# Revision Questions - Help!

• Nov 16th 2011, 01:37 PM
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...

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?
Zero
None of these
L
K
KL

I think the answer is 1 (i.e. none of these) as the units are to the power of 1, but am not sure.
Question 2

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.

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. :(

(Crying)
• Nov 16th 2011, 03:05 PM
emakarov
Re: Revision Questions - Help!
You need to know how to find derivatives of basic functions. In particular, if $\displaystyle c$ is a constant, then $\displaystyle (cx)'=\frac{d(cx)}{dx}=c$ and $\displaystyle c'=\frac{dc}{dx}=0$.

When a function has two or more variables and you take a partial derivative with respect to one of them, the other variables are considered constant. For example, $\displaystyle \frac{\partial (xy)}{\partial x}=y$ and $\displaystyle \frac{\partial y}{\partial x}=0$. Since the derivative is taken with respect to $\displaystyle x$, the variable $\displaystyle y$ is considered to be a constant.