Consider a two-firm industry. Firm 1 (the incumbent) chooses a level of output q1. Firm 2 (the potential entrant) observes q1 and then chooses its level of output q2. The demand for the product is P = 100 - Q, where Q is the total output sold by the two firms which equals q1 +q2. Assume that the marginal cost of each firm is zero.
a) Find the subgame perfect equilibrium levels of q1 and q2 keeping in mind that firm 1 chooses q1 first and firm 2 observes q1 and chooses its q2. Find the profits of the two firms-?1 and ?2- in the subgame perfect equilibrium. How do these numbers differ from the Cournot equilibrium?
b) For what level of q1 would firm 2 be deterred from entering? Would a rational firm 1 have an incentive to choose this level of q1? Which entry condition does this market have: Blockaded, Deterred, or Accommodated?
Now suppose that firm 2 has to incur a fixed cost of entry, F > 0.
c) For what values of F will entry be blockaded?
d) Find out the entry deterring level of q1, denoted by q1b, as a function of F. Next, derive the expression for firm 1's profit, when entry is deterred, as a function of F. For what values of F would firm 1 use an entry deterring strategy?