Chapter 3. Chapter 3

Work It Out
Chapter 3
true
true
Use the information given here to answer the following questions:
Manufacturing:
Sales revenue [MATH: ={P_M}\cdot{Q_M}=150](the price of manufacturing multiplied by the quantity of manufacturing, is 150)
Payments to labor [MATH: ={W}\cdot{L_M}=100](the wage multiplied by the quantity of labor employed in manufacturing, are 100)
Payments to capital [MATH: ={R_K}\cdot{K}=50](the rental rate on capital multiplied by the quantity of capital used in manufacturing, are 50)
Agriculture:
Sales revenue [MATH: ={P_A}\cdot{Q_A}=150](the price of agriculture multiplied by the quantity of agriculture, is 150)
Payments to labor [MATH: ={W}\cdot{L_A}=50](the wage multiplied by the quantity of labor employed in agriculture, are 50)
Payments to land [MATH: ={R_T}\cdot{T}=100](the rental rate on land multiplied by the quantity of land used in agriculture, are 100)
Holding the price of manufacturing constant, suppose the increase in the price of agriculture is 20% and the increase in the wage is 10%.

Question


a. Determine the impact of the increase in the price of agriculture on the rental on land and the rental on capital.
Rental on land = 76DelKIjUhqY1Hf3i/7ydOQLkYLR3IKu4IChqWq8iZ4YfJCDs/UPB1bRlUVg8cc9mA20XUvKXec= %
Rental on capital = rRNKpJEhKn7/IaCuDyn073mgAZk4M6Mvx8PJBqalzpV4/mu5wfxOjQ== %
Correct. Rental on land can be calculated as follows:

[MATH: \frac{\Delta {R_T}}{R_T}=\frac{(\frac{\Delta {P_A}}{P_A})\cdot{P_A}\cdot{Q_A}-(\Delta W - W)\cdot{W}\cdot{L_A}}{{R_T}\cdot{T}}](the percentage change in rental rate on land is equal to the percentage change in the price of agriculture multiplied by the price of agriculture multiplied by the quantity of agriculture, which is the sales revenue, minus the percentage change in the wage multiplied by the wage multiplied by the quantity of labor employed in agriculture, which are the payments to labor, all divided by the rental rate on land multiplied by the quantity of land used in agriculture, which are the payments to land.)
[MATH: \frac{\Delta {R_T}}{R_T}=\frac{20\%\cdot{150}-10\%\cdot{50}}{100}=25\%](the percentage change in rental rate on land is equal to change in price in agriculture which is 20%, the sales revenuewhich is 150, the change in the wage which is 10%, the payments to labor which are 50, and the payments to land which equal 100 to 25 %)
Recalling that the price of manufacturing remained constant, we get the rental on capital as:
[MATH: \Delta{R_K} = \frac{0\cdot{Q_M}-\Delta{W}\cdot{L_M}}{K}](the percentage change in rental rate on capital is equal to 0 multiplied by quantity of manufacturing minus the percentage change in the wage multiplied by the quantity of labor employed in manufacturing all divided by the quantity of capital used in manufacturing)
[MATH: \frac{\Delta{R_K}}{R_K} = \frac{-\Delta{W}}{W}\cdot{\frac{W\cdot{L_M}}{R_K\cdot{K}}}](the percentage change in rental rate on capital is equal to the percentage change in the wage multiplied by the ratio of the wage multiplied by the quantity of labor employed in manufacturing and rental rate on capital multiplied by the quantity of capital used in manufacturing)
[MATH: \frac{\Delta{R_K}}{R_K} = -10\%\cdot{\frac{100}{50}}=-20\%](the ratio of the percentage change in rental rate on capital and the rental rate on capital is equal to minus 10 percent multiplied by 100 divided by 50 which equals minus 20 percent )
Incorrect. Rental on land can be calculated as follows:

