Question

1) Suppose that the demand function of an industry can be described by Q(P) = 1500-

3P. Assume there are two firms with cost function C(g) = 20g.

(a) Determine the equilibrium outcome and profits when firms set quantities sequentially

as in the Stackelberg model. Assume that firm 1 is the leader.

(b) Assume firm 1 is the incumbent in a monopoly market and firm 2 a potential entrant.

Entry implies a fixed cost of F = 300. Can entry be deterred? Will the incumbent firm deter

entry?

(c) Suppose entry implies a fixed cost of F = 30000. Will the incumbent firm deter

entry?

(d) What would firm 1 do if there were no threat of entry? What does this mean for the

incumbent's strategy in part (C)?

Answer 1

$$TR=pQ$$

$$p=500-\frac{1}{3}Q$$

$$TR=500Q-\frac{1}{3}Q^2$$

$$MR=500-\frac{2}{3}Q$$

$$MC=20$$

$$500-\frac{2}{3}Q=20$$

$$Q=720$$

$$p=260$$

$$Profit=182,000$$

If F=300

$$Profit=181,700$$

if F-30000

$$Profit=152,000$$