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 1's marginal cost is $5 while firm 2's marginal cost is $4. Each firm has a fixed cost of $50.
Assuming that the two firms decide on prices independently and simultaneously, calculate the best response function of each firm in terms of prices. Calculate the resulting equilibrium price quantity combination for each firm. Illustrate your answer with a suitable graph. Also calculate optimal profits of each firm.