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Problem 3. Two independent ice cream vendors own stands at either end of a 1 mile long beach. Everyday there are 100 beachgoers 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 $6. 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. Both rms have a marginal cost of zero. 1. Each individual is also referenced by a location a: on the beach between 0 and 1. What are the utilities of purchasing from Early's and Cali for the person at location .75, given that Early's names price p8 and Cali names price pa? What are the utilities for each individual as a function of their location on the beach, :12? 2. What is the demand for Early's Ice Cream and Cali Creamery given that the rms charge prices 105 and pa, respectively? 3. What is Cali Creamery's best response function when Early's posts a price of pa? 4. What is the equilibrium prices both rms charge, if both rms have to determine their prices early in the morning without knowing the price of the other rm is going to charge