Firm 1 must decide whether to enter an industry in which firm 2 is an incumbent. To enter this industry, firm 1 must choose to build either a plant with a small output capacity (S), or large output capacity (L). A plant with small capacity costs $50 to set up; one with large capacity cost $175. In either case, the marginal cost of production is zero. But firm 1 can also opt to stay out (O), in which case it does not incur any type of cost. Firm 2 is able to observe firm 1's decision before deciding whether to expand or not its initial small output capacity operation. Expanding (E) costs firm 2 $86, whereas not expanding (N) incurs no cost for the firm. In either case, the marginal cost of production is also zero.

The revenues under the different scenarios are given below.

- If only one small firm exists, its revenue is $80, the other earns zero.

- If two small firms exist, each earns revenue of $70.

- If only one large firm exists, its revenue is $200, the other earns zero.

- If two large firms exist, each earns revenue of $90.

- If one small and one large firm exist, the small firm earns $40, while the large one earns $160.

Answer the following:

a) (0.5 marks) How many pure strategies are available for firm 1?

Answer for part 1

b) (0.5 marks) How many pure strategies are available for firm 2?

Answer for part 2

c) (1 mark) What is the sum of the firms' profits in the subgame perfect equilibrium?