2. Two firms i = 1, 2, are in a Cournot competition, producing a homogenous product qi. Their total cost function is given by TC (q;) = ciqui = 1,2. The inverse demand function is P(Q) = a - bQ, a,b > 0, a > max; c;, with Q = q1 + 92. (a) State the first-order conditions characterizing the Cournot-Nash solution of this game. [10 marks] (b) Rewrite the conditions of question (a) in matrix form and find the Cournot-Nash solution using the Cramer's rule. [20 marks] (c) Compute the total quantity, Q", set on the market by the firms and the induced price, P*, and the firms' profits at the Cournot-Nash solution. [20 marks]