Hotelling model (30 points) Consider a Salop's circle model, where two firms are located at the two symmetric points. The length of the circle is 1, and the consumers are evenly distributed over the circle. Transportation cost per unit is t. The utility of the good for each consumer is 3 and each consumer only consumes one unit of good. Consumer's utility is zero without purchase. Suppose price charged by firm i (i = 1; 2) is .

a). (5 points) Determine the consumer who is indifferent between purchasing from any of two firms.

b). (15 points) Derive demand function for both firms (note the locations are symmetric).

c). (10 points) Suppose marginal production cost is 1. Find firm 1's profit maximization decision in choosing the optimal price in equilibrium.