Consider a duopoly market, where two firms sell differentiated products, which are imperfect substitutes. The market can be modelled as a static price competition game. The two firms choose prices p1 and p2 simultaneously. The demand functions for the two firms are: D1 (p1,p2) = S/ 2 +p2,p1 /2t and D2 (p1,p2) = S /2 + p1,p2 /2t , where S > 0, and the parameter t > 0 measures the degree of product differentiation. Both firms have constant marginal cost c > 0 of production.

(a)Derive the Nash equilibrium of this game, including the prices, outputs and prots of the two firms.