Question

If the marginal product of labor is

fallingfalling​,

is the marginal cost of production rising or​ falling? Briefly explain.

If the additional output from each new worker is

fallingfalling​,

Answer 1

The marginal product of labor is the additional output generated from employing one extra unit of labor. Thus the marginal product of labor is given by the following formula:

MP =

where is the change in output (additional output) and is the change in labor (extra unit of labor employed)

The marginal cost of production is the additional cost incurred from producing one extra unit of output. It is given by the following formula:

MC =

where is the change in cost and is the change in output

Now, since fixed cost remains the same no matter how many units are produced, thus there will be no change in the fixed cost. So we can replace TC (total cost) with TVC (total fixed cost) here. The equation can be written as:

MC =

Now, the change in total variable cost can be written as (). This is because labor is a variable factor of production, and considering only one factor of production here, the total variable cost will be equal to wages*labor employed.

Thus, the marginal cost equation can be written as:

MC = =  

Now we can see that is the reciprocal of which is equal to the marginal product of labor (MP). Thus, we can find the relationship between MP and MC here as follows:

MC = W* (1/MP) = W/MP

Thus, we can see in the above equation that marginal cost (MC) and the marginal product of labor (MP) are inversely related to each other.

Thus if the marginal product of labor is falling, the marginal cost of production will rise.