100 consumers are uniformly distributed on a circle with a circumference of length 1. As depicted below, one firm is located at the top of the circle and the other at the bottom, so the distance between them in either direction is 1/2. In the figure, a particular person that is located at x lives a distance dA from A and dB from B. Firms A and B have zero costs and simultaneously set prices pA and pB . Consumers care about the price of a good and the distance they have to travel to get it. A consumer that lives a distance dA from firm A has utility for the good at A given by uA = 5 pA dA and her utility for good B is uB = 5 pB dB Every consumer, depending on her location, chooses the good that gives her the higher utility. Suppose instead there are N firms oriented symmetrically around this circle. This splits the circle into N equal pieces of length 1/N , which is the distance between any two neighboring firms. If all firms set prices simultaneously, find the symmetric equilibrium prices in terms of N. What