1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Lagrange with integral

  1. Apr 16, 2013 #1
    1. The problem statement, all variables and given/known data
    Maximize [itex]C_{t}[/itex] for any given expenditure level

    [itex] \int_{0}^{1}P_{t}(i)C_{t}(i)di\equiv Z_{t} [/itex]


    3. The attempt at a solution

    The Lagrangian is given by:
    [itex] L = \left(\int_{0}^{1}C_{t}(i)^{1-(1/\varepsilon)}di\right)^{\varepsilon/(\varepsilon-1)} - \lambda \left(\int_{0}^{1}P_{t}(i)C_{t}(i)di - Z_{t}\right) [/itex]

    I know that the first order condition is

    [itex] C_{t}(i)^{-1/\varepsilon}C_{t}^{1/\varepsilon} = \lambda P_{t}(i) [/itex] for all [itex] i \in (0,1) [/itex]

    But I do not understand how they get to this answer. Can anyone help me?
     
    Last edited by a moderator: Apr 16, 2013
  2. jcsd
  3. Apr 16, 2013 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

  4. Apr 16, 2013 #3
    No, I have to admitt I've never heard of it...
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Lagrange with integral
  1. Lagrange remainder (Replies: 7)

  2. Lagrange Multipliers (Replies: 8)

  3. Lagrange Multipliers (Replies: 8)

  4. Lagrange's Identity (Replies: 7)

Loading...