Final answer:
Demand functions are determined by prices and transport costs. In Bertrand equilibrium, both gas stations would set prices equal to marginal costs, resulting in zero profit due to price competition. This differs from general market equilibrium where quantity demanded meets quantity supplied at the equilibrium price.
Step-by-step explanation:
The demand functions for the two gas stations require a model of consumer behavior based on their location and transportation costs. Consumers will choose the station offering the lowest total cost, which includes the price of gasoline and the round-trip transportation cost. Since the transportation cost is 3d (where d is the distance to the station) and the cost function for each station is linear with C(q) = q, the demand function for each station will depend on the prices set by both stations and the distribution of consumers along the 8-mile street.
For Bertrand equilibrium prices, we assume that each firm sets its prices knowing the price of the competitor. The Bertrand model suggests both firms will end up setting prices at marginal cost, because if one of them sets a price even slightly above it, all consumers will buy from the other station. Hence, the equilibrium prices will be equal to the marginal cost of production, and because the cost function C(q) = q, the equilibrium price is likely to be 1. The equilibrium profit for each firm in this scenario would be zero, as they are setting prices equal to their marginal cost.
The example given in the reference about the equilibrium price in the market for gasoline, where the equilibrium price is the only price where quantity demanded is equal to quantity supplied, is useful for understanding general demand and supply dynamics but is different from a situation with Bertrand competition where firms compete on prices.