Q3. Hotelling Model with Non-Uniform Distribution (16 points) Assume that there exists a linear city. Firm 0 is located at 0 and rm 1 is at 1. Both rms sell an identical product except for their locations. The product is produced at marginal cost 0. Consumers value the good at V > c, and V is large enough that all consumers will make a purchase. Transportation within the city costs t dollars per unit. Firms simultaneously choose prices and each consumer decides whom to purchase from. (a) (3 pts) Assume that a mass N consumers are located at 0.5. Solve for the pure strategy Nash Equilibrium in prices. What is the prot for each rm in this equilibrium? (b) (3 pts) Assume that a mass N consumers are located at 0.2. Solve for the pure strategy Nash Equilibrium in prices. What is the prot for each rm in this equilibrium? (0) (hard) Assume that a mass N1 consumers are located at 0.5, and a mass N2 consumers are uniformly distributed on a line from 0 to 1. o (8 pts) Solve for the pure strategy Nash Equilibrium in prices. What is the price charged by each rm in this equilibrium? (Hint: Assume symmetric equilibrium that p3 = pf) o (2 pts) What are the equilibrium prices when N2 > 00? What are the equilibrium prices when N2 > 0? Discuss the results