Question

A firm recently stated that an extra unit of labor is expected to cost them $8.00 while an extra unit of capitol will cost $15.00. Likewise, they claim that each extra unit of labor will increase output by 24 units while each extra unit of capitol will produce an extra 40 units of output. the firm wishes to offer you a part time job. using economic analysis, evaluate this decision on the part of the firm

Answer 1

The firm should employ inputs such that the cost is minimized and profit is maximized. The cost is minimized for the input mix when the marginal productivity per dollar spent on each factor is equal. In other words, the cost is minimized at the levels of capital and labor such that the per dollar marginal product of capital is equal to the per dollar marginal product of labor.

Per dollar marginal product of labor is the marginal product of labor divided by the cost of labor and similarly per dollar marginal product of capital is the marginal product of capital divided by the cost of capital.

Given:

Labor's marginal productivity (MP_L) = 24 units

Capital marginal productivity (MP_K) = 40 units

Cost of per unit labor (w) = $8.00

Cost of per unit capital (r) = $15.00

Therefore the cost minimization condition is that:

And when the factor input doesn't comply with the condition, there is a need to making an adjustment. That is if the last dollar spends on an input yield more marginal products than the other. Than that factor must be employed more and the firm must increase its quantity. And while it must decrease the quantity of the input whose per dollar marginal product is more.

So, if the firm has an input mix such that,

Then it means that per dollar spent on capital is yielding more marginal output than the labor. And therefore it will be profitable as well as cost-minimizing for the firm to increase the capital employed and decrease the labor employed units.

While if the firm has an input mix such that,

Then it means that per dollar spends on capital is yielding more marginal output than the labor. And therefore it will be cost-minimizing for the firm to increase the labor employed and decrease the capital employed units.

Therefore keeping in mind these cost minimization conditions and disequilibrium, finding whether the firm is fulfilling the cost-minimizing condition and if not what changes it must do.

Per dollar marginal product of labor:

Per dollar marginal product of capital:

Therefore, as we can see;

It means that at present, the last dollar spent on labor is yielding more marginal product than the last dollar spent on capital. Therefore the firm must increase its labor employed and decrease capital employed such that it can minimize cost.

As an economic analyst, I would suggest the firm to increase its labor employed units and decrease its capital employe units. As I can see that at present, the input mix is such that the last dollar spent on labor is resulting in more output produced than the last dollar spent on capital. So if the firm increases labor units and capital units, it will have more productivity as well cost minimized. The firm must continue to increase labor units and decrease capital units until the balanced is achieved.

The firm must increase labor units and decrease capital units until,