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Economic Differential Equations

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  • 16-11-2011 6:54pm
    #1
    [Jackass]
    Closed Accounts Posts: 9,193 ✭✭✭


    I'm desperately struggling with some revision questions and am appealing / begging for someone to be amazingly kind and take some time to maybe help me a little bit? :(

    Ugggh, I'm so screwed in this subject and desperate, just fallen so far behind. I would really really appreciate it and am freaking out over not being able to understand these. :(

    Question 1

    Find the second cross-partial derivative for the following function:
    y = xz-2

    Answer

    -2z-3

    z-2

    2xz-2

    None of these

    -2xz-1

    I think the answer to this one is the first differentiation is the second option based on x being dropped after the first differentiation with no power (sorry, not really able to type my calculations)

    Question 2

    Suppose the utility of consuming goods x and y is given by U = x0.25y0.25
    What is the marginal utility of consuming x?
    Answer

    x-0.75y0.25

    0.25x-0.75

    None of these

    xy

    0.25x-0.75y0.25

    I think the last one is the answer, but couldn't get exact answer for any of these

    Question 3

    Suppose the utility of consuming goods x and y is given by U = x1/4y1/4
    How does the marginal utility of x change as x increases?
    Answer


    The marginal utility of x is the same at all levels of x

    None of these


    The marginal utility of x gets smaller at higher levels of x


    The marginal utility of x gets larger at higher levels of x

    I have no idea about this one

    Question 4

    Suppose the output of a firm is given by Y = KL where K denotes the number of units of capital, L denotes the number of units of labour, and Y denotes the number of units of output
    What is the first derivative of Y with respect to K?


    Answer

    0

    None of the above

    L

    K

    KL

    I think the answer is 1 (i.e. none of these) as none of the units are to a power of anything

    Question 5

    Suppose the output of a firm is given by Y = KL where K denotes the number of units of capital, L denotes the number of units of labour, and Y denotes the number of units of output
    What is the second derivative of Y with respect to K? How would you interpret this?
    Answer

    Second derivative of Y with respect to K is KL.
    This means that the marginal product of output with respect to capital increases as capital increases.

    Second derivative of Y with respect to K is K.
    This means that the marginal product of output with respect to capital increases as capital increases.

    Second derivative of Y with respect to K is L.
    This means that the marginal product of output with respect to capital increases as capital increases.

    Second derivative of Y with respect to K is 0.
    This means that the marginal product of output with respect to capital does not vary as capital increases.

    None of these

    Based on my previous answer, I have to go with none, but doubting I understand this part either...

    Sorry, some of those numbers are to the power of, but couldn't type properly.

    ANY help would be massively appreciated in explaining some or all of these...


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