There are two firms who compete by choosing how much to produce and sell in the market. In this market, firm 1 chooses its output q1 first and then firm 2, after observing q1, chooses its output level q2 The inverse demand is given by P(Q) = 120 0.4Q. Firm 1 has a constant marginal cost c1 = 30 and firm 2 has a constant marginal cost c2 = 20.

a. Find the Nash Equilibrium of this game. How much profit is each firm making in equilibrium? (10 pts)

b. Suppose that firm 2 could invest in a technology that would allow it to produce it's output before firm 1. That is, this technology switches the order of moves such that firm 2 chooses its output q2 first and then firm 1, after observing q2, chooses its output level q1. What are the new Nash Equilibrium prices and quantities in this game? How much profit is each firm making in the new equilibrium? What is the most firm 2 would be willing to pay for this technology?