Two non-identical firms A, B produce identical products for sale in a market. Market inverse demand is P = 12 - 2Q. The firms' cost functions are: C_A(Q) = Q / 4; C_B(Q) = Q / 2 .
(a) Consider a Bertrand model in which the above firms choose prices to post P_A and P_B simultaneously. Since the goods are identical, consumers will go to the firm with the cheaper price. To avoid complications, assume that if the prices are the same, consumers go to the firm with the lowest marginal cost (i.e. Firm A gets all the consumers). Find the unique nash equilibrium in pure strategies of the game.
(b) Consider a Cournot model in which the above firms choose quantities Q_A and Q_B simultaneously. Find the unique Nash equilibrium.
Note: the Nash equilibrium is expressed in terms of the actions of the players.