In Tuftsville everyone lives along Main Street, which is 10 miles long. There are 1000 people uniformly spread along Main Street, and each day each individual buys one fruit smoothie from one of the stores located at either end of Main Street. Transportation costs are 0.5 dollars/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 the store at the East end of Main Street.
- a) If Ben charges p1 and Will charges p2, what is the location of a customer who is indifferent between going to Ben's and to Will's Store? What are the demand functions that Ben and Will face? (Remember Main Street is 10 miles long. If you have trouble solving for this specification,you can assume instead that Main Street is 1 mile long (there will be a lower mark, though).
- b) If both Ben and Will charge 1 dollar per smoothie, how many will each of them sell in a day? What if Ben charges 1 dollar, and Will 1.40 dollars?
- c) Rewrite Ben's demand function with p1 on the left side. What is Ben's marginal revenue function?
c) Assume that marginal costs per smoothie are constant and equal to 1 dollar for both Ben and Will. In addition, they pay Tuftsville 250 dol- lars per day in business taxes. Find the equilibrium prices, quantities sold, and profits.
Industrial Organization: Contemporary Theory and Applications 5th Edition, Chapter 10 Problem 4