Question 1

Given the simple production function $\mathrm { Q } = 3 \mathrm {~K} + 4 \mathrm {~L}$, where $\mathrm { L }$ is the quantity of labor employed and $\mathrm { K }$ is the quantity of capital employed, assuming $\mathrm { K } = 2$ and $\mathrm { L } = 3$, what would it mean if output was less than 18 ?

Accepted Answer

If output is less than 18 with the given values of capital and labor, it means that the firm is not using its resources (capital and labor) efficiently. This is because the production function specifies that with K=2 and L=3, the maximum output the firm can produce is 18 (3K + 4L = 3(2) + 4(3) = 18). Therefore, if the firm is producing less than 18, it indicates that there is inefficiency in the production process. It does not mean that the firm is out of business or that the production function was not specified correctly. The option D is also incorrect, as the production function does not provide information about the relative productivity of capital and labor. If the output is less than 18, it means that the firm is not reaching their full potential production level given the amount of labor and capital employed. The production function is specified correctly, and the firm is still in business, but not utilizing their resources efficiently.

Question 2

-Average product reaches a maximum when labor equals:

Accepted Answer

Average product reaches its maximum when the total product is increasing at a decreasing rate. This typically occurs before the total product starts to decrease, which is usually at the point where additional units of labor start to have less output due to diminishing returns. Without specific data on the total product curve or the marginal product of labor, it's impossible to determine the exact point of maximum average product. Therefore, without additional context or a graph, any specific numerical answer (like 300) cannot be justified as correct over others. This response is based on the principles of production theory in economics, assuming the question intended to test understanding of these principles rather than referencing specific data.

Question 3

$$\begin{array} { l l } 
\hline \mathrm { L } & \mathrm { Q } \
\hline 0 & 0 \
1 & 20 \
2 & 50 \
3 & 90 \
4 & 125 \
5 & 140 \
6 & 150
\end{array}$$
-Given the table above, average productivity is maximized with the ____________ worker.

Accepted Answer

To maximize average productivity, we want to choose the worker who contributes the most to the overall productivity. Looking at the table, we can see that the difference in productivity between each worker is not constant. In other words, worker 2 contributes more than worker 1, but worker 3 contributes more than worker 2 AND worker 1 combined. Similarly, worker 4 contributes more than worker 3 AND worker 2 AND worker 1 combined. However, worker 5 contributes only 15 units more than worker 4, and worker 6 contributes only 10 units more than worker 5. Therefore, the most efficient choice would be worker 4, as they have the highest increase in productivity compared to the previous worker.

Question 4

$$\begin{array} { l l } 
\hline \mathrm { L } & \mathrm { Q } \
\hline 0 & 0 \
1 & 20 \
2 & 50 \
3 & 90 \
4 & 125 \
5 & 140 \
6 & 150
\end{array}$$
-Given the table above, marginal productivity is maximized with the ___________ worker.

Accepted Answer

Marginal productivity is maximized when the additional output produced by an additional worker is the highest. To find this, calculate the difference in output (Q) for each additional worker (L). From L=1 to L=2, the increase is 30 (50-20); from L=2 to L=3, the increase is 40 (90-50); from L=3 to L=4, the increase is 35 (125-90); and so on. The highest increase is from the second to the third worker, which is 40, making the third worker the one with the maximized marginal productivity.

Question 5

A labor requirements function represents:

Accepted Answer

A labor requirements function represents the minimum amount of labor necessary to produce a given level of output. It shows the relationship between the amount of output and the amount of labor required to produce that output, assuming all other factors remain constant. It is a crucial component in determining production costs and formulating production strategies. A labor requirements function represents the minimum amount of labor necessary to produce a given level of output. This function shows the minimum amount of input necessary to produce each level of output, which can vary depending on the technology used and the efficiency of the production process.

Question 6

Suppose a production function has only one input, labor. What can you tell about the slope of the production function, assuming output is on the y-axis and labor is on the x-axis, if production exhibits constant marginal returns to labor?

