1. (18 total points) Suppose there are 8 firms located equidistantly around a circle whose circumference is equal to 1. There are 400 consumers distributed uniformly around the circle. Each consumer gets utility U=3.5 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 4 times the distance that the consumer is located from the firm. So a consumer who buys from firm i gets utility given by U; = 3.5 -4x; where x; 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 = Uj-P;. 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. a) (6 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. Write a general expression for Firm 2's demand