Consider a beach that is 2 miles long. 2,000 people are uniformly spread along the beach. At one end of the beach is firm A selling cold (ie. refrigerated) bottles of water. At the other end of the beach is firm B selling warm (ie. non-refrigerated) bottles of water. Everyone on the beach prefers cold water to warm water. There is a travel cost to walking along the beach to either of these firms. The utility that individual i located at xi [0, 2] obtains from purchasing a bottle of water from firm A is: uiA =10pA xi If individual i were to purchase a bottle of water from firm B, their utility would be: uiB =8pB (2xi) Assume there are no fixed costs for any of the firms. Marginal cost for firm A is 3 and the marginal cost for firm B is 1.

a) Assuming that all consumers will buy a bottle of water from one of these firms, what is the location of the consumer who is indifferent between buying from firm A or firm B? (This location should be a function of the prices of the two firms.)

b) What is the demand function for firm A and firm B respectively?

c) Write down the profit functions for each of the two firms.

d) Assuming the firms choose prices, solve for the Nash equilibrium prices.

e) Compute the matrix of own- and cross-price elasticities at these equi- librium prices. Which product is more elastic? How can you tell these two products are substitutes?