Accepted Answer

The answer of Suppose a production function has only one...

Question 7

The production set represents:

Accepted Answer

The production set represents all technically feasible combinations of inputs and outputs. It includes both efficient and inefficient combinations. The production set is the set of all technically feasible combinations of inputs and outputs, meaning all possible combinations of inputs and outputs that a firm can produce with its technology and resources. It includes both efficient and inefficient combinations.

Question 8

$\begin{array}{ll}
\hline \mathrm{L} & \mathrm{Q} \
\hline 0 & 0 \
1 & 20 \
2 & 50 \
3 & 90 \
4 & 125 \
5 & 140 \
6 & 150
\end{array}$
-Given the table above, the marginal productivity of the third worker is:

Accepted Answer

The marginal productivity of the third worker is calculated by subtracting the total productivity (Q) with two workers from the total productivity with three workers. From the table, Q with two workers is 50 and with three workers is 90. Therefore, the marginal productivity of the third worker is 90 - 50 = 40.

Question 9

-Marginal product reaches a maximum when labor equals:

Accepted Answer

The answer of 
-Marginal product reaches a maximum when labor...

Question 10

The production function represents:

Accepted Answer

The answer of The production function represents:
...

Question 11

Which one of these is false when compared to the relationship between marginal and average product?

Accepted Answer

The statement in option C is true. The relationship between marginal and average product is a unique feature of production functions and does not necessarily apply to other variables. Therefore, statement C is false. The remaining options A, B, and D are true statements. The relationship between marginal and average product is always the same. When marginal product is greater than average product, average product must be increasing. When marginal product is less than average product, average product must be decreasing. When marginal product is equal to average product, average product must be at its maximum. The relationship between the marginals and averages of other variables may differ. Therefore, statement C is false.

Question 12

For a simple graph of a production function with Q on the y-axis and L on the x-axis, which of the following statements is true?

Accepted Answer

The slope of the production function at a specific point represents the marginal product of labor, which is the additional output produced by adding one more unit of labor. The slope between the origin and a specific point on the production function represents the average product of labor, which is the total output divided by the number of units of labor used. Therefore, statement C is true. Statement A is partially correct because the slope of the production function at a specific point equals the marginal product of labor, but the average slope of the production function does not necessarily equal the average product of labor. Statement B is incorrect because the slope of the ray from the origin to the apex of the production function represents the marginal rate of technical substitution, not the average product of labor. Statement D is incorrect because statement C is true; the average product of labor can be equal to the slope between the origin and a specific point on the production function. The slope of the production function at a specific point equals the marginal product of labor, which is the additional output produced when one more unit of labor is added. The slope between the origin and a specific point on the production function represents the average product of labor, which is the total output produced divided by the total amount of labor used. Therefore, C is the correct statement. A is incorrect because the average slope of the production function would represent the average product of labor and not the slope. B is incorrect because the slope of the ray from the origin to the apex would not necessarily be equal to the average product of labor for all values of L. D is also incorrect because there are certain points on the production function where the slope of the ray from the origin to that point would be equal to the average product of labor.

Question 13

$$\begin{array} { l l } 
\hline \mathrm { L } & \mathrm { Q } \
\hline 0 & 0 \
1 & 20 \
2 & 50 \
3 & 90 \
4 & 125 \
5 & 140 \
6 & 150
\end{array}$$
-Given the table above, the average productivity of the fifth worker is:

Accepted Answer

The average productivity of the fifth worker is calculated by taking the total production (Q) when there are 5 workers (140) and dividing it by the number of workers (5). So, it's 140 / 5 = 28.

Question 14

If marginal product is greater than average product:

Accepted Answer

When marginal product is greater than average product, it means that adding an additional unit of input increases the total product, hence total product must be increasing.

Question 15

Factors of production are:

Accepted Answer

Factors of production refer to the inputs used in the production of goods and services. These inputs include land, labor, capital, and entrepreneurship. Therefore, the correct choice is C) inputs only. Factors of production refer to the inputs used in the production process. These inputs include land, labor, capital, and entrepreneurship. Therefore, the best choice is C, which states that factors of production are inputs only.

