Problem 4. Two independent ice cream vendors own stands at either end of a 2 mile long beach. Everyday there are 200 beach-goers who come to the beach and distribute themselves uniformly along the water. Every beach-goer one wants exactly one ice cream during the day, and values the ice cream from both stands at $5. All of the beach-goers would rather be sunbathing or in the water, so they have a disutility to walking on the beach of $1 per mile. Earlys Ice Cream, the firm at location 0, is an early riser and always posts his price first. Cali Creamery, at location 2, is more laid back and posts her price just before the beach opens (the beach requires all prices be posted by the time the beach opens). Both firms have a marginal cost of zero.

1. Each individual is also referenced by a location x on the beach between 0 and 2. What are the utilities of purchasing from Earlys and Cali for the person at location .75, given that Earlys names price pe and Cali names price pc? What are the utilities for each individual as a function of their location on the beach, x?

2. What is the demand for Earlys Ice Cream and Cali Creamery given the firms name prices pe and PC?

3. What is Cali Creamerys best response function when Earlys posts a price of pe?

4. What is the Stackleberg equilibrium outcome for this market? Report prices, quantities, and profits for each firm.

5. Earlys owner feels that his hard work is not paying off, he hires you as a business consultant. Hes annoyed that Cali is always undercutting his price and is considering waiting to post so that Cali will not learn his price before naming her own. He wants you to predict how waiting to post his price will affect his profits. What will Earlys profits be under this new regime? What advice do you give him?