Assume market demand is given by P=a-Q. Suppose there are two firms (1 and 2) that engage in Cournot competition. Firm 1's marginal cost of production is 1 while firm 2's marginal cost of production is c.
a. Calculate firms' production levels and profits.
b. Calculate the Herfindahl index of market concentration when market shares are measured as production shares. The Herfindahl index is a function of c. When is the Herfindahl index increasing in c? Decreasing in c?
c. Suppose a=14 and c=3. For what discount factors can collusion be sustained in which q1 = 4 and q2 =2?