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Math Help - Revision Questions - Help!

  1. #1
    Newbie
    Joined
    Nov 2011
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    2

    Unhappy Revision Questions - Help!

    Hi, I am doing some revision questions to keep up with some course work, and I am afraid that the course is starting to get away from me slightly.

    I would be very much obliged if someone would be kind enough to give me a brief explanation about the following questions...

    Question 1


    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


    1. 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


    1. 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


    Question 4


    1. 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


    1. 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...

    Uggggh, exams coming up soon, and to be honest, on this part of the course, I am clueless, would really really appreciate some help.

    Thanks so much.

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  2. #2
    MHF Contributor

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    Re: Revision Questions - Help!

    Quote Originally Posted by EcoPaddy View Post
    Hi, I am doing some revision questions to keep up with some course work, and I am afraid that the course is starting to get away from me slightly.

    I would be very much obliged if someone would be kind enough to give me a brief explanation about the following questions...

    Question 1


    1. Find the second cross-partial derivative for the following function:
      y = xz-2
    1. So you want \frac{\partial^2 y}{\partial x\partial z}?
      What is \frac{\partial y}{\partial x}?

      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)
    I get "none of these".

    Question 2


    1. Suppose the utility of consuming goods x and y is given by U = x0.25y0.25
    1. Do you mean U= x^{0.25}y^{0.25}?

      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
    Okay, why do you think that? What is the definition of "marginal utility"?

    Question 3


    1. 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?
    1. Again, do you mean U= x^{1/4}y^{1/4}? This is the same function as in (2) then?

      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
    That is, is the marginal utility positive or negative? Again, what is your understanding of the definition of "marginal utility"?

    Question 4


    1. 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
    What does "a power" have to do with anything? You have a constant, L, times K. What is the derivative, with respect to x, of f(x)= Ax?

    Question 5


    1. 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.
    1. No! Y itself is KL, a constant times L. What is the second derivative of such a function?

      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...

    Uggggh, exams coming up soon, and to be honest, on this part of the course, I am clueless, would really really appreciate some help.

    Thanks so much.

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  3. #3
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    Re: Revision Questions - Help!

    Quote Originally Posted by EcoPaddy View Post
    Hi, I am doing some revision questions to keep up with some course work, and I am afraid that the course is starting to get away from me slightly.

    I would be very much obliged if someone would be kind enough to give me a brief explanation about the following questions...

    Question 1


    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


    1. 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


    1. 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


    Question 4


    1. 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


    1. 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...

    Uggggh, exams coming up soon, and to be honest, on this part of the course, I am clueless, would really really appreciate some help.

    Thanks so much.

    Please don't post more than two questions in a thread. Otherwise the thread can get convoluted and difficult to follow. See rule #8: http://www.mathhelpforum.com/math-he...hp?do=vsarules.

    Thread closed.
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