Work It Out, Chapter 5, 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 solve for the amount of capital and labor used in each industry. Let’s look at the information given.

(Description)
The following equations are written: K subscript C equals 4 times L subscript C. K subscript S equals 0.2 times L subscript S. The following text is written below the equations: There are 200 workers and 200 units of capital in the economy.

(Speaker)
We’re told that computers use 4 units of capital for each worker so that capital in the computer industry is equal to 4 multiplied by the quantity of labor in the computer industry, or KC equals 4 times LC. Shoes use 0.2 units of capital for each worker so that capital in the shoe industry is equal to 0.2 multiplied by the quantity of labor in the shoe industry, or KS equals 0.2 times LS. Finally, we’re told that there are 200 workers and 200 units of capital in the economy. We’re also given a hint on how to solve the problem. We’re reminded that the amount of labor and capital used in the production of each good must add up to the total for the economy. Therefore, capital in the computer industry plus capital in the shoe industry must equal 200. This can be expressed by the following formula: KC plus KS equals 200.

(Description)
The following equation is written below the previous text: K subscript C plus K subscript S equals 200.

(Speaker)
Similarly, labor in the computer industry plus labor in the shoe industry must equal 200, which can be expressed as LC plus LS equals 200.

(Description)
The following equation is written below the previous one: L subscript C plus L subscript S equals 200.

(Speaker)
We can use the facts that KC equals 4 times LC and KS equals 0.2 times LS to rewrite these equations as: 4 times LC plus 0.2 times LS equals 200 and LC plus LS equals 200.

(Description)
The following text is written: Use the facts that K subscript C equals 4 times L subscript C and K subscript S equals 0.2 times L subscript S to rewrite these equations as: 4 times L subscript C plus 0.2 times L subscript S equals 200 and L subscript C plus L subscript S equals 200.

(Speaker)
We can now use these two equations to solve for LC and LS and then calculate the amount of capital used in each industry using KC equals 4 times LC and KS equals 0.2 times LS. Now let’s solve to find the amount of labor and capital used in each industry. We have two equations and two unknowns, so we can multiply our second equation by 4 and then subtract to eliminate one of our unknowns. This allows us to solve for LS.

(Description)
The following equations are written: 4 times L subscript C plus 0.2 times L subscript S equals 200. 4 times L subscript C plus 4 times L subscript S, all divided by negative 3.8 times L subscript S equals 800 divided by negative 600.

(Speaker)
LS equals 600 divided by 3.8 equals 157.9. It follows from the same equations that LC equals 42.1 and that KC equals 4 times LC equals 168.4 and KS equals 0.2 times LS equals 31.6.

(Description)
The following equations are written: L subscript S equals 600 divided by 3.8 equals 157.9. L subscript C plus L subscript S equals 200 equals L subscript C plus 157.9 equals 200 equals L subscript C equals 42.1. K subscript C equals 4 times L subscript C equals 4 times 41.2 equals 168.4. K subscript S equals 0.2 times L subscript S equals 0.2 times 157.9 equals 31.6.

Work It Out, Chapter 5, Question 2

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

(Speaker)
This problem will ask you to again solve for the amount of capital and labor used in each industry, but in this case, the number of workers in the economy has increased from 200 to 250 due to immigration. Let’s recall the information given. We’re told that computers use 4 units of capital for each worker so that capital in the computer industry is equal to 4 multiplied by the quantity of labor in the computer industry, or KC equals 4 times LC. Shoes use 0.2 units of capital for each worker so that capital in the shoe industry is equal to 0.2 multiplied by the quantity of labor in the shoe industry, or KS equals 0.2 times LS. Finally, we’re told that there are now 250 workers and 200 units of capital in the economy.

(Description)
The following equations are written: K subscript C equals 4 times L subscript C. K subscript S equals 0.2 times L subscript S. The following text is written below the equations: There are 250 workers and 200 units of capital in the economy.

(Speaker)
We’re reminded to use the same equations we used in part a but to make sure to use the new quantity in labor in the economy in our formula. Labor in the computer industry plus labor in the shoe industry is equal to 250, LC plus LS equals 250.

(Description)
The following equations are written below the previous text: K subscript C plus K subscript S equals 200. L subscript C plus L subscript S equals 250. The following text is written below the equations: Use the facts that K subscript C equals 4 times L subscript C and K subscript S equals 0.2 times L subscript S to rewrite these equations as: 4 times L subscript C plus 0.2 times L subscript S equals 200 and L subscript C plus L subscript S equals 250.

(Speaker)
Now let’s solve to find the amount of labor and capital used in each industry. We have two equations and two unknowns, so we can multiply our second equation by 4 and then subtract to eliminate one of our unknowns. This allows us to solve for LS.

(Description)
The following equations are written: 4 times L subscript C plus 0.2 times L subscript S equals 200. 4 times L subscript C plus 4 times L subscript S, all divided by negative 3.8 times L subscript S equals 1000 divided by negative 800.

(Speaker)
LS equals 800 divided by 3.8 equals 210.5. It follows from the same equations that LC equals 39.5, and that KC equals 4 times LC equals 158 and KS equals 0.2 times LS equals 42.

