Chapter . Chapter 4

Work It Out

Chapter 4

true

Suppose there are drastic technological improvements in shoe production at Home such that shoe factories can operate almost completely with computer-aided machines. Consider the following data for the Home country: Computers:
Sales revenue

[MATH: ={P_C}{Q_C}=100](the product of the price and quality in the computer industry, is 100)

Payments to labor

[MATH: =W{L_C}=50](the product of the wage for a unit and quantity of labor in the computer industry is 50)

Payments to capital

[MATH: =R{K_C}=50](payments to capital in the computer industry is 50)

Percentage increase in the price

[MATH: =\frac{\Delta{P_C}}{P_C}=0\%](percentage increase in the price in the computer industry is 0)

Shoes:
Sales revenue

[MATH: ={P_S}{Q_S}=100](the product of the price and quality in the shoe industry, is 100)

Payments to labor

[MATH: =W{L_S}=10](the product of the wage for a unit and quantity of labor in the shoe industry is 10)

Payments to capital

[MATH: =R{K_S}=90](payments to capital in the shoe industry is 90)

Percentage increase in the price

[MATH: =\frac{\Delta{P_S}}{P_S}=40\%](percentage increase in the price for computers in the shoe industry is 40)

Question

true

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Question

true

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Video transcript

Work It Out, Chapter 4, 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 which sector is capital-intensive. To determine this, we will compare the payments ratio to labor and capital in both the computer and shoes sectors by using the basic formula payments to labor in the computer industry divided by payments to capital in the computer industry, WLC to RKC, and payments to labor in the shoe industry divided by payments to capital in the shoe industry, WLS to RKS.

(Description)
The following relations are shown: WL subscript C divided by RK subscript C. WL subscript S divided by RK subscript S.

(Speaker)
Now we will add the given data into each equation: payments to labor in the computer industry, WLC equals 50, payments to capital in the computer industry, RKC = 50. Therefore, the ratio of payments to labor to capital in the computer industry, WLC to RKC equals 50 to 50. Payments to labor in the shoe industry, WLS equals 10, payments to capital in the shoe industry, RKS equals 90 Therefore, the ratio of payments to labor to capital in the shoe industry, WLS to RKS equals 10 to 90.

(Description)
The data inserted into the equations as following: WL subscript C divided by RK subscript C equals 50 divided by 50. WL subscript S divided by RK subscript S equals 10 divided by 90.

(Speaker)
We now compare the values to determine the relationship and find that the ratio of payments to labor to payments to capital in the computer industry, WLC to RKC, is greater than the ratio of payments to labor to payments to capital in the shoe industry, WLS to RKS.

(Description)
The following text is written: Compare the two equations to determine the greater than sign, less than sign, equals sign relationship: 50 divided by 50 is greater than 10 divided by 90.

(Speaker)
Since the ratio of payments to labor to payments to capital in the computer industry, WLC to RKC, is greater than the ratio of payments to labor to payments to capital in the shoe industry, WLS to RKS, this implies that the labor to capital ratio in the computer industry, LC to KC, is greater than labor to capital ratio in the shoe industry, LS to KS. The production of shoes is therefore capital-intensive.

(Description)
The following text is added below the previous relations: WL subscript C divided by RK subscript C is greater than WL subscript S divided by RK subscript S, which implies L subscript C divided by K subscript C is greater than L subscript S divided by K subscript S; therefore, the computer industry is labor-intensive, and the shoe industry is capital-intensive.

(Speaker)
This is a reasonable question, even though the same industry can be capital-intensive in one country and labor-intensive in another, because the factor intensities will allow us to determine the effect that international trade will have on real wages and rental within each country.

Question

b. Given the percentage changes in output prices in the data provided, calculate the percentage change in the rental on capital.

The percentage change in the rental on capital is l8Hq3ROuRJEy1566eq/tfQTQJ4JqQAuqAHkCE/RtPgl3iJOD36tHdw== %.

Correct.

[MATH: \frac{\Delta{R}}{R}=\frac{\left(\frac{\Delta{P_C}}{P_C}\right)({P_C}{Q_C})-\left(\frac{\Delta{W}}{W}\right)(W{L_C})}{R{K_C}}](the percentage change in the rental rate on capital is equal to the percentage change in price multiplied by the sales revenue, minus the percentage change in the wage multiplied by the payments to labor, all divided by the payments to capital)

, for computers

[MATH: \frac{\Delta{R}}{R}=\frac{\left(\frac{\Delta{P_S}}{P_S}\right)({P_S}{Q_S})-\left(\frac{\Delta{W}}{W}\right)(W{L_S})}{R{K_S}}](the percentage change in the rental rate on capital is equal to the percentage change in price multiplied by the sales revenue, minus the percentage change in the wage multiplied by the payments to labor, all divided by the payments to capital)

, for shoes

Inserting the data for computers and shoes into these formulas:

[MATH: \frac{\Delta{R}}{R}=\frac{(0\%)(100)-(\frac{\Delta{W}}{W})(50)}{50}](the percentage change in the rental rate on capital is equal to the 0 percent multiplied by the 100, minus the percentage change in the wage multiplied by the 50, all divided by 50)

, for computers

[MATH: -\frac{\Delta{W}}{W}](is equal to minus percantage change in wage)

[MATH: \frac{\Delta{R}}{R}=\frac{(40\%)(100)-(\frac{\Delta{W}}{W})(10)}{90}](the percentage change in the rental rate on capital is equal to the 40 percent multiplied by the 100, minus the percentage change in the wage multiplied by 10, all divided by 90)

, for shoes

[MATH: \frac{40}{90}-\frac{\Delta{W}}{W}{\left(\frac{10}{90}\right)}](is equal to minus percantage change in wage)

Substituting the computer equation into the shoes equation:

[MATH: \frac{\Delta{R}}{R}=\frac{40}{90}+\frac{\Delta{R}}{R}{\left(\frac{10}{90}\right)} = \frac{\Delta{R}}{R}{\left(\frac{80}{90}\right)} = \frac{40}{90}](is equal to 40 by 90 minus percentage in wage times 10 by 90)

[MATH: =\frac{40}{80}=50\%](equals 40 by 80 equals 50 percent)

This implies:

[MATH: =\frac{\Delta{W}}{W}=-\frac{\Delta{R}}{R}=-50\%](percentage change in the wage equals minus the percentage change in the rental rate on capital equals minus 50 percent)

Incorrect.

[MATH: \frac{\Delta{R}}{R}=\frac{\left(\frac{\Delta{P_C}}{P_C}\right)({P_C}{Q_C})-\left(\frac{\Delta{W}}{W}\right)(W{L_C})}{R{K_C}}](the percentage change in the rental rate on capital is equal to the percentage change in price multiplied by the sales revenue, minus the percentage change in the wage multiplied by the payments to labor, all divided by the payments to capital)

, for computers

[MATH: \frac{\Delta{R}}{R}=\frac{\left(\frac{\Delta{P_S}}{P_S}\right)({P_S}{Q_S})-\left(\frac{\Delta{W}}{W}\right)(W{L_S})}{R{K_S}}](the percentage change in the rental rate on capital is equal to the percentage change in price multiplied by the sales revenue, minus the percentage change in the wage multiplied by the payments to labor, all divided by the payments to capital)

, for shoes

Inserting the data for computers and shoes into these formulas:

[MATH: \frac{\Delta{R}}{R}=\frac{(0\%)(100)-(\frac{\Delta{W}}{W})(50)}{50}](the percentage change in the rental rate on capital is equal to the 0 percent multiplied by the 100, minus the percentage change in the wage multiplied by the 50, all divided by 50)

, for computers

[MATH: -\frac{\Delta{W}}{W}](is equal to minus percantage change in wage)

[MATH: \frac{\Delta{R}}{R}=\frac{(40\%)(100)-(\frac{\Delta{W}}{W})(10)}{90}](the percentage change in the rental rate on capital is equal to the 40 percent multiplied by the 100, minus the percentage change in the wage multiplied by 10, all divided by 90)

, for shoes

[MATH: \frac{40}{90}-\frac{\Delta{W}}{W}{\left(\frac{10}{90}\right)}](is equal to minus percantage change in wage)

Substituting the computer equation into the shoes equation:

[MATH: \frac{\Delta{R}}{R}=\frac{40}{90}+\frac{\Delta{R}}{R}{\left(\frac{10}{90}\right)} = \frac{\Delta{R}}{R}{\left(\frac{80}{90}\right)} = \frac{40}{90}](is equal to 40 by 90 minus percentage in wage times 10 by 90)

[MATH: =\frac{40}{80}=50\%](equals 40 by 80 equals 50 percent)

This implies:

[MATH: =\frac{\Delta{W}}{W}=-\frac{\Delta{R}}{R}=-50\%](percentage change in the wage equals minus the percentage change in the rental rate on capital equals minus 50 percent)

Video transcript

Work It Out, Chapter 4, Question 2

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

(Speaker)
This problem is asking you to identify the percentage change in the rental on capital, given the percentage change in output prices provided. In order to find this, we use the basic formula for the percentage change in rental on capital for each sector, computers and shoes. The formula is the percentage change in price multiplied by the sales revenue, minus the percentage change in the wage multiplied by the payments to labor, all divided by the payments to capital.

(Description)
The following formulas are written: The change in R divided by R equals the change in P subscript C divided by P subscript C multiplied by P subscript C multiplied by Q subscript C minus the change in W divided by W multiplied by WL subscript C, all divided by RK subscript C, for computers. The change in R divided by R equals the change in P subscript S divided by P subscript S multiplied by P subscript S multiplied by Q subscript S minus the change in W divided by W multiplied by WL subscript S, all divided by RK subscript S, for shoes.