[MATH: \frac{\Delta {R_T}}{R_T}=\frac{(\frac{\Delta {P_A}}{P_A})\cdot{P_A}\cdot{Q_A}-(\Delta W - W)\cdot{W}\cdot{L_A}}{{R_T}\cdot{T}}](the percentage change in rental rate on land is equal to the percentage change in the price of agriculture multiplied by the price of agriculture multiplied by the quantity of agriculture, which is the sales revenue, minus the percentage change in the wage multiplied by the wage multiplied by the quantity of labor employed in agriculture, which are the payments to labor, all divided by the rental rate on land multiplied by the quantity of land used in agriculture, which are the payments to land.)
[MATH: \frac{\Delta {R_T}}{R_T}=\frac{20\%\cdot{150}-10\%\cdot{50}}{100}=25\%](the percentage change in rental rate on land is equal to change in price in agriculture which is 20%, the sales revenuewhich is 150, the change in the wage which is 10%, the payments to labor which are 50, and the payments to land which equal 100 to 25 %)
Recalling that the price of manufacturing remained constant, we get the rental on capital as:
[MATH: \Delta{R_K} = \frac{0\cdot{Q_M}-\Delta{W}\cdot{L_M}}{K}](the percentage change in rental rate on capital is equal to 0 multiplied by quantity of manufacturing minus the percentage change in the wage multiplied by the quantity of labor employed in manufacturing all divided by the quantity of capital used in manufacturing)
[MATH: \frac{\Delta{R_K}}{R_K} = \frac{-\Delta{W}}{W}\cdot{\frac{W\cdot{L_M}}{R_K\cdot{K}}}](the percentage change in rental rate on capital is equal to the percentage change in the wage multiplied by the ratio of the wage multiplied by the quantity of labor employed in manufacturing and rental rate on capital multiplied by the quantity of capital used in manufacturing)
[MATH: \frac{\Delta{R_K}}{R_K} = -10\%\cdot{\frac{100}{50}}=-20\%](the ratio of the percentage change in rental rate on capital and the rental rate on capital is equal to minus 10 percent multiplied by 100 divided by 50 which equals minus 20 percent )
Video transcript

Work It Out, Chapter 3, Question 1

(Transcript of audio with descriptions. Transcript includes narrator headings and description headings of the visual content)

(Speaker)
This problem will ask you to determine the impact of the increase in the price of agriculture on the rental of land and the rental on capital.

(Description)
The following text is written: Manufacturing: Sales revenue equals P subscipt M times Q subscipt M equals 150. Payments to labor equals W times L subscipt M equals 100. Payments to capital equals R subscript K times K equals 50. Agriculture: Sales revenue equals P subscript A times Q subscript A equals 150. Payments to labor equals W times L subscript A equals 50. Payments to land equals R subscript T times T equals 100.

(Speaker)
Let’s look at the information given. For manufacturing, the sales revenue, which is equal to the price of manufacturing multiplied by the quantity of manufacturing, is 150. Payments to labor in manufacturing, which are equal to the wage multiplied by the quantity of labor employed in manufacturing, are 100. Payments to capital, which are equal to the rental rate on capital multiplied by the quantity of capital used in manufacturing, are 50. For agriculture, the sales revenue, which is equal to the price of agriculture multiplied by the quantity of agriculture, is 150. Payments to labor in agriculture, which are equal to the wage multiplied by the quantity of labor employed in agriculture, are 50. Payments to land, which are equal to the rental rate on land multiplied by the quantity of land used in agriculture, are 100.

(Description)
The following text is added below the previous one: Holding the price of manufacturing constant, suppose the increase in the price of agriculture is 20 percent and the increase in the wage is 10 percent.

(Speaker)
We also know that the price of manufacturing is held constant, the price of agriculture increases by 20 percent, and the wage increases by 10 percent. Now let’s take the information given and determine the impact of the 20% increase in the price of agriculture on the rental of land and the rental on capital.

(Description)
The following formula is shown: The change in R subscript T divided by R subscript T equals the change in P subscript A over P subscript A multiplied by P subscript A multiplied by Q subscript A minus the difference of the change in W and W multiplied by W multiplied by L subscript A, all divided by R subscript T multiplied by T.

(Speaker)
We’ll start by using our formula for the rental rate on land, which is equal to the percentage change in the price of agriculture multiplied by the price of agriculture multiplied by the quantity of agriculture, which is the sales revenue, minus the percentage change in the wage multiplied by the wage multiplied by the quantity of labor employed in agriculture, which are the payments to labor, all divided by the rental rate on land multiplied by the quantity of land used in agriculture, which are the payments to land. Now we can substitute the information we’ve been given into the formula and calculate the impact of the increase in the price of agriculture on the rental of land.

(Description)
The following formula is added below the previous one: The change in R subscript T divided by R subscript T equals 20 percent multiplied by 150 percent minus 10 percent multiplied by 50 percent, all divided by 100 equals 25 percent.

(Speaker)
We know that the change in price in agriculture is 20 percent, the sales revenue is 150, the change in the wage is 10 percent, the payments to labor are 50, and the payments to land are 100. We can now solve our equation and find that the rental on land will increase 25 percent due to the increase in the price of agriculture. Now let’s determine the impact of the increase in the price of agriculture on the rental of capital.

(Description)
The following formula is shown: The change in R subscript K equals 0 multiplied by Q subscript M minus the change in W multiplied by L subscript M, all divided by K.

(Speaker)
Recall that the price of capital is held constant, so the percentage change in wage will be 0. Reordering our terms, we can calculate the change in the rental of capital by substituting and solving our equation.

(Description)
The following equations are added below the previous one: The change in R subscript K divided by R subscript K equals the negative change in W divided by W multiplied by W divided by R subscript K multiplied by L subscript M divided by K. The change in R subscript K divided by R subscript K equals negative 10 percent multiplied by 100 divided by 50 equals negative 20 percent.

