Problem 3. 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 beachgoer one wants exactly one ice cream during the day, and values the ice cream from both stands at $5. All of the beachgoers would rather be sunbathing or in the water, so they have a disutility to walking on the beach of $1 per mile. Early's Ice Cream, the rm at location 0, is an early riser and always posts his price rst. 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 rms have a marginal cost of zero. 1. Each individual is also referenced by a location m on the beach between 0 and 2. What are the utilities of purchasing from Early's and Cali for the person at location .75, given that Early's names price pa and Cali names price pa? What are the utilities for each individual as a function of their location on the beach, m? 2. What is the demand for Early's Ice Cream and Cali Creamery given the rms name prices 398 and pa? 3. What is Cali Creamery's best response function when Early's posts a price of pa? 4. What is the Stackleberg equilibrium outcome for this market? Report prices, quantities, and prots for each rm. 5. Early's owner feels that his hard work is not paying off, he hires you as a business consultant. He's 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 prots. What will Early's prots be under this new regime? What advice do you give him