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", determine the best response function for each firm. Calculate the profit maximizing output of each firm and the market price. Calculate optimal profit of each firm.
(b) Assume that the two firms collude and form a cartel to maximize their joint profit. Calculate the optimal output and profit for each firm and the market price. Also, calculate the resulting profit of cartel. Determine 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 own profit. Firm 2 acts as a follower and sets its own quantity in response to the output set by firm 1. Calculate optimal outputs price and profits.