal cost functions. Remember there are 12 firms each with marginal cost 20 + 4q. If price rises to p = 44 will supply be sufficient to meet demand? What about p = 48? What about p = 52?

(d) In the long run, new firms can enter the market (and existing firms can build new plants). What do you expect to be the price in the long run after firms have had a chance to adjust to the unexpected demand increase?