Question

Consider the infinitely repeated version of the Cournot duopoly model where price in the market is given by

P = 100 – Q for Q= q1 + q2

and marginal cost of production for both firms is given by c= 10.

a) What is the Nash equilibrium of the static game? What is the profit of each firm?
b) If there was only one firm in the market, and P = 100-q1, what is the static monopoly optimum? What is the monopoly profit?
c) Suppose we want the firms to play half the monopoly quantity in each period. Construct a
trigger strategy such that this can be sustained as a subgame perfect equilibrium. What is
required threshold on the discount factor, ??
d) Fix some discount factor ?. Suppose that the firms want to agree to produce a quantity q* every
period: produce q* every period, and if anyone every deviates switch to Nash equilibrium. Show
that the lowest value of q* that can be sustained as a Nash equilibrium is given by
q* = 30 (9-5?)/(9-?)
e) Show that as ? approaches zero, q* becomes equal to your answer in (a). And, when ?
approaches the threshold you calculated in part (c) q* becomes equal to half the monopoly
quantity.

Answer 1