1. (22 total points) Suppose there are 6 firms located equidistantly around a circle whose circumference is equal to 1. There are 300 consumers distributed uniformly around the circle. Each consumer gets utility U = 4 from buying a unit of the good from a firm which sells their ideal brand (a firm located at the consumer's location). Also, the consumer's utility decreases by 3 times the distance that the consumer is located from the firm. So a consumer who buys from firm i gets utility given by U_i = 4 - 3x_i where x_i is the distance from the consumer's location to firm i's location. The consumer's surplus from purchasing a unit of the good from firm i is the difference between their utility from purchasing a unit of the good from firm i and the price that firm i charges. So CS = U_i - P_i. Also, the consumer has no alternatives, so the consumer will buy a unit of the good if maximum surplus gained from purchasing from any firm is greater than 0.

c) (6 points) Suppose the firm has no close neighbors so that it acts as a monopolist. Therefore it captures all of the consumers whose surplus is greater than or equal to 0. general expression for the firm's demand

d) (5 points) Suppose the firm can produce its good at constant marginal cost, MC = 1.5. What price should the firm charge if it wants to maximize its profit?