Assume the two identical firms form the widgets, and that they are the only firms in the market. Their total costs are given by the C1=30Q1 and C2=30Q2, where Q1 is the output of Firm 1 and Q2 output of Firm 2. Price is measured by the following inverse demand curve:
P= 150 - Q, where Q= Q1+Q2
1. Identify the Cournot-Nash Equilibrium. Determine the profits of each firm at this equilibrium.
2. Assume the two firms form a cartel to maximize the joint profits, which they agree to share equally. Determine how many widgets will each firm form? Calculate each firm profit.
3. Assume the Firm 1 was the only firm in the industry. Discuss how would the market output and firm 1's profit differ from that found in part (b) above?