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 the 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?