Internet users in a small Colorado town can access the Web in two ways: via their television cable or via a digital subscriber line (DSL) from their telephone company. The cable and telephone companies are Bertrand competitors, but because changing providers is slightly costly (waiting for the cable repairman can eat up at least small amounts of time!), customers have some slight resistance to switching from one to another. The demand for cable Internet services is given by qC = 100 - 3pC + 2pT, where qC is the number of cable Internet subscribers in town, p C is the monthly price of cable Internet service, and pT is the price of a DSL line from the telephone company. The demand for DSL Internet service is similarly given by qT = 100 - 3pT + 2pC. Assume that both sellers can produce broadband service at zero marginal cost.
a. Derive reaction functions that show the price each competitor should charge in response to the price charged by the other.
b. Solve for each competitor's price, quantity, and profit, assuming that average total costs are zero.
c. Suppose that the cable company begins to offer slightly faster service than the telephone company, which alters demands for the two products. Now qC = 100 - 2pC + 3pT and qT = 100 - 4pT + pC. Show what effect this increase in service has on the prices and profit of each competitor.