Question

Suppose there are two firms in the market. Let Q1 be the output of the first firm and Q2 be the output of the second. Both firms have the same marginal costs: MC1 = MC2 = $5 and zero fixed costs. The market demand curve is P = 53 − Q.

(a) (6 points) Suppose (as in the Cournot model) that each firm chooses its profit-maximizing level of output assuming that its competitor’s output is fixed. Find each firm’s reaction curve.

(b) (2 points) Find the equilibrium values of Q1 and Q2 for which each firm is doing as well as it can given its competitor’s output.

(c) (2 points) What are the resulting market price and profits of each firm?

(d) (4 points) Draw the firms’ reaction curves and show the Cournot equilibrium.

(e) (5 points) How will the Cournot equilibrium change if more firms enter the oligopoly? Why does the size of oligopoly matter? Explain.

(f) (4 points) Suppose Firm 1 is the Stackelberg leader (i.e., makes its output decisions before Firm 2). Find the reaction curve of each firm.

(g) (6 points) How much will each firm produce, and what will its profit be?

(h) (2 points) Compare the Stackelberg equilibrium to the Cournot equilibrium. How do the profits of each firm differ? How do the price and total output differ?

Answer 1