The market for cellular service is dominated by two sellers, AT&T and Verizon. AT&T and Verizon are Bertrand competitors, but because the services offered by those two sellers are not identical, customers have some degree of preference that makes them slightly resistant to switching from one to another. The demand for AT&T services is given by qA = 1,000 - 3pA + 2pV, where qA is the number of customers in a particular service area, pA is the price of AT&T service, and p V is the price of Verizon service. The demand for Verizon services is given by qV = 1,000 - 3pV + 2pA. Assume that both sellers can produce cellular service at zero marginal cost.
a. Derive AT&T's reaction curve. Your answer should express pA as a function of pV. If Verizon raises its price by $9, how should AT&T respond to that price increase?
b. Derive Verizon's reaction curve. Your answer should express pV as a function of pA.
c. Solve for the price AT&T should charge to maximize profit.
d. Solve for the price Verizon should charge to maximize its profit.
e. Determine the quantity each seller will sell. Then calculate its profits, assuming that its marginal and average total costs are zero.