Consider a market with aggregate demand 100439 if pg25 9(1)): 1 0 if p>25 There are two rms. Each rm 1's cost function is c1(q1) = %q1 and rm 2's cost function is 020112) = %q2. 2. Suppose the firms act as " Cournot-Nash Duopolists", simultaneously and independently choosing their output quantities. If firms 1 and 2 choose output quantities q1 2 0 and q2 2 0 respectively, then the market clearing price would be given by the inverse demand function evaluated at the total quantity, P(q1 + 92). (a) Find the payoff functions for both firms, that is compute 71(91, 92) and 72(91, 92). (b) Find the best responses for the first firm, B1(q2), and the best response for the second firm, B2(q1)