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