Consider a market with 10 firms. Simultaneously and independently, each firm chooses between locating downtown or locating in the suburbs. The profits earned by each firm depend on the number of the other firms that locate in the same area. Specifically, the profits of a firm that locates downtown are given by =5 2 +50, where denotes the number of firms that locate downtown. Similarly, the profits of a firm that locates in the suburbs are given by =48, where denotes the number of firms that locate in the suburbs. a. In equilibrium, how many firms locate downtown? In the suburbs? Show your work. b. What are the equilibrium profits earned by firms locating downtown? In the suburbs? Show your work. c. Suppose the profits from locating in the suburbs declines to =28. How would your answers to parts a-b change in this case? Show your work.