Question

1. Two cell phone companies A and V are located at the extremes of a line of length one and transportation cost t = 4.. Consider an initial situation where both firms offer a generic phone that consumers value the same (except obviously for the transportation cost.) Marginal cost is zero. (this problem was answered in class.)

(a) Find the Bertrand equilibrium. Letting N = 800 denote the total population, show that profits for each firm will be 1600.

(b) Suppose now company A offers a new phone (call it the eye phone) and that all consumers enjoy an extra utility of 3 when using that phone (note that only company A offers that phone.) Show that at the new Bertrand equilibrium pA = 5, pT = 3, and market shares sA = 5/8 and sT = 3/8 and profits are respectively, pA = 2500 and pT = 900.

(c) Explain why if both firms carry the eye phone the equilibrium is the same as the one obtained in (a).

(d) Now suppose the eye phone is actually produced by company a. Company a can either sign an exclusive deal with A to be the single carrier of the eye phone or sign an agreement with both companies.

i. If it signs an exclusive deal with A, what is the maximum it could charge to A?

ii. Suppose instead it auctions the deal and gives exclusivity to the highest bidder (and in case both firms bid the same it flips a coin.) Notice that this puts the firms in "Bertrand competitors" for this deal. How much will A get?.

iii. Would it gain any more by selling the right to sell the phone to the two firms?