4. What happens to the "location " of the marginal consumer as the price of the heavy beer increases ? 5. Using this expression , what is the demand curve for the two beers ? 6. What is the profit function for each firm ? 7. What is the best response function of each firm ? 8. Solve for the pure strategy Nash Equilibrium in prices . What are profits in this equilibrium Problem 3 (Stackelberg). 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. Early's 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 r on the beach between 0 and 2. What are the utilities of purchasing from Early's and Cali for the person location .75, given that Early's names price p. and Cali names price pe? What are the utilities for each individual as a function of their location on the beach , 2. What is the demand for Early's Ice Cream and Cali Creamery given the firms name prices p. and p.? 3. What is Cali Creamery's best response function when Early's posts a price of Pe