My Math Forum Hotelling Model

 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 Display Modes Linear 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