Recall example 15.6, which covers tacit collusion. Suppose (as in 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 = 5,000 - 100P

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

is .

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 in n. Hint: two conditions are involved.