Question

1. 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 c=60.

1. Derive the equation for the follower firm’s best response function. Draw this equation on a graph 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.

2. Determine the equilibrium output of each firm in the leader-follower game. Show that this equilibrium lies on firm 2’s best response function, and label this on your graph (with firm 1’s best response function) in part a. What are firm 1’s profits in equilibrium?

3. Now let the two firms choose their outputs simultaneously. Compute the Cournot equilibrium outputs and industry price. Who loses and who gains when the firms play a Cournot game instead of the Stackelberg one? Explain why. Show on your graph in part a the Cournot equilibrium

Answer 1