Consider a market where the demand curve is P = 1 − Q , and where there are no production costs.
The market consists of n firms.
a. Find the Cournot equilibrium level of output for each firm.
b. How much profit does each firm earn?
c. Find the level of output that maximizes total profit in the market.
d. If the firms split the output in (c) equally, how much profit does each firm earn?
e. How much output should firm 1 produce to maximize its own profit, if every other firm follows the agreement in (d)?
f. How much profit does firm 1 earn with the outcome in (e)?
g. Suppose the firms try to form a cartel using the following strategy: “Let’s start by producing the joint profit-maximizing output, and keep doing it as long as everyone is cooperating. If anyone ever deviates, we’ll play the Cournot equilibrium forever after.” For what values of the interest rate is the cartel sustainable, using this strategy?
h. Is cooperation easier or more difficult as n increases? Use economics to explain why.