Thread: 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.

Originally Posted by EcoPaddy

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 ?
   What is ?
   
   
   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 ?
   
   
   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 ? 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.

Originally Posted by EcoPaddy

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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