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Thread: Consumer Utility Maximization with Calculus

  1. #1
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    Consumer Utility Maximization with Calculus

    Hey guys, Im currently struggling with this HW question. I was really confused by the condition that f '(x) > 0 for all x > 0, since I thought I need to set f '(..) to zero for maximizing the utility function.


    ______
    Calculate the consumer's system of demand funcations D1(P1, P2, I) and D2(P1, P2, I) if the consumer's utility functions is defined by:


    U(X1, X2) = f [X1^(1/2) * X2^(1/2)]


    where f is a continuously differentiable function of one variable which has f '(x) > 0 for all x > 0.
    ______


    Thank you very much in advance!
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  2. #2
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    Re: Consumer Utility Maximization with Calculus

    Hey Paradox233.

    If you have such a function you can still optimize it if it is over some fixed interval [i.e. not over the whole real line or geometric space - but instead a subset of that space that is bounded]
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  3. #3
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    Re: Consumer Utility Maximization with Calculus

    You are dealing with CONSTRAINED optimization if, as I suspect, I is an income or budget constraint.

    All f'(x) > 0 means is that more is better. If I is an income constraint, that means utility is maximized when all income is spent.

    Do you know Lagrangian multipliers?
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