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 restaurants production cost is 0. Consumers are uniformly distributed on the street, which is the interval [0, 1], where at each point on the interval lives one consumer. Suppose that the transportation cost for each consumer is $t per km. The utility of a consumer who lives y kms from the restaurant is u=v-p-ty where p is the price of a meal and v is the gross benefit of eating at the restaurant and is a constant. If the consumer does not eat at the restaurant, then her utility is u=0.

Provide a full characterisation of the equilibrium. This means you have to show the conditions for which the entire market is covered and the market is partially covered, that is some consumers do not eat.