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

- 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

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...

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.