There is a market with inverse demand given by p(Q) = 240Q. Firm A (the incumbent) has to make an irreversible decision on how much capacity to build. After A decided on its capacity, Firm B (the entrant) will decide whether or not to enter this market. If B enters, it has to pay a sunk cost of entry of F = 100. (Firm A has already paid the entry cost, so we do not need to consider it here.) After paying the entry cost, B has to decide on its own capacity. Both firms can produce the good at zero marginal cost.
a. If B enters, what is Bs optimal capacity for any given capacity of rm A?
b. If A accommodates B, how much capacity should A build? What are As and Bs profits if A accommodates?
c. How much capacity would A have to build in order to deter Bs entry? Is entry deterrence profitable for A?
d. Suppose the entry cost is F = 2500 (instead of F = 100). Would entry deterrence now be profitable for A?