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 subgame perfect equilibrium.What is required threshold on the discount factor, δ?
d)Fix some discount factor δ. 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 (9-5δ)/(9-δ)
e)Show that as δapproaches zero, q*becomes equal to your answer in (a). And, when δapproaches the threshold you calculated in part (c) q* becomes equal to half the monopoly quantity.