## Solve for the Cournot Nash Equilibrium

3. Suppose two firms compete in an industry with an inverse demand function given by P = 200 − 2Q . Each firm has a marginal cost of $40. a. Solve for the monopoly profits, quantity, and price. b. Solve for the Cournot Nash Equilibrium. State the quantities and profits for each firm and the market price.c. Suppose firm 2 produced ½ of the joint profit maximizing output (i.e., colluded) and firm 1 cheated. What would be firm 1’s one-period profit maximizing output be? What is the resulting market price? d. What would firm 1’s profits be under this scenario (in part c)? e. Suppose these firms compete repeatedly, such that the end of the game is unknown. At the end of each year, the probability the firms will compete against each other again is given as .6 and they discount future profits at a rate of .8. What is the present discounted value of expected profits if both firms collude in each period? f. Suppose firm 1 believes that firm 2 has adopted a “grim trigger strategy” in which they will produce half the joint profit maximizing output if firm 1 always does the same, but if firm 1 ever produces more then firm 2 will punish by producing the Cournot equilibrium output level forever after. What is the present discounted value of profits for firm 1 if they decide to cheat in the first period. g. Can the firms sustain collusion in equilibrium?