5.7 At a busy intersection on Route 309 in Quakertown, Pennsylvania, the convenience store and gasoline station, Wawa, competes with the service and gasoline station, Fred’s Sunoco. In the Nash-Bertrand equilibrium with product differentiation competition for gasoline sales, the demand for Wawa’s gas is qW = 680 - 500pW + 400pS, and the demand for Fred’s gas is qW = 680 - 500pS + 400pW. Assume that the marginal cost of each gallon of gasoline is m = $2. The gasoline retailers simultaneously set their prices.

a. What is the Bertrand-Nash equilibrium?

b. Suppose that for each gallon of gasoline sold, Wawa earns a profit of 25¢ from its sale of salty Exercises 549 snacks to its gasoline customers. Fred sells no products that are related to the consumption of his gasoline. What is the Nash equilibrium?

(Hint: See Solved Problem 14.3.) M