4. In Tuftsville, everyone lives on Main Street, which is ten miles long. 1,000 people are evenly distributed on Main Street and each of them purchases a fruit smoothie each day from one of two stores located at either end of Main Street. Customers ride their motor scooters to and from the store, and motor scooters consume SO.50 gas per mile. Customers buy their fruit smoothies from the store that offers the lowest price, which is the sum of the store's smoothie price and the customer's travel costs 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 a price of SI per smoothie, how many smoothies will each of them sell per day? If Ben charges $1 per smoothie and Will charges $1.40 per smoothie, how many smoothies will each of them sell per day?
b. If Ben charges S3 per smoothie, at what price can Will sell 250 smoothies a day? At what price can Will sell 500 smoothies a day? Will at any price per day Can you sell 1,000 smoothies?
c. If Ben charges p and Will charges p2, then there is no difference between going to Ben's shop and going to Will's shop.
Where is each customer located? How many customers go to Will's shop and how many customers go to Ben's shop? What are the demand functions Ben and Will face?
d. Rewrite Ben's demand function with p on the left side. What is Ben's marginal revenue function?
e. Let the marginal cost of the smoothie be constant and SI for both Ben and Will. In addition, Ben and Will each have to pay Tuftsville $250 per day to secure the right to sell the smoothie. Find the equilibrium price, equilibrium quantity, and equilibrium profit.