15.6 Recall Example 15.6, which covers tacit collusion. Suppose (as in the example) that a medical device is produced at constant average and marginal cost of $10 and that the demand for the device is given by Q ¼ 5,000 $ 100P:

The market meets each period for an infinite number of periods. The discount factor is d.

a. Suppose that n firms engage in Bertrand competition each period. Suppose it takes two periods to discover a deviation because it takes two periods to observe rivals’ prices. Compute the discount factor needed to sustain collusion in a subgame-perfect equilibrium using grim strategies.

b. Now restore the assumption that, as in Example 15.7, deviations are detected after just one period. Next, assume that n is not given but rather is determined by the number of firms that choose to enter the market in an initial stage in which entrants must sink a one-time cost K to participate in the market. Find an upper bound on n. Hint: Two conditions are involved.