Two identical firms, Firm 1 and Firm 2, compete in quantity in a market where inverse demand is P(Q) = 100 − Q and there exists a constant marginal cost of 20 per unit.
(a) Find the Cournot equilibrium
i. Find the response functions q1(q2) and q2(q1)
ii. Plot the response functions on a single graph with the axes labeled
iii. Find the quantities ˆq1 and ˆq2 corresponding to the intersection of the response functions
(b) Find the Stackelberg equilibrium
i. If Firm 1 moves first, what is the profit maximizing level of production, q ∗ 1?
ii. Find Firm 2’s level of production, q ∗ 2 , given what you found in part i.