economic question

1. In Tuftsville, everyone lives along Main Street which is 10 miles long. There are 1000 people uniformly 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 $050 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 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 p1 per smoothie. Will owns the store at the east end of Main Street and sells smoothies at a price of pg per smoothie. The marginal cost of a smoothie is $1. In addition, each owner pays the city $250 per day for the right to sell smoothies. Assume that prices are chosen simultaneously. (a) Write down the equation that determines the location of the consumer who is indifferent between buying from Ben or Will. (b) Formulate Ben's optimization problem and derive his best reply to p2. (c) Formulate Will's optimization problem and derive his best reply to p1. (d) Find the equilibrium prices, quantities and prots