Answer :
In the original economy with 1500 units of capital and 1000 workers, the computer industry uses 800 units of capital and 200 workers, while the shoe industry uses 700 units of capital and 800 workers. In the scenario where the number of workers increases to 1250 while keeping the total capital fixed at 1500, the computer industry will use 1000 units of capital and 250 workers, while the shoe industry will use 500 units of capital and 1000 workers.
A. To solve for the amount of labor and capital used in each industry, we'll use the given information and the equations provided.
Let's denote:
Kc = Capital used in the computer industry
Lc = Labor used in the computer industry
Ks = Capital used in the shoe industry
Ls = Labor used in the shoe industry
From the given information, we have:
Total capital stock (Kc + Ks) = 1500 units
Total labor force (Lc + Ls) = 1000 workers
We also have the equations:
Kc = 4Lc (Computer production requires 4 units of capital per worker)
Ks = 1Ls (Shoe production requires 1 unit of capital per worker)
Using the equations, we can substitute the values and solve for the unknowns.
From the equation Kc = 4Lc, we can substitute Kc in the total capital stock equation:
4Lc + Ks = 1500
From the equation Ks = 1Ls, we can substitute Ks in the total capital stock equation:
4Lc + 1Ls = 1500
Now we can use the equation Lc + Ls = 1000 to solve for the labor variables.
We have a system of equations:
4Lc + 1Ls = 1500
Lc + Ls = 1000
Solving this system of equations will give us the values for Lc, Ls, Kc, and Ks.
B. To solve for the distribution of labor and capital between the two sectors after the increase in the number of workers to 1250 while keeping the total capital fixed at 1500, we need to adjust the equations accordingly.
Let's denote the new labor force as Lc' + Ls' = 1250.
Using the same equations as before:
4Lc' + 1Ls' = 1500
Lc' + Ls' = 1250
Solving this new system of equations will give us the updated values for Lc', Ls', Kc', and Ks'.
Note that the total capital remains fixed at 1500, so Kc' + Ks' = 1500.
By solving the system of equations, we can determine the distribution of labor and capital in each industry after the increase in the number of workers.
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The computer industry uses 800 capital units and 200 workers in the original economy, which had 1500 capital units and 1000 workers, whereas the shoe industry uses 700 capital units and 800 workers.
How does the economy benefit from capital?
In a financial sense, capital also refers to funds made available for a business improvement or expansion. The reason why capital is valuable is because it makes it possible for people to consume more and better goods and services than they otherwise could.
From the given information:
Total capital stock = 1500 units of capital
Total labor force = 1000 workers
We can set up the following equations:
(1) Kc + Ks = total capital stock
(2) Lc + Ls = total labor force
(3) Kc = 4Lc (capital per worker in the computer industry)
(4) Ks = 1Ls (capital per worker in the shoe industry)
Substituting equations (3) and (4) into equation (1), we get:
4Lc + Ls = 1500
Substituting equation (2) into the equation above, we have:
4Lc + (1000 - Lc) = 1500
4Lc + 1000 - Lc = 1500
Lc ≈ 166.67
Substituting Lc back into equation (3), we find:
Kc = 4Lc
Kc ≈ 666.67
Substituting Ls into equation (4), we find:
Ks = 1Ls
Ks ≈ 833.33
B. If the number of workers increases to 1250 while keeping the total capital fixed at 1500, we can solve for the new distribution of labor and capital between the two sectors.
Using equation (2):
Lc + Ls = total labor force
166.67 + Ls = 1250
Ls ≈ 1083.33
Using equation (4):
Ks = 1Ls
Ks ≈ 1083.33
Since the total capital stock is fixed at 1500, we can find the capital used in the computer industry:
Kc = total capital stock - Ks
Kc ≈ 416.67
Therefore, The computer industry will use 1000 units of capital and 250 workers in the scenario where the total amount of capital remains constant at 1500, while the shoe industry will use 500 units of capital and 1000 workers.
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