(Speaker)
Now let’s put the numbers into our equations.

(Description)
The following equations are shown: The change in R divided by R equals the 0 percent multiplied by 100 minus the change in W divided by W multiplied by 50, all divided by 50 equals minus the change in W divided by W, for computers. The change in R divided by R equals the 40 percent multiplied by 100 minus the change in W divided by W multiplied by 10, all divided by 90 equals 40 divided by 90 minus the change in W divided by W multiplied by 10 divided by 90, for shoes.

(Speaker)
Now we can substitute our computer equation into our shoes equation and solve it. The percentage change in the rental rate on capital is 50 percent.

(Description)
The following text and equation are written below the previous equations: Substitute the equation for computers into the equation for shoes: The change in R divided by R equals 40 divided by 90 plus the change in R divided by R multiplied by 10 divided by 90 equals the change in R divided by R multiplied by 80 divided by 90 equals 40 divided by 90 equals 40 divided by 80 equals 50 percent.

(Speaker)
Because we know that the percentage change in R over R equals the negative percentage change in W over W, we can determine how the percentage change in the rental rate on capital compares to the percentage change in the wage, which is negative 50 percent.

(Description)
The following equation is written below the previous one: The change in R divided by R equals the negative change in W divided by W equals negative 50 percent.

Question

ridGxEQBICEDrUDalF2AKfl0/XB7epbxMfjjrd+5nUEDesLnoD0VfwN1q5bp7Z2Wwn3CfnFOR8hcgjYlkqhF5WXfbbaxe607aUZMKoyZcyUhlnA4luoW+z1xUsPeRn20nVv9vOJF4OoiR0uS80NkYRNlKeupob0a5NzuD2CLfJPhs0icX9CHDknrfNvu3PSmv/UWNtuNEkeFwfC7MAtBRcurFY+haiLM6ut2/iUpqEHVAneGKBq5DhQxQ2+h5NP8RhxIYqknHwKW90P/0QP552Q0NfbZ3hOCGbVkg8MIITmeONgoqBCrR3qi780P/2x7TRjNqR4ddHlbGxvEtha3YcxiHyqnGa0YIK8Q9XLJpZXZAyjwdR6/LMdvTbNLPs1z

Video transcript

Work It Out, Chapter 4, Question 3

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

(Speaker)
Now we will determine how the magnitude of the percentage change in the rental rate on capital compares to the percentage change in the wage paid to labor.

(Description)
The following equation is briefly written: The change in R divided by R equals the negative change in W divided by W equals negative 50 percent.

(Description)
The following equation is written: The change in R divided by R equals the negative change in W divided by W.

(Speaker)
Using our previous solution and the formula, we can see that the rental rate on capital increased 50 percent and the wage decreased by 50 percent.

(Description)
The following equations are added below the previous one: 50 percent equals the negative change in W divided by W. The negative change in W divided by equals negative 50 percent.

(Speaker)
The magnitude of the change is therefore the same, but with the opposite sign.

Question

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Question

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Video transcript

Work It Out, Chapter 4, Question 4

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

(Speaker)
Now we will determine what factor gains in real terms, and what factor loses.

(Description)
The equations from the previous slide are briefly shown.

(Speaker)
We will start by looking at the percentage changes in output prices. The price of computers was unchanged, and the price of shoes increased by 40 percent.

(Description)
The following equations are written: The change in P subscript C divided by P subscript C equals 0 percent. The change in P subscript S divided by P subscript S equals 40 percent.

(Speaker)
Now let’s look at the percentage changes in the rental rate on capital and wages. The rental rate on capital increased 50 percent, and the wage decreased by 50 percent.

(Description)
The following equations are written below the previous ones: The change in R divided by R equals 50 percent. The change in W divided by W equals negative 50 percent.

(Speaker)
In real terms, which factor gained, and which factor lost? Well, because the increase in capital returns, plus 50 percent, exceeds the price changes in both sectors, capital gains in real terms.

(Description)
The following relation is written below the equations: The change in R divided by R is greater than both the change in P subscript C divided by P subscript C equals and the change in P subscript S divided by P subscript S.

(Speaker)
Similarly, because there is a decrease in wages, negative 50 percent, and the prices of outputs in computers remained the same and increased for shoes, labor loses in real terms.

(Description)
The following relation is written below the previous one: The change in W divided by W is less than both the change in P subscript C divided by P subscript C equals and the change in P subscript S divided by P subscript S.

(Speaker)
Are these the results consistent with the Stolper–Samuelson theorem? Recall that, according to the theorem, an increase in the relative price of a good will cause the real earnings of labor and capital to move in opposite directions, with a rise in the real earnings of the factor used intensively in the industry whose relative price went up and a decrease in the real earnings of the other factor. Therefore, our results are consistent with the theorem.

(Description)
The following text is written: Stolper–Samuelson theorem: An increase in the price of a good will cause an increase in the price of the factor used intensively in that industry and a decrease in the price of the other factor.