Consider an industry with an incumbent monopolist, who is currently producing, and a potential entrant, who might or might not choose to enter.
There is a range of possible production technologies for producing this good, which differ in the level of marginal and fixed costs. Each technology is a constant marginal cost technology with marginal cost somewhere between 1 and 3 per unit. In the technology with marginal cost c (from the range from 1 to 3), fixed costs are 15-4c. That is, lower marginal costs bring with them higher fixed costs. Any firm in this industry may choose whatever technology it wishes to employ, but it can make this choice once only. The choice of technology of any firm is known to all potential and actual competitors.
We imagine that there are two periods of production. In each, demand is given by D(P) = 9 - P. In the first period, the incumbent monopolist is definitely a monopolist. The monopolist begins this period by selecting her production technology and then producing. In the second period, the entrant decides whether to enter at all. If he does enter, he picks his production technology. And then the two compete Cournot-style, simultaneously picking quantities. If he does not enter, then the monopolist retains her monopoly and picks the quantity she wishes to sell. We assume that the entrant will enter only if he believes he will make positive profits, and the incumbent monopolist acts in a way that maximizes her sum of profits in the two periods. (Adding a discount factor only complicates the arithmetic.)
(a) Suppose there was no threat of entry. What technology would the monopolist select?
(b) Suppose· the monopolist selects the technology you got as the answer to part (a). will the entrant enter? If so, with which technology?
(c) If the monopolist, in the first period, picks a technology that discourages the entrant from entering in the second period, we say that the monopolist has blockaded entry. Is there a technology the monopolist could pick in the first period that would blockade entry? If so, what range of technologies accomplishes this?
(d) Given the threat of entry, what is the optimal course of action for the monopolist? How does the entrant respond to this? (What solution concept are you using?)