Q. Consider a market for an electronic component used in airport radar systems. Two firms hold a patent on the component and only they can sell the product. The market demand function is given by:
P = 100 - 1/2Q
Where Q = Q1 + Q2, is the industry output and P the price. Q1 and Q2 are the outputs of the two firms respectively.
The total cost functions for the two firms are given by:
TC1=5Q1+300
TC2=1/2Q2^2+100
(a) Assume that the two firms behave as Cournot Duopolists. Explaining the concept of "best response" or "reaction function", conclude best answer about function for each firm. Calculate the profit maximizing output of each firm and the market price. Compute optimal profit of each firm.
(b) Assume that the two firms collude and form a cartel to maximize their joint profit. Compute most favorable output also profit for each firm and the market price. Also, compute the resulting profit of cartel. Verify whether firm 1 has any incentive to "cheat" the cartel by overproducing.
(c) Suppose that firm 1 acts as a "Stackelberg" leader and sets its quantity first to maximize its personal profit. Firm 2 operates as a follower and sets its own quantity in response to the output set by firm 1. Compute optimal outputs price and profits.