Suppose that computers use 4 units of capital for each worker so that the capital in the computer industry is equal to 4 multiplied by the quantity of labor in the computer industry whereas shoes use 0.2 units of capital for each worker so that the capital in the shoe industry is equal to 0.2 multiplied by the quantity of labor in the shoe industry . There are 200 workers and 200 units of capital in the economy.
a. Solve for the amount of labor and capital in each industry.Hint: The box diagram shown in Figure 5-6 indicates that the amount of labor and capital used in each industry must add up to the total for the economy so that:
the capital in the computer industry plus capital in the shoe industry equals 200 and the labor in the computer industry plus labor in the shoe industry must equal 200
Use the facts that the capital in the computer industry is equal to 4 multiplied by the quantity of labor in the computer industry and the capital in the shoe industry is equal to 0.2 multiplied by the quantity of labor in the shoe industry
to rewrite these equations as:
4 times quantity of labor in the computer industry plus 0.2 times quantity of labor in the computer industry equals 200 and the labor in the computer industry plus labor in the shoe industry must equal 200
Use these two equations to solve for labor in the computer industry and labor in the shoe industry and then calculate the amount of capital used in each industry using the capital in the computer industry is equal to 4 multiplied by the quantity of labor in the computer industry and the capital in the shoe industry is equal to 0.2 multiplied by the quantity of labor in the shoe industry .
labor in the computer industry equals , labor in the shoe industry equals , capital in the computer industry equals , and capital in the shoe industry equals
4 times quantity of labor in the computer industry plus 4 times quantity of labor in the computer industry equals 800
minus 3.8 labor in the shoe industry equals minus 600
so that labor in the shoe industry equal 600 divided by 3.8 is 157.9 . It follows from the same equations that labor in the computer industry equals 42.1 and that capital in the computer industry equal 4 times labor in the computer industry is 168.4 and capital in the shoe industry equal 0.2 times labor in the computer industry is 31.6
4 times quantity of labor in the computer industry plus 4 times quantity of labor in the computer industry equals 800
minus 3.8 labor in the shoe industry equals minus 600
so that labor in the shoe industry equal 600 divided by 3.8 is 157.9 . It follows from the same equations that labor in the computer industry equals 42.1 and that capital in the computer industry equal 4 times labor in the computer industry is 168.4 and capital in the shoe industry equal 0.2 times labor in the computer industry is 31.6