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Economics 201 Microeconomics

Tutorial 10

Question 1:

In a homogeneous product duopoly, the market demand curve is given by P = 120 – Q where Q is the sum of the outputs produced by each of the two firms, i.e., Q = Q1 + Q2. For the sake of simplicity assume MC = 0 (or that the only costs for these firms are fixed costs so that maximizing profit is the same as maximizing revenue).

(a) What are the Cournot equilibrium quantities and price in this market?

(b) What would be the equilibrium price in this market if the two firms acted as a profit-maximizing cartel?

(c) Why is it difficult for the two firms to act in collusion and sustain the monopoly outcome?

Question 2:

There are only two firms in an industry each with the same cost function TC1 = 30Q1 and TC2 = 30Q2 implying AC = MC = $30 for each firm. The market inverse demand function is P(Q) = 150 − Q,  where Q = Q1 + Q2 the output of firm 1 and firm 2 respectively.

(a) Find the Nash equilibrium when the firms simultaneously choose their output levels, and calculate the equilibrium levels of profit.

(b) Now, suppose that firm 2 behaves as a follower and firm 1 as a leader. Calculate the Stackelberg equilibrium output and profit for each firm.

(c) Reconsider part (b). Suppose firm 2 has fixed costs of $300. What level of output would firm 1 have to produce to deter firm 2 from participating in this market? Is it optimal for firm 1 to do so?

Question 3:

Consider a market served by three firms. The market demand is given by P = 120 - Q where Q is the aggregate demand produced by the three firms i.e. Q = q1 + q2 + q3. Assume, without loss of generality, only fixed costs and therefore MC = 0. This means that we can solve profit and revenue as being interchangeable. Suppose Firm 1 moves first and the other two firms follow with Firms 2 and 3 entering simultaneously. What output does each firm produce and what is the market price?