1) Consider two companies competing in a market by choosing their output level. Assume the inverse demand function is given by p = 58 - q1 - q2. Where q1 and q2 are production levels for firm 1 and 2 respectively and p the market price. Assume that firm 1 has a marginal cost of production of c1 = 8 and that firm 2 has a marginal cost of production of c2 = 0. Further assume that each firmSbaximizes profits given by Π1 = pq1 - c1q1 and Π2 = pq2 - c2q2
a) Find the reaction function for each company and graph.
b) What is the Nash equilibrium (quantities produced by each firm) and profits at this Nash equilibrium?
c) If the companies decided instead to collide and act as single company (Monopoly) what are the profits to each company assuming that they use the efficient cost c2 = 0 to produce?
d) What are the profits for each company if firm 1 chooses to produce the monopoly level and firm 2 the level indicated by its reaction function?
e) What are the profits for each company if firm 2 chooses to produce the monopoly level and firm 1 the level indicated by its reaction function?
f) Use the profits found in b)-e) to construct a payoff matrix where the actions for each firm is to collude or to compete.
g) Would you expect collusion to be stable? Is there a level of "trust" (Probability that the game will be repeated) that guarantees collusion for several periods?
h) Assume now that the game is played sequentially. Firm 1 is considered the leader and moves first and firm 2 is considered the follower and moves second. What is the level of output and profits for this game?