Suppose two identical firms produce widgets, and that they are the only firms in the market. Their total costs are given by C1=30Q1 and C2=30Q2, where Q1 is the output of Firm 1 and Q2 output of Firm 2. Price is determined by the following inverse demand curve:
P= 150 - Q, where Q= Q1+Q2
a) Find the Cournot-Nash Equilibrium. Calculate the profits of each firm at this equilibrium.
b) Suppose the two firms form a cartel to maximize joint profits, which they agree to share equally. How many widgets will each firm produce? Calculate each firm profits.
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 duopoly of part (b), Firm 2 knows that firm 1 will abide by the agreement, but Firm 2 decides to take advantage of Firm 1's credible faithful commitment by increasing Firm 2's production. How many widgets will firm 2 produce? what will be each firm's?