Assume a linear town with 100 potential costumers that are uniformly distributed on a unit mile. Each consumer has a willingness to pay for a great tasting hamburger of $30, and would buy only one these hamburgers per week. It cost a resident $10 per mile to travel. Assume two hamburger stores are considering opening shops on opposite ends of the street. After opening, each store would have a marginal cost of $5 per hamburger, an there is no fixed cost for opening a store.
(a) What are the prices each store will charge for hamburgers? What would their profits be?
(b) Intuitively, would both stores be happy with their price and location choice, or would one of them want to change their price/location? In fact, what would happen to the firm’s prices if they were located right next to each other?
(c) Suppose the firms decide to merge (i.e., they become a monopolist). What would the firm’s incentive to merge be (assume that the firms would serve the entire market after the merger)?