Consider a town with a single street of 1 km long with 3,000 people spread uniformly along it.

5. (26%) Consider a town with a single street of 1 km long with 3,000 people spread unifonmly along it. TWo stores, 1 and 2, are located at the opposite ends of the street and sell the same product (store 1 is located at the left end). The cost of walking is t; = $6 per km to store 1 and t2 = $9 per km to store 2 for each consumer. The net utility of a consumer located at point x from buying a product at store 1 is 11;fo = 100 p1 bx, where p,- is a price of the product at store 1' = 1,2. The net utility from buying at store 2 is tight) = 100 - p2 - MI x). The average cost of the product for each store is c = 4. (a) Assume that all consumers buy product from the sellers. Find the demand functions Difp1,p2) and the prot functions mtpbpzl for each store i = 1,2 as functions of prices mm. {b} Find the equilibrium prices