(Description)
The following equations are written: L subscript S equals 800 divided by 3.8 equals 210.5. L subscript C plus L subscript S equals 250 equals L subscript C plus 210.5 equals 250 equals L subscript C equals 39.5. K subscript C equals 4 times L subscript C equals 4 times 39.5 equals 158. K subscript S equals 0.2 times L subscript S equals 0.2 times 210.5 equals 42.

Work It Out, Chapter 5, Question 3

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

(Speaker)
This problem will ask you to again solve for the amount of capital and labor used in each industry, but in this case, the amount of capital in the economy has increased from 200 to 250 due to foreign direct investment (FDI). We’re told that computers use 4 units of capital for each worker so that capital in the computer industry is equal to 4 multiplied by the quantity of labor in the computer industry, or KC equals 4 times LC. Shoes use 0.2 units of capital for each worker so that capital in the shoe industry is equal to 0.2 multiplied by the quantity of labor in the shoe industry, or KS equals 0.2 times LS. Finally, we’re told that there are 200 workers and now 250 units of capital in the economy.

(Description)
K subscript C equals 4 times L subscript C. K subscript S equals 0.2 times L subscript S. The following text is written below the equations: There are 200 workers and 250 units of capital in the economy.

(Speaker)
We’re reminded to use the same equations we used in part a but to make sure to use the new quantity in capital in the economy in our formula. Capital in the computer industry plus capital in the shoe industry is equal to 250, KC plus KS equals 250.

(Description)
The following equations are written below the previous text: K subscript C plus K subscript S equals 250. L subscript C plus L subscript S equals 200. The following text is written below the equations: Use the facts that K subscript C equals 4 times L subscript C and K subscript S equals 0.2 times L subscript S to rewrite these equations as: 4 times L subscript C plus 0.2 times L subscript S equals 250 and L subscript C plus L subscript S equals 200.

(Speaker)
Now let’s solve to find the amount of labor and capital used in each industry. We have two equations and two unknowns, so we can multiply our second equation by 4 and then subtract to eliminate one of our unknowns. This allows us to solve for LS.

(Description)
The following equations are written: 4 times L subscript C plus 0.2 times L subscript S equals 250. 4 times L subscript C plus 4 times L subscript S, all divided by negative 3.8 times L subscript S equals 800 divided by negative 550.

(Speaker)
LS equals 550 divided by 3.8 equals 144.7. It follows from the same equations that LC equals 55.3 and that KC equals 4 times LC equals 221 and KS equals 0.2 times LS equals 29.

(Description)
The following equations are written: L subscript S equals 550 divided by 3.8 equals 144.7. L subscript C plus L subscript S equals 200 equals L subscript C plus 144.7 equals 200 equals L subscript C equals 55.3. K subscript C equals 4 times L subscript C equals 4 times 55.3 equals 221. K subscript S equals 0.2 times L subscript S equals 0.2 times 144.7 equals 29.

Work It Out, Chapter 5, Question 4

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

(Speaker)
This problem will ask you to explain how your results in parts b and c are related to the Rybczynski theorem. Let’s look at part b first. Recall that the production of shoes is labor-intensive and the production of computers is capital-intensive. Comparing part a with part b, the increase in the amount of labor in the economy has increased the amount of labor and capital devoted to shoes (from LS equals 157.9 and KS equals 31.6 to LS equals 210.5 and KS equals 42) and decreased the amount of labor and capital devoted to computers (from LC equals 42.1 and KC equals 168.4 to LC equals 39.5 and KC equals 158).

(Description)
The following text is written: Shoe Industry. (a) L subscript S equals 157.9, K subscript S equals 31.6. (b) L subscript S equals 210.5, K subscript S equals 42. Computer Industry. (a) L subscript C equals 42.1, K subscript C equals 168.4. (b) L subscript C equals 39.5, K subscript C equals 158.

(Speaker)
Therefore, the output of shoes increases, and the output of computers decreases due to the overall increase in labor. Shoes are labor-intensive because they use 0.2 units of capital per unit labor; computers are capital-intensive because they use 4 units of capital per unit of labor. So the change in outputs is in accordance with the Rybczynski theorem; the increase in labor has increased the output of the labor-intensive good and decreased the output of the other good. Now let’s look at part c. Comparing part a with part c, there has been an increase in the amount of capital in the economy. Consistent with the Rybczynski theorem, there has been a rise in the amount of capital and labor devoted to computer production (from LC equals 42.1 and KC equals 168.4 to LC equals 55.3 and KC equals 221) and a fall in the amount of labor and capital devoted to shoe production (from LS equals 157.9 and KS equals 31.6 to LS equals 144.7 and KS equals 29).

(Description)
The following text is written: Shoe Industry. (a) L subscript S equals 157.9, K subscript S equals 31.6. (c) L subscript S equals 144.7, K subscript S equals 29. Computer Industry. (a) L subscript C equals 42.1, K subscript C equals 168.4. (c) L subscript C equals 55.3, K subscript C equals 221.