Suppose that two identical firms produce widgets and that they are the only firms in the market.Their costs are given by:

TC(q1) = 40q1andTC (q2) = 40q2

The aggregate demand facing the firms is:

P = 100 - Qwhere 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?