Directions: Complete the problems presented below. You may (should) work on this problem set with others. Your solutions are due at the beginning of class on the date above. 1. ln Tuftsville, everyone lives along Main Street which is 10 miles long. There are 1000 people uniformly spread up and down Main Street, and each (lay they each buy one fruit smoothie from one of the two stores located at either end of Main Street. Customers ride their motor scooters to and from the store and the motor smoters use $0.50 worth of gas per mile. Customers buy their smoothies from the store offering the lowest prioe, which is the store's price plus the customer's travel costs getting to and from the store. Ben owns the store at the west end of Main Street and sells smoothim at a price of pi, per smoothie. Will owns the store at the east and of Main Street and sells smoothies at a. price of pm per smoothie. The marginal cost of a. smoothie is $1. in addition, each owner pays the city $254] per day for the right to sell smoothies. Ass-11mm that Ben and Will choose their prices simultaneously. a} Write down the equation that determines the location of the consumer who is indiiferent between buying from Ben or Will. Hint: Make Sure you get the transportation mst ear-rent. b) Formulate Ben's optimization problem and derive his best reply to pm. c} Formulate Will's optimization problem and derive his best reply to pb. (1) Find the equilibrium prices, quantities and prots. 2. lGeorge is attracted by the prots that Ben and Will are earning and decides to Open a store at the midpoint of Main Street. His costs are the same as Ben and Will. Denote the price he charges as pg. a} Write down equations that determine the location oi the consumer who is indifferent between buying from Ben and George and the location of the consumer who is indifferent between buying item George and Will. b} if Will and Ben do not change their priecs (your answer to (d) in problem 1}, what is George's best reply? How much prot would he earn? c} Derive the brst replies for Will and Ben and nd the equilibrium prices and quantities