Suppose that two identical firms produce widgets and that they are the only firms in the market. Their costs are given by C1  60Q1 and C2  60Q2, where Q1 is the output of Firm 1 and Q2 the output of Firm 2. Price is determined by the following demand curve:
P  300  Q
where Q  Q1  Q2.
a. Find the Cournot-Nash equilibrium. Calculate the profit of each firm at this equilibrium.
b. Suppose the two firms form a cartel to maximize joint profits. How many widgets will be produced? Calculate each firm’s profit.
c. Suppose Firm 1 were the only firm in the industry. How would market output and Firm 1’s profit differ from that found in part b above?
d. Returning to the duopoly of part b, suppose Firm 1 abides by the agreement, but Firm 2 cheats by increasing production. How many widgets will Firm 2 produce? What will be each firm’s profits?