ECC3830 Sample question

Suppose that in a linear city there is only one restaurant, located at the center of the street of length 1 km. Assume that the restaurant's production cost is 0. Consumers are uniformly distributed on the street, vvhich is the interval [0, 1], where at each point on the interval lives one consumer. Suppose that the transportation cost for each consumer is $c per km. The utility of a consumer vvho lives :1: kms from the restaurant is u = v p ex Where p is the price of a meal and I? is the gross benet of eating at the restaurant and is a constant. If the consumer does not eat at the restaurant, then her utility is u = 0. Suppose v = Etc where .1 :2 0. Provide a full characterisation of the equilibrium