Homework Assignment 4

Intermediate Microeconomics (Econ 100A)
Kristian López Vargas
UCSC

Instructions:

You will scan your homework into a single PDF file to be upload.
Only legible assignments will be graded.
Late assignments will not be accepted.

Only two randomly-chosen questions will be graded.

Question 1:

Consider the following production function that depends only on labor:$Q=4L^{1/3}$

1. Write a combination of input and output that are technically efficient. In other words, for what level of $L$ and $Q$, is the technology efficient?

2. Write a combination of input and output that are technically inefficient. In other words, for what level of $L$ and $Q$, is the technology inefficient?

3. Write a combination of input and output that are technically unattainable. In other words, for what level of $L$ and $Q$, is the technology unattainable?

Question 2:

Consider the following production function that depends only on labor:$Q=4L+12L^{2}-6L^{3}$

1. Compute the $APL$ $($average product of labor$)$.

2. Compute the $MPL$ $($marginal product of labor$)$.

3. What is the value of $L^{*}$ at which $APL$ is the highest?

4. For $L > L^{*}$, which one is bigger, $APL$ or $MPL$? How about when $L < L^{*}$ and $L = L^{*}$?

5. Draw $APL$ and $MPL$ on the y-axis as a function of $L$ on the x-axis. Label the point of the intersection of $APL$ and $MPL$.

Question 3:

Consider the following production function: $Q=AL^{a}K^{b}$. Assume $A>0$. Further assume $0<a<1$, and $0<b<1$.

1. What is the Marginal Product of Labor $(MP_{L})$? Is it diminishing as $L$ increases? What is the Marginal Product of Capital $(MP_{K})$? Is it diminishing as $K$ increases?

2. What is the Average Product of Labor $(AP_{L})$? What is the Average Product of Capital $(AP_{K})$?

3. What is the $TRS_{L,K}$ ? Is the absolute value of $TRS_{L,K}$ diminishing in $K$? Is it diminishing in $L$?

4. Are there constant, decreasing, or increasing returns to scale? How does this depend on the parameters?

Question 4:

Consider the following production function: $Q=\left(6L+3K\right)^{1/2}$

1. What is the Marginal Product of Labor $(MP_{L})$? What is the Marginal Product of Capital $(MP_{K})$? Are they diminishing?

2. What is the Average Product of Labor $(AP_{L})$? What is the Average Product of Capital $(MP_{K})$?

3. What is the $TRS_{L,K}$ ? Is the absolute value of $TRS_{L,K}$ diminishing in $L$ or $K$?

4. Are there constant, decreasing, or increasing returns to scale?