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WA3. Production and Cost

Statement

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, describe how the firm should adjust its mix of capital and labor? What will be the result?

Answer

Marginal product of labour (MPL) is the additional output produced by an additional unit of labour, which means that hiring one more worker will increase the output by 20 units. Marginal product of capital (MPC) is the additional output produced by an additional unit of capital, which means adding one more unit of capital will increase the output by 60 units. At a glimpse and assuming everything unchanged, capital seems to be more productive, but that’s not enough to make a decision (Rittenberg & Tregarthen, 2009).

There is another statistic we can compute, which is the marginal product per dollar, and we can get it by dividing the marginal product by the price of the input. In this case, the marginal product per dollar of capital is 60/6 = 10, and the marginal product per dollar of labor is 20/2.5 = 8, and this means that capital is more productive per dollar than labor (Wyzant, 2022).

The least cost rule is a way a firm follows to adjust its mix of capital and labor to maximize output while minimizing costs. The rule uses the marginal product per dollar of each of production factors and says that production is ats peak when the marginal product per dollar of each input is equal. If the ratios are not equal, a firm would reduce cost by employing more of the resource with a higher ratio and less of the resource with a lower ratio. (Resource Combinations - Least Cost & Profit Max - ReviewEcon.com, 2022).

The marginal product per dollar of capital is 10 > 8; the firm should adjust its mix of capital and labor by allocating more capital, less labor, or both. As increasing capital will reduce its marginal product per dollar, and decreasing labor will increase its marginal product per dollar, until both meet at an equal level (Wyzant, 2022).

The result of the change is an increase in the productivity of labor with a bit of decrease in the productivity of capital; but the overall output of the firm will increase, and the production process will be more efficient and less costly.

References

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