1. {2" total points) Suppose there are a fmns located equidistantly around a circle whose circumference is equal to 1. There are 3130 consumers distributed uniformly around the circle. Each consumer gets utility L" = 4 from buying a unit of the good 'om a firm which sells their ideal brand (a firm located at the consumefs location). Also. the consumers utility decreases by 3 times the distance that the consumer is located from the firm. So a consumer 1who buys om firm i gets utility given by U; = 4 in where K,- is the distance 'om the consumers location to firm is location. The consumers surplus from purchasing a unit of the good from firm i is the difference between their utility from purchasing a unit of the good 'om firm i and the price that firm i charges. So CE = L] P5. Also= the consumer has no alternatives so the consumer will buy a unit of the good if maximum surplus gained 'om purchasing 'om any firm is greater than ID. a) (a points) Consider a particular firm denoted Firm 2. Let Firm 1 be the firm located on one side of Firm 2. and let Firm 3 be the firm located on the other side of Firm 2. Suppose Firm 1 charges a price P1 = .2. and Firm 3 charges a price P3 = 2. 1Write a general expression for Firm 2's demand. b) (5 points} Suppose Firm 2 can produce its good at constant marginal cost. MC = 1.5. 1What price should firm 2 charge if it wants to maximize its profit? c) (a 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. Write a general expression for the firm's demand. d) (5 points} Suppose the firm can produce its good at constant marginal cost: ME = 1.5. 1iWhat price should the firm charge if it wants to maximize its profit