Two firms produce differentiated products and set prices to maximize their individual profits. Demand functions for the firms are given by
Q1 =64 -4P1 +2P2
Q2 =50 -5P2+ P1
where P1, P2, Q1, Q2, refer to prices and outputs of firms 1 and 2 respectively. Firm 1â??s marginal cost is $5 while firm 2â??s marginal cost is $4. Each firm has a fixed cost of $50.
Supposing that the two firms decide on prices independently and simultaneously, find out the best response function of each firm in terms of prices. find out the resulting equilibrium price quantity combination for each firm. Illustrate your answer with a suitable graph. Also find out optimal profits of each firm.