The beach in Asbury Park is roughly 3 miles long. Each day there are 1000 people spread uniformly across the beach. On each end of the beach there is a hoagie shop. People travel up and down the beach at a constant cost of $1 per mile. People buy the hoagie from the shop offering the lowest price, which has two components for each individual: 1) the price paid to the shop owner and 2) the travel cost of getting to the store. Soumya owns the shop at the North end of the beach and sells hoagies at the pricep1per sandwich. Snigdha owns the shop at the South end of the beach andsells hoagies at the price ofp2per sandwich. The marginal cost of a sandwich is $1.In addition, each shop pays the city of Asbury Park $25 per day for the right to sell hoagies. Soumya and Snigdha choose their prices simultaneously.

(a) Assume everybody likes the sandwiches enough that all consumers purchase one. Measure the location of each individual on the beach with respect to the southern endpoint. What is the location of the person who is indifferent between buying from Snigdha and buying from Soumya?

(b) What is Soumya's best response function to Snigdha's price?

(c) What is Snigdha's best response function to Soumya's price?(d) What are the equilibrium prices, quantities, and profits?