Suppose a firm finds that the marginal product of capital is 60 and the marginal product of labor is 20. If the price of capital is $6 and the price of labor is $2.50, how should the firm adjust its mix of capital and labor? What will be the result?

If a firm finds that the marginal product of capital is 60 and the marginal product of labor is 20, it will recognize that each dollar spent on capital will outproduce a dollar spent on labor. The marginal benefit of capital is 10 versus 8 for labor. $1 spent on capital will yield 25% more than $1 spent on labor until the firm begins to experience diminishing returns on capital.

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If a firm finds that the marginal product of capital is 60 and the marginal product of labor is 20, it will recognize that each dollar spent on capital resources will produce more than a dollar spent on labor resources.

With the price of capital at $6, the marginal benefit...

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If a firm finds that the marginal product of capital is 60 and the marginal product of labor is 20, it will recognize that each dollar spent on capital resources will produce more than a dollar spent on labor resources.

With the price of capital at $6, the marginal benefit of capital is 60 divided by $6, or 10. The price of labor is $2.50, and the marginal product of labor is 20, as noted. Therefore, the marginal benefit of capital is 20 divided by $2.5, or eight. Each additional dollar spent on capital versus on labor will yield 25% more product. This indicates that the firm should deploy its additional funds more aggressively into expanding capital resources than labor resources until it begins to experience diminishing returns on capital.

According to the law of diminishing returns, the incremental return of increasing an element of production will eventually fall. At some point in the future, the marginal product of capital will decline from 10 units, and it will no longer make sense for the firm to continue expanding its capital resources. It could be that the added production volume will put too much stress on the capital machinery used in the production process and the machines will require more and more maintenance. The machines will also be out of service more frequently at a certain level of output, and that will, in turn, constrain production.

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The idea in question here is that money in the firm is finite, and therefore the budget must be maximized with what it currently has. Therefore, if you spend an extra dollar on capital, you must spend a dollar less on labor. We want to calculate marginal benefit of each expenditure by dividing marginal product by price.

For capital, Marginal Benefit = 60/6, or 10, and for labor, Marginal benefit = 20/2.5, or 8. Therefore, for each dollar spent on capital, the company gains 10 units of production, and for each dollar spent on labor, the firm gains 8 units of production.

Extrapolating this using the principle in question, if you move a dollar from labor to capital, you will gain 10 units of production but lose 8 at the same time, therefore totaling a net positive of 2 units. Therefore, you will want to move funds to capital until you begin to see diminishing returns from reducing labor.

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First, we can find the firm's marginal benefit per additional dollar that it spends on both factors of production: capital and labor.

To find the marginal benefit of a factor of production, take its marginal product, or MP, and divide it by its price, or P.

For capital, this is equivalent to the calculation 60/$6 = 10 units of product per additional dollar spent.

Similarly, for labor, this is equivalent to 20/$2.50 = 8 units of product per additional dollar spent.

We have now found that the firm has a rationale to become more capital-heavy, since its money is more productive when fed into its capital holdings. Usually, as a firm acts on such insight and feeds more money into the more effective factor of production, the firm will discover new efficiencies, and its ratio MP/P for each factor of production will equilibrate (tend toward equality).

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In this example, you are attempting to minimize the amount the firm spends on labor and capital by mixing it appropriately. In order to accurately identify how much of each item—labor and capital—to utilize, you need to know the amount of units given to you, such as a total budget for labor and capital.

If, for example, we were given $100 for this project, you could make a budget to determine the most effective use of your finances. You need to employ both capital and labor to make your machinery work and can't simply throw all of your resources into one arena, but by analyzing the cost per unit of production, you can see where the most value for your money lies.

In this example, each dollar of capital gives you 10 units of production, and each dollar of labor gives you 8 units of production (60/$6 and 20/$2.50, respectively). Knowing this, you find that—when mixing labor and capital—capital will give you 25% more production than labor.

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Based on Economics (Tregarthen and Rittenberg), if we spend $1 more on capital, we must spend $1 less on labor.

Since the marginal product of capital is 60, and the price of capital is $6, the marginal benefit of $1 spent on capital is Marginal Product of Capital/ Price of Capital= 60/6= 10.

So, the firm will gain 10 units of output by spending an additional $1 on capital.

Then, we are told that the marginal product of labor is 20 and the price of labor is $2.50. The marginal disadvantage of $1 less spent on labor would be Marginal Product of Labor/ Price of Labor= 20/2.50= 8.

The firm would lose 8 units of output from spending $1 less on labor.

To compare, MPC/P > MPL/P

 60/6 > 20/2.50

So, the company achieves a net gain of 2 units of output if it transfers $1 from labor to capital. It will continue to transfer funds as long as it gains more output from the additional capital than it loses in output by reducing labor. Essentially, the company will increase in output and be capital-intensive for a period of time.

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