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marshallian demand function

  • 30-04-2009 1:38am
    #1
    alibek
    Closed Accounts Posts: 2 ✭


    Hi everyone!

    Does smb know how to derive demand function for this kind of utility function:
    U(x,y,z)= min(x,y) + z

    I cant understand what MRS will be here.


Comments

  • #2
    [Deleted User]
    Posts: 5,589 ✭✭✭ [Deleted User]


    min(x,y) is a Leontieof function so x will always equal y. You should be able to solve it out using the utility function and the budge constraint. You can't differentiate a function like that.


  • #3
    alibek
    Closed Accounts Posts: 2 ✭alibek


    As I understand, if price of z is bigger than price of y and price of x, demand for z will be zero and smth for x=y.
    Also if price(z)<price(x) and price(z)<price(y) then demand for x and y will be zero.
    But I cant understand what will happen if price(z)<price(x) and price(z)>price(y) for example?


  • #4
    [Deleted User]
    Posts: 5,589 ✭✭✭ [Deleted User]


    With a leontief, X will always equal Y.

    So if you have U = min(x,y) and a budget constraint of m = py.y + px.x, then we know that x = y so we have m = py.x + px.x so we get m = x(py + px) which leads to x = y = m / (py + px).

    The case you asked about is an extension of this.


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