In UAville 1000 people live on Main Street that is 10 miles long. Every day each of the 1000 people will buy 1 fruit smoothie from one of the two vendors located at the two ends of Main
Street: Ben is located at the east end; Jerry is located at the west end. Each customer rides a scooter to and from the store of their choice and the scooter uses $0.1 worth of gas for each mile traveled (note: this is per mile expense, not two-way cost). Each customer purchases their smoothie at the store where the total cost, i.e. price of smoothie plus travel cost, is the lowest.
a. If Ben charges $3 per smoothie and Jerry charges $2, how many would each store sell?
b. If Ben charges a price p1 and Jerry charges a price p2, how many smoothies would each store sell?
c. Based on part (c), what is Ben's profit as a function of p1 and p2, assuming that the marginal cost per smoothie is $1 for both stores. Then derive Ben's best response function. Jerry's best response function is symmetric.
d. What is the equilibrium price that each store will charge?
e. How much profit will each store earn?