ECON 235 Cronin Problem Set 4: Oligopoly with Heterogeneous Goods [Due March 12, 2019) Directions: Complete the problems prestmted 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. In 'l'ultsville, everyone lives along Main Street which is 10 miles long. There are 1000 people unlformly spread up and down Main Street, and each day 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 scooters use $0.50 worth of gas per mile. Customers buy their smoothies from the store oering the lowest price, whieh 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 smoothies at a price of pi, per smoothie. Will owns the store at the east end of Main Street and sells smoothies at a price of pm per smoothie. The marginal cost of a smoothie is $1. In addition, eaeh owner pays the eity $250 per day for the right to sell smoothies. Assimie that Ben and Will choose their prices sinnultaneously. a) Write down the equation that determines the location of the consumer who is indifferent between buying from Ben or Will. Hint: Make sure you get the transportation cost comet. b) Formulate Ben's optimization problem and derive his best reply to pm. e) Formulate Will's optimization problem and derive his best reply to p5. d) Find the equilibrium prices, quantities and prots. 2. George 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 oi the consumer who is indifferent between buying irom George and Will. b) H Will and Ben do not change their pricrs (your answer to (d) in problem 1}, what is George's best reply? How much prot would he earn? e} Derive the best replies for Will and Ben and nd the equilibrium prices and quantities