Firms are engaged in Cournot competition (i.e., simultaneously determining their quantity). Market-level inverse demand is given by: P = 400-10Q. Firms have the same cost functions: C = 40q. (30 points)

(a)Let's begin by assuming there are two firms in the market. Solve for equilibrium production levels of each firm, total market quantity, the market price, the profits of each firm, and consumer surplus. [Hint: In this case, each firm simultaneously chooses a quantity and then both firms sell all of their quantity at the pricesuch that aggregate demand equals aggregate supply. Start by solving for Firm 1's choice of q₁ as a function of Firm 2's quantity q₂, then solve for Firm 2's choice of q₂ as a function of Firm 1's quantity q₁. Then solve the two equations simultaneously for the two variables q₁ and q₂.] (20 points)

(b)As a brief aside, which will be useful soon, solve for the market quantity, price, and consumer surplus under perfect competition (when each firm in the market takes prices as given). (10 points)

(c)(Bonus) Now assume there are N firms engaged in Cournot competition (as before, in part a and b). As a function of N, solve for equilibrium production levels of each firm, total market quantity, the market price, the profits of each firm, and consumer surplus. What happens as N rises? [Hint: 1. think about that one firm is competing against other firms, so the firm chooses q based on (N-1) other firms' quantity. 2. compare to your response in part b]. (20 points)

Part 2:

Stackelberg Competition

Firms are engaged in Stackelberg Competition. Market-level inverse demand is given by: P = 400-10Q. Firms have the same cost functions: C = 40q.

Now assume there are two firms in the market, but Firm 1 has an opportunity to publicly commit first to a chosen quantity level (as in the case of Stackelberg Competition). Then Firm 2 observes Firm 1's choice, and responds to this. (30 points)

(a)Solve for the equilibrium production levels of each firm,total market quantity,the market price, the profits of each firm, and consumer surplus. Which firm (or firms) are better off or worse off than before? Are consumers better off or worse off? (15 point)

(b)Given Firm 2's production level, would Firm 1 want to change its production and, if so, what production level would it choose? What would be the market price? If that was the production level of Firm 1, what production level would Firm 2 choose? And what would be the market price? If they keep adjusting to each other, what would be the market price and production level of each firm? (15 points)