1. Boeing and Airbus are the two major producers of airplanes. Let yA denote the number of A340's produced by Airbus, and yB denote the number of 777's produced by Boeing. Prospective buyers regard the two types of planes as perfect substitutes. The (inverse) market demand is estimated to be P = 58-Y/2 where Y = yA + yB. Boeing and Airbus have identical cost functions for these new models: C(yi) = 10yi, i = A, B.

(a) Suppose the two firms try to collude and jointly produce the monopoly output. Show that they would each produce 24 planes.

(b) How much could Boeing gain if, instead of producing 24 planes, it reneges on the agreement and maximizes profits under the expectation that Airbus will produce 24 planes?

(c) Suppose the two firms try for an agreement in which each produces 32 planes. Derive each firm's best reply and show that neither firm will have an incentive to cheat on this agreement.

(d) Characterize this solution graphically as an intersection of the firms best reply functions.