Question

2. Consider a version of the Hotelling model in which prices are endogenously determined. Two firms sell horizontally differentiated products located at opposite ends of the one-dimensional product space. Firm O is located at 0. Firm 1 is located at 1. M consumers are uniformly distributed between 0 and 1, with each consumer's location giving his most preferred type of product. Each consumer places value v on one unit of his most preferred product, but incurs a transportation cost. AD when purchasing a product which is located a distance D away. Assume vis sufficiently large that all consumers purchase one unit. Firms have no fixed costs but marginal costs of c per unit. Firms compete by choosing prices simultaneously. a. Derive the demand curve for each firm as a function of the prices chosen. Explain the presence of firm j's price p; in the demand function for firm iſi # i). Is i's demand increasing or decreasing in pj? Why? Find the Nash equilibrium prices. How do the Nash equilibrium prices vary with ? Provide some intuition for your answer. Now suppose firm 0 can move to any location a between zero and 1 before the price- ه ن ا

Answer 1

so Po BR = (a+c+P)/2, similarly by 8 yametry, PBR (At CfPo)/2 20 T DATE: / PAGE No sowing two BR apo = Altc) + Catcapo)/2 Q Po= Atc) + 05 (O+ c) + Po/2 3P012= 3% (Arc) sol Po*=P, *= Atc. I Ans c.) əPolar =1, 80 prices Tincrease one to one with a Bo2 as transportation cost per unit x 1, firms will take advantage of it & www raise their prices. Buod à makes produds horizon tally differentiated & provides 1 fioms local Monopoly power 80 as a 1, Pleice cost prangin (P-C) also the