Question

Find all the equilibrium locations if there are five firms competing over locations in the Hotelling linear city (product space is the unit interval, prices are fixed, and there is uniform distribution of consumers' tastes).

Answer 1

“Linear city” is the interval . Consumers are distributed uniformely along this interval. There are 5 firms, located at each extreme who sell the same good. The unique difference among firms is their location. c= cost of 1 unit of the good t= transportation cost by unit of distance squared. This cost is up to the consumer to pay. If a consumer is at a distance d to one of the sellers, its transportation cost is td2 . This cost represents the value of time, gasoline, or adaptation to a product, etc. Consumers have unit demands, they buy at most one unit of the good .