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A firm employs 100 workers at a wage rate of $10 per hour, and 50 units of capital at a rate of $21 per hour. The marginal product of labor is 3, and the marginal product of capital is $5. The firmA) could reduce the cost of producing its current output level by employing more capital and less labor. B) could reduce the cost of producing its current output level by employing more labor and less capital. C) could increase its output at no extra cost by employing more capital and less labor. D) could reduce the cost of producing its current output level by employing more capital and more labor. E) is producing its current output level at minimum cost.

Respuesta :

Answer:

We can increase the output with the same cost increasing the relation work/capital factor relation.

We can keep the same output reducing the cost increasing the relation work/capital factor relation.

Explanation:

The actual situation is:

Work units: 100 units

Work cost: $10 per unit

Marginal productivity of work: $3 per unit

Capital units: 50 units

Capital cost: $21 per unit

Marginal productivity of capital: $5 per unit

For each dollar that we use to increase the work factor, we get 3/10=$0.30 more output.

For each dollar that we use to increase the capital factor, we get 5/21=$0.24 more output.

This values are negative for each dollar of factor of production that is decreased.

With these calculations, we can estimate that the output will grow if we increased the proportion of the work factor in place of the capital factor.

We can measure the cost for two different combinations with the same output.

One is the actual combination, with cost:

[tex]C=10*W+21*C=10*100+21*50=1000+1050=2050[/tex]

If we have 5 more work hours (output grows 5*3=$15), and reduced the capital by 3 units (output is reduced (-3)*5=-$15), we have the same output and its cost is:

[tex]C=10*(W+5)+21*(C-3)=10*105+21*47=1050+987=2037[/tex]

We have proved that if we increase the work/capital relation, we can have the same output with less cost.

anthougo

The firm B) could reduce the cost of producing its current output level by employing more labor and less capital.

Data and Calculations:

The number of workers employed = 100

Wage rate per hour = $10

The number of units of capital = 50 units

Rate of return on capital per hour = $21

The marginal product of labor = 3 units

The marginal product of capital = 5 units

For every unit of the product, the company pays workers = $3.33 ($10/3)

For every unit of the product, the firm pays a capital rate = $4.20 ($21/5)

Thus, it is more profitable for the firm to employ one additional worker than one additional unit of capital.

Learn more: https://brainly.com/question/4186143

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