1. 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

-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?

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?

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?

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?

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.

2. Re: 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
1. So you want $\frac{\partial^2 y}{\partial x\partial z}$?
What is $\frac{\partial y}{\partial x}$?

-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?

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?

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?

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?

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.

3. Re: 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

-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?

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?

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?

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?

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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