(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_i = 3.5 - 4x_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.

a)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.Writee a general expression for Firm 2's demand.

b) 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.Writ a general expression for the firm's demand.

c)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.Writee a general expression for the firm's demand.

d) 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?