An ice
cream company is going to open businesses in Linear City. The
city has
a population of 2,000 people, all of whom enjoy ice cream and get a utility
level
of $10
from a scoop of ice cream. The city is 1 mile long and the people are uniformly
distributed
across the city. City addresses run from 0 to 1 from left to right. There-
and-back
travel costs within the city are $1 per mile. A scoop of ice cream costs $2 to
produce.
For each store the ice cream company opens, it incurs fixed cost of 50.
1. Show
that, even if the ice cream shop open up only one store, it is optimal to sell
ice cream
to the entire market.
2. Write
down an expression for total profit when the firm optimally locates and sets
prices
fornstores.
3.
Suppose the ice cream firm opens 5 stores, what would be the optimal locations
for these
stores? What would be the profits of the ice cream store.
4. How
many stores should the monopolist open?
5. Write
down an expression for total costs that a social planner would like to minimize in
this market.
6. What is the socially efficient
number of stores to open?





