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 - 500(W + 400(S, and the demand for Fred's gas is qW = 680 - 500(S + 400(W. 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 snacks to its gasoline customers. Fred sells no products that are related to the consumption of his gasoline. What is the Nash equilibrium?