Question

Imagine that you work for the U.S. Department of Justice as an economic analyst. Your boss emails you and asks you to analyze the following scenarios for a market made up of two firms that compete by simultaneously setting quantities. Firm 1’s quantity is denoted by q1 and the cost of production in its factory is summarized by a cost function C(q1) = 20q1. Firm 2’s quantity is denoted by q2 and the cost of production in its factory is given by C(q2) = 80q2. The market price is given by the inverse demand equation: P = 2000 - 2Q, where Q denotes the market quantity the output from the two firm, i.e., Q = q1 + q2.

d) What would be the impact on the market if firm 1 was forced to exit the market leaving firm 2 as a monopolist. Using the firm 2’s best response function, find the quantity it would produce. Given the firm’s output choice, find the market price that would result. How much less output is firm 2 producing than it would produce if it was producing the total surplus maximizing (efficient) amount?

e) Now assume that, rather than one firm exiting, the firms have successfully lobbied for an antitrust law exemption and are free to act as a cartel. Assuming the firms have agreed to split the total profits evenly, how should they distribute their production of output across their factories? What level of output would maximize their joint profits, at what price would their output sell, and what profits would each earn?

Answer 1

D).

So, if “firm1” was forced to exit the market, => there will be only one firms, => “q1=0”. Now, the best response function of “firm2” is given by.

=> q2 = 480 - q1/2, => q2 = 480 for “q1=0”. So the output supplied by “firm2” is given by “q2=480”, => the market price is given by “P=2000-2*Q=2000-2*480=1040”. Now, the total surplus will be maximum where “p=MC”, => 2000-2*Q=80, => Q=960. So, the “firm2” is producing “960-480=480” units less from the efficient level of output.

E).

Now, let’s assume that both the firms will act as cartel and will evenly split the profit evenly. So, here the MR is given by.

=> P=2000-2*Q, => MR = 2000 - 4*Q. Now, here “MC1=20” and “MC2=80”, => “firm1” having lower marginal cost compare to “firm2”, => here only “firm1” produce, => at the optimum.

=> MR=MC1, => 2000-4*Q=20, Q=1980/4 = 495, => Q=495, => P=2000-2*Q=1,010. So, here “q1=495” and “q2=0”.

Now, here the total profit is given by, “(P-MC)*Q = (1,010 - 20)*495 = 490,050. So, there they will split the profit evenly, => each will get “490,050/2=245,025” as a profit.