(1) Consider a product differentiated duopoly market. There are two firms labeled firm A and B. Since the products are imperfect substitutes in the market, the number of units sold depends on the price the firm charges, but also on the price charged by the competitor. Let qa = a - Pa - Bp denote the demand curve for firm A and qb = a - Pb - BPa be the demand curve for firm B. Assume a > 0 and B E (0, 1). Further, let the cost function be C(qi) = kq; with k > 0. (a) Given this description, formally define the game. (b) Solve for the Nash Equilibrium