Consider a simple Hotelling city setup. There are two firms located at either end of a street of length one mile (so, Firm 1 is at 0 and Firm 2 is at 1). 100 consumers are uniformly located along the street. Consumers bear a transportation cost of $t per unit of distance. Each consumer will buy 1 and only 1 unit of the good. The firms can produce the good at zero marginal cost. Denote Firm 1's price p1 and Firm 2's price p2.

a. Call x (where x must be between 0 and 1 inclusive), the location of the consumer who is indifferent between buying from Firm 1 and from Firm 2. Write down a formula for x. (Hint: it should have a p1 in it, a p2 in it, and a t in it!).