Consider the Cournot quantity . Suppose two firms compete by choosing quantities. Suppose they both have a marginal cost of 2. The market demand is given by P = 20 Q where Q = q1 + q2 and q1, q2 are the quantities chosen by each player.

(a) Find out the Nash Equilibrium by using best response analysis.

(b) (10 points) Now suppose that Firm 1 can lobby with the government and achieve monopoly rights to the market before any firm can sell to the consumers. If Firm 1 does not lobby, the game is the same as in part (a) of the problem. However, it costs 2 units of currency (the same currency in which profits are calculated) in the lobbying effort. So, the bigger game looks like in the diagram below. Notice that now this is a sequential game. Find out the Subgame Perfect Nash Equilibrium of this game. Write the SPNE strategy profile carefully. Will Firm 1 choose to lobby to become a monopoly in the SPNE? How does this depend on the behavior of Firm 2?

Hint: This is a sequential game with two periods: How do we solve such games?