A salesman’s territory is a single, mile-long street. Consumers of his product are equally distributed along the street. He has decided to set up a store to sell his product. In addition to this salesman, there is a second vendor of the same product who is also considering establishing a store on the street. Each store will sell its goods for the same price and each consumer will shop at the store located closest to them (purchasing from the store with the lowest travel costs). It may be helpful to draw simple diagram to accompany your answers.
(a) If the first salesman were the only retailer on the street, where should he locate himself in order to minimize the distance travelled (and hence the costs incurred) by his consumers.
(b) What is the socially optimal location for the two stores to be located? That is, what location is best for all consumers in terms of reducing travel distances?
(c) Will the vendors choose the socially optimal locations? Why or why not?
(d) Suppose the store owners can freely choose their locations. Where will they locate? Find the locations such that each store has no incentive to move. Is this allocation efficient? Why or why not?