Consider a market with two firms and each firm produces the same product. The price of the product is determined by P = 60 Q, where Q = Q1 + Q2 is the total output of both firms. Both firms have zero marginal cost and zero fixed cost.

1. (a)(3pts) First, find Firm 1's best response function, namely optimal output Q1 as a function of Firm 2's output Q2.
2. (b)(1pts) Next, use symmetry to get Firm 2's best response function.
3. (c)(4pts) Now, find the Cournot-Nash equilibrium for these two firms. How much profit does each firm earn in the equilibrium?
4. (d)(4pts) If the two firms could collude how much would the total output be? How much is the total profit in collusion?