Consider the following variant of the Spatial Bertrand Model: There is a line of unit length along which 300 consumers are uniformly distributed. There are two firms in this market located at the two endpoints of the linex=0andx=1. Firm1ischargingpricep1forgood1andfirm2ischargingapricep2forgood2. Both firms have a constant marginal costc= 10. Define a consumer's locationxas her most preferred product. Each consumer is willing to pay$50 for their most preferred product. However, there is a disutility associated with purchasing a good that is not your most preferred. Specifically, for a consumer located atx, the disutility of purchasing good 1 is 15xand the disutility of purchasing good 2 it 15(1x)

a) Consider the consumer located at pointx. What is the (net) utility that she gets from purchasing the plan from firm 1? What is the (net) utility of purchasing from firm 2?

b) Where is the marginal consumer located? What is the demand for each firm?

c) How much profit does each firm make? Find each firm's best response function?

d)What price will both firms set in equilibrium? How much profit is each firm making in equilibrium?