User Name Remember Me? Password

 Economics Economics Forum - Financial Mathematics, Econometrics, Operations Research, Mathematical Finance, Computational Finance

 July 1st, 2013, 04:03 AM #1 Newbie   Joined: Jul 2013 Posts: 1 Thanks: 0 Hotelling Model Hi, I'd like some help with the problem below. There are 2 companies A en B. Both have fixed locations 0 and 4. Consumers are uniformly distributed on the interval [0,4+$]. Every consumer has linieair transportcosts, and buys 1 unit of the product where it is the cheapest. I.E., if prices are pA and pB and the distance from the consumer to company A is equal to x and the distance to company B is y. Then the consumer buys at A when pA +x < pB + y. If the consumer is indifferent he chooses the company with chance 1/2. The companies have constant marginal cost equal to zero and prices pA and pB are strategic variables. The locations are fixed My question: Determine the Bertrand-Nash equilibrium in this model and show that this equilibrium only exists when 36 - 12$ - 5$^2 >= 0 holds. (This is what I have come up with to solve) To answer the question I first write down the demand for the product for producer A and B: qA= { 4 +$ als pA=pB+4 qB= { 4 + $als pB=pA+4 To find the Betrand-Nash equilibrium I maximalize both profitfunctions, and find the reactioncurves. piA=(2+0,5(pB-pA))pA -> via 1st derivative -> pA=2+0,5pB Als for piB -> pB=2+0,5pA+$ Using A in B gives the Bertrand Nash equilibrium: pA=4+2/3 $pB=4+4/3$ From this point on I don't know how to find the equation: 36 - 12$- 5$^2 >= 0 ??? Many thanks in advance! Tags hotelling, model Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post zeeka Calculus 2 May 24th, 2011 08:53 PM fantasista Applied Math 0 April 27th, 2011 06:56 AM donald coolme Advanced Statistics 0 April 14th, 2011 03:36 AM rsen Computer Science 0 April 5th, 2011 02:47 AM kaushiks.nitt Number Theory 3 June 7th, 2009 07:44 AM

 Contact - Home - Forums - Cryptocurrency Forum - Top

Copyright © 2019 My Math Forum. All rights reserved.      