Results 1 to 1 of 1

Thread: Homogenous Products

  1. #1
    Nas is offline
    Apr 2010

    Exclamation Homogenous Products

    I am having great difficulty with this question... I don't know how to do from part c to part e, i managed to do a and b. Please can some one point me in the right direction.

    1. Double Margins

    Consider a market for a homogenous product with a demand function Q=a-P

    The sole manufacturer of the product has a per unit cost of c and sells the product through a sole retailer who has no other costs apart from the per unit price that the manufacturer charges (d).

    a) If the retailer takes d as given, what price maximizes his profit (PR)? What is the retailer’s profit (πR)?

    b) Given that the manufacturer knows what price the retailer will set (as a function of d and a), what value of d (dM) maximizes the manufacturer’s profit? What is the corresponding profit (πM)?

    c) Who, the retailer or the manufacturer, gets the largest profit?

    d) If the manufacturer could bypass the retailer and sell directly to the consumers, show that its profits (πMR) would be larger that the sum of the profits that the retailer and manufacturer would earn if they acted independently (πR+πM)

    e) Show that if the manufacturer charges the retailer d=c, plus a fixed fee of [(a-c)2]/4, it would earn the same as it would in b) above.

    My answers
    Part a: PR = (a+d)/2
    ΠR = (a-d)2/4

    Part b: PM = (a+c)/2
    ΠM = (a-c)2/4
    Thank you
    Last edited by Nas; Apr 29th 2010 at 01:00 AM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Need help with solving Non-homogenous 2Nd ODE Eqn.
    Posted in the Differential Equations Forum
    Replies: 6
    Last Post: Dec 17th 2010, 07:09 AM
  2. homogenous
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: May 6th 2010, 02:40 AM
  3. ...norm takes products to products.
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: Apr 23rd 2010, 08:55 PM
  4. Homogenous D.E
    Posted in the Calculus Forum
    Replies: 3
    Last Post: Sep 3rd 2008, 08:19 AM
  5. homogenous
    Posted in the Calculus Forum
    Replies: 11
    Last Post: Sep 17th 2007, 09:54 PM

Search Tags

/mathhelpforum @mathhelpforum