Question

Suppose that in a linear city, there is only one restaurant, located at the center of Main Street (which has a length of one kilometer). Consumers are distributed uniformly on this street. Let the street be denoted by the interval [0,1] where at each point on the interval lives one consumer. Assume that the costs of production are zero. However, transport costs are positive. Suppose that transportation costs are c=$1 for each unit of distance. Let utility be U=B-c-p, where B is a

constant, c is units of distance and p is the price of meal.

a. Suppose 0<B<1. Find the number of consumers eating at this restaurant. Calculate the monopoly restaurant’s price and profits.

b. Suppose B>1. Find the number of consumers eating at this restaurant. Calculate the monopoly restaurant’s price and profits.

Answer 1

If through advertising, X percent of the population knows only about Pizzeria1 and (1-X) percent of the population knows about the two Pizzerias then since the percent of people knowing about Pizzeria1 is more as compared to people knowing about Pizzeria2. This is so because people knowing about pizzeria1 is included in both X as well as (1-X) percent of population. Thus the demand for Pizzeria1 would be obviously higher. Thus taking the advantage of this higher demand, Pizzeria1 may set its price higher than Pizzeria2.

Now, if X decreases then Pizzeria1 faces strong competition with Pizzeria2, since people are familiar with both the Pizzeria and thus they have an equal demand for both Pizzeria1 and Pizzeria2, as a result, Pizzeria1 reduces its price to the price level of Pizzeria2 and thus the market of Pizzeria faces a perfect competition