Exercise 3 Consider a town with a single street, which is 1 km long with 2,000 people spread uniformly along the town. Two gas stations, 1 and 2 are located at the ends of the town and sell the same type of as (suppose that station 1 is located at the left end). There is a driving cost t=3 /km for each consumer. The utility of an individual located at point x from buying a full tank of gas at station 1 is U1(x) = 12 p1 tx Where phi = 1,2 is a price of a full tank at station 1' = 1,2. (assume that all consumers have similar cars and need to III a full tank). If the individual buys gas at station 2, his/her utility is: U2(x) = 12 p2 (1 x)t There are no fixed costs for the gas stations. The marginal cost for each gas station is equal to c = 4. 1. Assume that all consumers buy a tank at one of the two stations. What is the location of the consumer who is indifferent between buying at station 1 or 2 for as a function of prices p1 and pz? 2. What are the demand functions and the prot functions for each station as functions of prices p1 and pz? 3. Assuming that the stations compete by prices, End the best-response function 3R1 (192) for station 1. 4. Solve for the Nash equilibrium prices