Suppose that two rms compete in quantities (Cournot) in a market in which demand is described by:
P = 130 ???? Q . Each rm incurs no xed cost but has a marginal cost of 10.
(a) What is the one-period Nash equilibrium market price? What is the output and prot of each
rm in this equilibrium?
(b) What is the output of each rm if they collude to produce the monopoly output? What prot
does each rm earn with such collusion?
(c) Suppose that after the cartel is established, one rm decides to cheat on the collusion, assuming
that the other rm will continue to produce its half of the monopoly output. Given the deviating
rm’s assumption, how much will it produce?
(d) If the deviating rm’s assumption is correct, what will be the industry price and the deviating
rm’s prot in this case?
(e) Suppose that the market game is now repeated indenitely. What is the smallest discount factor
that can maintain the collusive agreement under the grim strategy?
(f) Suppose that the market game is now repeated indenitely. What is the smallest discount factor
that can maintain the collusive agreement under the tic for tac strategy?