Problem 3. Consider a mile-long city laid out along a line segment between 0 and 1. A mass of 7 thousand consumers is uniformly distributed within the city (e.g., N = 7). Two movie theaters are located at either endpoint of the city: ZeroFilm is located at 0 and UniFlick is located at 1. All residents agree that the sound quality is slightly better at ZeroFilm than at UniFlick, so the value of seeing a movie at ZeroFilm is 9 dollars, while the value of seeing the same movie at UniFlick is 7 dollars. Traveling costs within the city are 3.5 dollars per mile (there and back). The movie theaters have a marginal cost of zero for serving an additional customer, and have 7 thousand seats, so they both can serve the entire city. The theaters compete by setting prices simultaneously. You may assume that everyone in the city goes to one of the two movie theaters. 1. Suppose ZeroFilm sets a price of pa and UniFlick sets a price of p1 what is the address of the marginal consumer? 2. What is the demand curve for ZeroFilm? 3. What is the demand curve for UniFlick? 4. What price does each rm set under Nash Equilibrium? 5. How many people attend UniFlick? 6. Explain what feature of this model exhibits horizontal differentiation. 7. Explain what feature of this model exhibits vertical differentiation. 8. Show that the assumption that the entire population attends one of the two theaters is correct. The utility of not seeing a movie is zero