Question

1. Consider two firms facing the demand curve P = 50 ? 5Q, where Q = Q1 + Q2. The
firms cost functions are C1(Q1) = 20 + 10Q1 and C2(Q2) = 20 + 10Q2.
a. Suppose both firms have entered the industry. What is the joint profit-maximizing level
of output? How much will each firm produce? How would your answer change if the firms
have not yet entered the industry?
b. How much should Firm 1 be willing to pay to purchase Firm 2 if collusion is illegal but
a takeover is not?
c. Calculate the price, profit and quantity if the market is under Bertrand competition.
2. We have two firms with the same constant average and marginal cost, AC = MC = 5,
facing the market demand curve Q1 + Q2 = 53 ? P. Now we will use the Stackelberg model
to analyze what will happen if one of the firms makes its output decision before the other.
a. Suppose Firm 1 is the Stackelberg leader (i.e., makes its output decisions before Firm 2).
Find the reaction curves that tell each firm how much to produce in terms of the output of
its competitor.
b. How much will each firm produce, and what will its profit be?

Answer 1