Consider the following variant of the Cournot Model: Two firms simultaneously choose how much to produce and sell on the market. The inverse demand is given by P(Q) = 500 5Q. Firm 1 has a marginal cost c1 = 10 and firm 2 has a marginal cost c2 = 15.

a. Find the Cournot-Nash Equilibrium quantities of this game. How much profit is each firm making in equilibrium? (5 pts)

b. Suppose that firm 2 could invest in a new technology that reduced its unit cost to c2 = 5 (firm 1's costs are the same). Find the new Cournot-Nash Equilibrium quantities of this game. How much would firm 2 be willing to pay for this technology? (10 pts)