Suppose two firms compete by selecting quantities q1 and q2, respectively, with the market price given by p = 1000 – 3q1 -3q2. Firm 1 (the incumbent) is already in the market. Firm 2 (the potential entrant) must decide whether or not to enter, and if she enters, how much to produce. First the incumbent commits to its production level q1. Then the potential entrant having seen q1, decides whether or not to enter the industry. If firm 2 chooses to enter, then it selects its production level q2. Both firms have the cost function c(qi) = 100qi + F, where F is a constant fixed cost. If firm 2 decides not to enter, then it obtains a payoff of zero. Otherwise it pays the cost of production, including the fixed cost. Note that firm i in the market earns a profit of pqi-c(qi).
A) Find incumbent’s optimal choice of output and the outcome of the game in the following cases: (i) F = 18,723, (ii) F = 8,112 (iii) F=1,728 and (iv) F=108