(solution) Consider Hotelling's location model. The length of the city is 20

(solution) Consider Hotelling's location model. The length of the city is 20

Consider Hotelling’s location model. The length of the city is 20 miles. Two firms, 1 and 2, want to sell a good in the city. Each firm has a constant marginal and average cost of $1. Consumers are distributed evenly along the main street. Each consumer buys at most one unit of the good and his reservation price for the good is $50. Each consumer faces a transportation cost of $1 per mile.

(1) Suppose that the two firms must charge $2 per unit. Find a pure-strategy Nash equilibrium (or equilibria) in location strategies. Explain your answer.

(2) Suppose that firm 1 is permanently located 2 miles from the left end of city and firm 2 is permanently located 2 miles from the right end of city. Find a pure-strategy Nash equilibrium (or equilibria) in prices