There are two firms competing in the market for the same good by simultaneously and inde- pendently selecting their supply quantities q1 ≥ 0 and q2 ≥ 0. The market price is given by P(Q) = 1−Q where Q = q1 +q2. Both firms have the same constant marginal cost c > 0 for producing the good (0 < c < 1). Firms are maximizing their profits. To sum up, the payoffs are given by:
π1(q1,q2) =P(Q)q1 −cq1 =[1−(q1 +q2)]q1 −cq1
π2(q1,q2) =P(Q)q2 −cq2 =[1−(q1 +q2)]q2 −cq2
(a) Find best response functions for both firms and plot them on the same graph.
(b) Find the Nash equilibrium.
(c) Find market price, firms’ margins and firms’ profits at equilibrium.
Hint: Follow the same steps we took in class to solve the “Partnership Game”.