Question 16

-*Diminishing marginal returns set in at labor equals:

Accepted Answer

Diminishing marginal returns occur when each additional unit of labor contributes less to output than the previous unit. This typically happens after a certain point of labor input, which is given as 200 in this context.

Question 17

When labor is the only input to the production function, why must it be true that when the marginal product of labor is greater than the average product of labor, the average product of labor is increasing and vice versa?

Accepted Answer

When the marginal product of labor is greater than the average product of labor, it means that the additional unit of labor is producing more output than the average unit of labor. This will increase the average product of labor because the new unit of labor increases the total output by a larger amount than the increase in the number of units of labor. This is the definition of the average product of labor increasing. The opposite is true when the marginal product of labor is less than the average product of labor. When the marginal product of labor is greater than the average product of labor, an additional unit of labor will produce a greater marginal product than average, which means the average product of labor will increase. This is because the additional unit of labor is contributing more to the production of output than the existing units of labor, thus increasing the average product. The opposite is also true: when the marginal product of labor is less than the average product of labor, an additional unit of labor will contribute less to production than the existing units of labor, decreasing the average product of labor. Therefore, only statement A is accurate.

Question 18

-When labor equals 100:

Accepted Answer

The answer of 
-When labor equals 100:
...

Question 19

The labor requirements function is derived from:

Accepted Answer

The labor requirements function is derived from the production function, which shows the relationship between the inputs (including labor) and the outputs of a firm. The production function helps determine how much labor is needed to produce a certain level of output. The labor requirements function is derived from the production function, which shows the relationship between inputs (such as labor and capital) and output. The production function specifies the amount of labor required to produce a given level of output, which forms the basis for determining the labor requirements function. The demand and supply curves and the capital requirement function are not directly related to the labor requirements function.

Question 20

Technically inefficient points are:

Accepted Answer

Technically inefficient points are those that are in the production set (i.e. all feasible combinations of inputs) but not on the production function (i.e. the set of technically efficient combinations of inputs). This means that these points represent input combinations that do not achieve the highest level of output possible given the technology. Points on the production function are technically efficient but not all points in the production set will be on the production function. Points contained in neither the production set nor the production function are not relevant to production possibilities. Points that are never observed in practice are not necessarily technically inefficient.

Quiz 6: Inputs and Production Functions

-Average product reaches a maximum when labor equals:

$\begin{array} { l l } \hline \mathrm { L } & \mathrm { Q } \\\hline 0 & 0 \\1 & 20 \\2 & 50 \\3 & 90 \\4 & 125 \\5 & 140 \\6 & 150\end{array}$ -Given the table above, average productivity is maximized with the ____________ worker.

$\begin{array} { l l } \hline \mathrm { L } & \mathrm { Q } \\\hline 0 & 0 \\1 & 20 \\2 & 50 \\3 & 90 \\4 & 125 \\5 & 140 \\6 & 150\end{array}$ -Given the table above, marginal productivity is maximized with the ___________ worker.

A labor requirements function represents:

Suppose a production function has only one input, labor. What can you tell about the slope of the production function, assuming output is on the y-axis and labor is on the x-axis, if production exhibits constant marginal returns to labor?

The production set represents:

$\begin{array}{ll}\hline \mathrm{L} & \mathrm{Q} \\\hline 0 & 0 \\1 & 20 \\2 & 50 \\3 & 90 \\4 & 125 \\5 & 140 \\6 & 150\end{array}$ -Given the table above, the marginal productivity of the third worker is:

-Marginal product reaches a maximum when labor equals:

The production function represents:

Which one of these is false when compared to the relationship between marginal and average product?

For a simple graph of a production function with Q on the y-axis and L on the x-axis, which of the following statements is true?

