In Tuftsville, everyone lives along Main Street, which is 10 miles long. There are 1,000 people uniformly spread up and down Main Street, and every day they each buy a fruit smoothie from one of the two stores located at either end of Main Street. Cus- tomers ride their motor scooters to and from the store using $0.50 worth of gas per mile. Customers buy their smoothies from the store offering the lowest price, which is the store’s price plus the customer’s travel expenses getting to and from the store. Ben owns the store at the west end of Main Street and Will owns the store at the east end of Main Street.

a) If both Ben and Will charge $1 per smoothie, how many will each of them sell in a day? If Ben charges $1 per smoothie and Will charges $1.40, how many smoothies will each sell in a day?

b) If Ben charges $3 per smoothie, what price would enable Will to sell 250 smoothies per day? 500 smoothies per day? 750 smoothies per day? 1,000 smoothies per day?

c) If Ben charges p1 and Will charges p2, what is the location of the customer who is indifferent between going to Ben’s or Will’s shop? How many customers go to Will’s store and how many go to Ben’s store? What are the demand functions that Ben and Will face?

d) Rewrite Ben’s demand function with p1 on the left-hand side. What is Ben’s marginal revenue function?

e) Assume that the marginal cost of a smoothie is constant and equal to $1 for both Ben and Will. In addition, each of them pays Tuftsville $250 per day for the right to sell smoothies. Find the equilibrium prices, quantities sold, and profits net of the $250 license fee.