Competitive Analysis Question

3. Hotelling Model. (14 points) Consider the following setting for the _I:I_gt_e_l_l_i_r_1gjs model. There is a street of length one km, with 100 consumers uniformly distributed along the street, each consumer has a transportation cost equal to t per km traveled. Assume t = 1. Suppose there are two gas stations, one located at 1/3 km (rm 1) and the other located at 1 km (rm 2). Assume the production cost for both gas stations is zero and the consumer's valuation for gas (v) is very large. (a) Calculate the demand functions for each of the two gas stations. (6 points) (b) Assume the two gas stations compete in prices. Find the Nash equi librium price for each gas station. Explain carefully whether they will charge the same price. (8 points)