$\begin{array} { l l } \hline \mathrm { L } & \mathrm { Q } \\\hline 0 & 0 \\1 & 20 \\2 & 50 \\3 & 90 \\4 & 125 \\5 & 140 \\6 & 150\end{array}$ -Given the table above, the average productivity of the fifth worker is:

If marginal product is greater than average product:

Factors of production are:

-*Diminishing marginal returns set in at labor equals:

When labor is the only input to the production function, why must it be true that when the marginal product of labor is greater than the average product of labor, the average product of labor is increasing and vice versa?

-When labor equals 100:

The labor requirements function is derived from:

Technically inefficient points are:

Quiz 6: Inputs and Production Functions

-Average product reaches a maximum when labor equals:

LQ00120250390412551406150\begin{array} { l l } \hline \mathrm { L } & \mathrm { Q } \\\hline 0 & 0 \\1 & 20 \\2 & 50 \\3 & 90 \\4 & 125 \\5 & 140 \\6 & 150\end{array}L0123456​Q0205090125140150​​ -Given the table above, average productivity is maximized with the ____________ worker.

LQ00120250390412551406150\begin{array} { l l } \hline \mathrm { L } & \mathrm { Q } \\\hline 0 & 0 \\1 & 20 \\2 & 50 \\3 & 90 \\4 & 125 \\5 & 140 \\6 & 150\end{array}L0123456​Q0205090125140150​​ -Given the table above, marginal productivity is maximized with the ___________ worker.

A labor requirements function represents:

Suppose a production function has only one input, labor. What can you tell about the slope of the production function, assuming output is on the y-axis and labor is on the x-axis, if production exhibits constant marginal returns to labor?

The production set represents:

LQ00120250390412551406150\begin{array}{ll}\hline \mathrm{L} & \mathrm{Q} \\\hline 0 & 0 \\1 & 20 \\2 & 50 \\3 & 90 \\4 & 125 \\5 & 140 \\6 & 150\end{array}L0123456​Q0205090125140150​​ -Given the table above, the marginal productivity of the third worker is:

-Marginal product reaches a maximum when labor equals:

The production function represents:

Which one of these is false when compared to the relationship between marginal and average product?

For a simple graph of a production function with Q on the y-axis and L on the x-axis, which of the following statements is true?

LQ00120250390412551406150\begin{array} { l l } \hline \mathrm { L } & \mathrm { Q } \\\hline 0 & 0 \\1 & 20 \\2 & 50 \\3 & 90 \\4 & 125 \\5 & 140 \\6 & 150\end{array}L0123456​Q0205090125140150​​ -Given the table above, the average productivity of the fifth worker is:

If marginal product is greater than average product:

Factors of production are:

-*Diminishing marginal returns set in at labor equals:

When labor is the only input to the production function, why must it be true that when the marginal product of labor is greater than the average product of labor, the average product of labor is increasing and vice versa?

-When labor equals 100:

The labor requirements function is derived from:

Technically inefficient points are:

$\begin{array} { l l } \hline \mathrm { L } & \mathrm { Q } \\\hline 0 & 0 \\1 & 20 \\2 & 50 \\3 & 90 \\4 & 125 \\5 & 140 \\6 & 150\end{array}$ -Given the table above, average productivity is maximized with the ____________ worker.

$\begin{array} { l l } \hline \mathrm { L } & \mathrm { Q } \\\hline 0 & 0 \\1 & 20 \\2 & 50 \\3 & 90 \\4 & 125 \\5 & 140 \\6 & 150\end{array}$ -Given the table above, marginal productivity is maximized with the ___________ worker.

$\begin{array}{ll}\hline \mathrm{L} & \mathrm{Q} \\\hline 0 & 0 \\1 & 20 \\2 & 50 \\3 & 90 \\4 & 125 \\5 & 140 \\6 & 150\end{array}$ -Given the table above, the marginal productivity of the third worker is:

$\begin{array} { l l } \hline \mathrm { L } & \mathrm { Q } \\\hline 0 & 0 \\1 & 20 \\2 & 50 \\3 & 90 \\4 & 125 \\5 & 140 \\6 & 150\end{array}$ -Given the table above, the average productivity of the fifth worker is: