Assume Cournot competition in an industry in which demand curve is described by P = 260 - 2Q and in which each firm has a marginal cost of 20. However, instead of 2 firms, let there be 4.

a) What is the one-period Nash equilibrium market price? What are the outputs and profits of each firm in this equilibrium?

b) What is the output of each firm if they decide to collude to produce the monopoly output? What profits does each firm earn with this collusion?

Now, suppose that one firm decides to deviate and cheat on the collusion, assuming that each of the three other firms continue to produce one-fourth of the monopoly output.

c) Given this assumption, how much will the deviating firm produce?

d) Assuming that its assumption is correct, what will be the industry price and the deviating firms profit?

Now, suppose the game in the problemis repeated indefinitely, and the probability-adjusted discount factor is Consider the following strategy for a firm:

In Period : produce the cartel level of output

In Period : produce the cartel level of output if all firms produced the cartel level of output in every previous period. Otherwise, produce the one-period Cournot Nash level of output.

Consider a period such that all firms chose the cartel level of output in all previous periods:

a.Assuming the other three firms are behaving according to the strategy above, compute the discounted sum of a firm's profit stream, starting from period t, if it also uses this strategy.

b.Assuming the other three firms are behaving according to the strategy above, compute the discounted sum of a firm's profit stream, starting from period tif it deviates once from this strategy by producing the output from (c) in period , but then behaves according to this strategy from period t+1onwards.

c.Derive the lowest value of p (rho)for which this firm would prefer to stick to this strategy and not deviate from it.