Consider the following duopoly game: each of 2 firms can produce as much of a good as he wishes at marginal cost 1 (i.e., producing q units costs 1q = q in total), and the market demand curve is given by Q(p) = 10p - p.
(a) Find the inverse market demand curve, specifying the price at which Q units can be sold.
(b) Write out each firms profit expression, if firm 1 produces quantity q1 and firm 2 produces quantity q2.
(c) We found in class that the NE of this game is for each firm to produce 3 units. If you did (c) correctly, you will see that this yields a profit of 9 to each firm. However, if firms could agree at the start to each produce only 2 units, they would both earn a higher profit, namely 10. Explain why such an agreement might not work. The profit-maximizing quantity, Q.