(Speaker)
Doing this yields an answer of negative 20 percent, which is the percentage change in the rental rate on capital as a result of the increase in the price of agriculture.

Work It Out
Chapter 4
true
true

Question

Next goes the question with several drop-downs to be filled-in b. j0RPJbrOCM13eHr/3Z6fA/rM0olisCx6qENRQtUEF0hc/xx7cREUJRPWkkn1QoNeXpu6Kiygssmtw/0Sqb93oPZ5nbVyCURUen9joyqJ4MxNxjMP6oekBA5Zp35sNjmdLu7+DsM5ZkGgPBlszXTpbBvogFsL03nqynsOL/IuCTfkG80MiWnaIQ== ZtgEXr/Tug4DBkgvU9sUlVs+YYKUeaCkaFZtawmtny7cJYnRFfNVpanlqTGQ+INjPUfsOq1BOQY= PYSyMWVC8eUEGFrh59oKyS8Aq41/BsTdYriTxgRiR/ifTSUr2eRTCK6oMyzAKaV2NqHwmM6/LhTap6iZaNjZp+bB43YjoDLAAFSdUwaWKqkFRJRz. iaOSvaUAfYctfOOuWI6QzkJTEZfkau8EuBQw7pccL6rS+eQ3o3agYOpNRNkqoLSDLmVucLChK0mlmwYK5i2oKFfyJCcjepFWem697ajVlugmfH9ZPpHDug==
Correct. Because of the 20% increase in the price of agriculture, the real rental on land rose, whereas the real rental on capital fell. Therefore, landowners are better off because the percentage increase in the rental on land is greater than the percentage increase in the price of agriculture, whereas the price of manufacture is constant. Capital owners are worse off in terms of their ability to purchase both manufacture and agriculture because the rental to capital has fallen.

Real rental on capital falls, the change in the real wage is ambiguous, and real rental on land rises:

[MATH: \frac{\Delta{R_K}}{R_K} < 0 < \frac{\Delta{W}}{W} < \frac{\Delta{P_A}}{P_A} < \frac{\Delta{R_T}}{R_T}](the percentage change in the rental on capital is less than 0 and less than the percentage increase in the wage which is less than the percentage increase in the price of agriculture and the percantage increase in the price of agriculture) , for an increase in [MATH: P_A](the price of agriculture) .
Incorrect. Because of the 20% increase in the price of agriculture, the real rental on land rose, whereas the real rental on capital fell. Therefore, landowners are better off because the percentage increase in the rental on land is greater than the percentage increase in the price of agriculture, whereas the price of manufacture is constant. Capital owners are worse off in terms of their ability to purchase both manufacture and agriculture because the rental to capital has fallen.

Real rental on capital falls, the change in the real wage is ambiguous, and real rental on land rises:

[MATH: \frac{\Delta{R_K}}{R_K} < 0 < \frac{\Delta{W}}{W} < \frac{\Delta{P_A}}{P_A} < \frac{\Delta{R_T}}{R_T}](the percentage change in the rental on capital is less than 0 and less than the percentage increase in the wage which is less than the percentage increase in the price of agriculture and the percantage increase in the price of agriculture) , for an increase in [MATH: P_A](the price of agriculture) .
Video transcript

Work It Out, Chapter 3, Question 2

(Transcript of audio with descriptions. Transcript includes narrator headings and description headings of the visual content)

(Speaker)
This problem asks you to explain what has happened to the real rental on land and the real rental on capital. We’re given the percentage increase in the price of agriculture as 20 percent and the percentage increase in the wage as 10 percent. We’ve solved the percentage change in the rental on land as a result of the increase in the price of agriculture as 25 percent and the percentage change in the rental on capital as a result of the increase on the price of agriculture as negative 20 percent.

(Description)
The following relations are written: The change in P subscript A divided by P subscript A equals 20 percent. The change in W divided by W equals 10 percent. The change in R subscript T divided by R subscript T equals 25 percent. The change in R subscript K divided by R subscript K equals negative 20 percent.

(Speaker)
Because of the 20 percent increase in the price of agriculture, the real rental on land rose, whereas the real rental on capital fell. Therefore, landowners are better off because the percentage increase in the rental on land is greater than the percentage increase in the price of agriculture, whereas the price of manufacture is constant. Capital owners are worse off in terms of their ability to purchase both manufacture and agriculture because the rental to capital has fallen.

(Description)
The following relation is added below the previous ones: The change in R subscript K divided by R subscript K is less than 0 is less than the change in W divided by W is less than the change in P subscript A divided by P subscript A is less than the change in R subscript T divided by R subscript T, for an increase in P subscript A.

(Speaker)
Real rental on capital falls, the change in the real wage is ambiguous, and real rental on land rises.