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Homework Help: 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

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  4. Apr 16, 2013 #3
    No, I have to admitt I've never heard of it...
     
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