Suppose that any firm intending to produce SOMA must build an integer

number of plants: 0, 1, 2, etc. Building Q plants costs a firm 3.5 ~ Q dollars. Each plant

produces one unit of SOMA. If Firm 1 builds Q1 plants and Firm 2 builds Q2 plants, then

the market price p for one unit of SOMA will turn out to be 9(Q1 +Q2). For example, if

Firm 1 builds 2 plants and Firm 2 builds 4 plants, the market price will be 9 (2 + 4) = 3

per unit. At this price Firm 1 will make a profit of 2 ~ 3 2 ~ 3.5 = 1 while Firm 2 will

make a profit of 4 ~ 3 4 ~ 3.5 = 2.

1. If there was a single firm capable of producing SOMA, how many plants would it install

to maximize profit?

2. Suppose now there are two firms (aware of each other) capable of producing SOMA

with the technology described above. Each chooses the number of plants its must build

independently of the other and at the same time. What is the equilibrium number of

plants that will be built by each?

3. Suppose that Firm 1 builds before Firm 2 (Firm 1 is aware that Firm 2 will decide

after Firm 1 decides). How many plants should Firm 1 build and what will Firm 2's

reaction be?

In answering this question it will be useful to construct a payoff table.