Question

Question 4 Consider the following game. Firm 1, the leader, selects an output, q1, after which firm 2, the follower, observes the choice of q1 and then selects its own output, q2. The resulting price is one satisfying the industry demand curve P = 200 - q1 - q2. Both firms have zero fixed costs and a constant marginal cost of $60. a. Derive the equation for the follower firm’s best response function. Draw this equation on a diagram with q2 on the vertical axis and q1 on the horizontal axis. Indicate the vertical intercept, horizontal intercept, and slope of the best response function. b. Determine the equilibrium output of each firm in the leader–follower game. Show that this equilibrium lies on firm 2's best response function. Compute profits in the equilibrium for firm 1 and 2. If the leader firm were a monopoly what would the equilibrium and output and price be? Would the monopoly price be higher or lower than in the Stackelberg case. c. Now let the two firms choose their outputs simultaneously. Compute the Cournot equilibrium outputs and industry price. Draw a graph with the Cournot best response functions. Label the intercepts. Also using your computations in part (a) and (b) label the Stackelberg and Cournot output levels. Who loses and who gains when the firms play a Cournot game instead of the Stackelberg one?

Answer 1