consider a standard hotelling model in which 1,000 consumers are uniformly distributed along a line between zero and one. There are two firms. Firm 1 is located at x1=0.2 and firm 2 is located at x2=0.9. Therefore, both firms have some consumers located on either side of their location. The consumer surplus for consumer i located at xi who purchases from firm 1 is Ui1 = 100 - p1 - t I xi - x1 I where t is the cost of travel and x is the round trip distance traveled to firm 1. The consumer surplus for consumer i if he or she purchases from firm 2 is Ui2 = 100 - p2 - t I xi - x2 I assume t = 30 and the firms have set the prices p1 = 10, p2 = 20.

i) what is the location of the consumer who is indifferent between purchasing from either firm

ii) how many consumers will choose to purchase from firm 1

iii) if firm 1 were to raise its price by 1%, what is the percent increase in demand for firm 2?