In economics, the marginal product of labor (MPL) is the change in output that results from employing an added unit of labor. It is a feature of the production function and depends on the amounts of physical capital and labor already in use.
Definition
The marginal product of a factor of production is generally defined as the change in output resulting from a unit or infinitesimal change in the quantity of that factor used, holding all other input usages in the production process constant.
The marginal product of labor is then the change in output (Y) per unit change in labor (L). In discrete terms the marginal product of labor is:
In continuous terms, the MPL is the first derivative of the production function:
Graphically, the MPL is the slope of the production function.
Examples
There is a factory which produces toys. When there are no workers in the factory, no toys are produced. When there is one worker in the factory, six toys are produced per hour. When there are two workers in the factory, eleven toys are produced per hour. There is a marginal product of labor of five when there are two workers in the factory compared to one. When the marginal product of labor is increasing, this is called increasing marginal returns. However, as the number of workers increases, the marginal product of labor may not increase indefinitely. When not scaled properly, the marginal product of labor may go down when the number of employees goes up, creating a situation known as diminishing marginal returns. When the marginal product of labor becomes negative, it is known as negative marginal returns.
Marginal costs
The marginal product of labor is directly related to costs of production. Costs are divided between fixed and variable costs. Fixed costs are costs that relate to the fixed input, capital, or rK, where r is the rental cost of capital and K is the quantity of capital. Variable costs (VC) are the costs of the variable input, labor, or wL, where w is the wage rate and L is the amount of labor employed. Thus, VC = wL . Marginal cost (MC) is the change in total cost per unit change in output or ∆C/∆Q. In the short run, production can be varied only by changing the variable input. Thus only variable costs change as output increases: ∆C = ∆VC = ∆(wL). Marginal cost is ∆(Lw)/∆Q. Now, ∆L/∆Q is the reciprocal of the marginal product of labor (∆Q/∆L). Therefore, marginal cost is simply the wage rate w divided by the marginal product of labor
(the change in quantity of labor to effect a one unit change in output) Therefore
Thus, if the marginal product of labor is rising, then marginal costs will be falling, and if the marginal product of labor is falling, marginal costs will be rising (assuming a constant wage rate).
Relation between MPL and APL
The average product of labor (APL) is the total product of labor divided by the number of units of labor employed, or Q/L. The average product of labor is a common measure of labor productivity. The APL curve is shaped like an inverted “u”. At low production levels the APL tends to increase as additional labor is added. The primary reason for the increase is specialization and division of labor. At the point the APL reaches its maximum value APL equals the MPL. Beyond this point the APL falls.
During the early stages of production MPL is greater than APL. When the MPL is above the APL the APL will increase. Eventually the MPL reaches it maximum value at the point of diminishing returns. Beyond this point MPL will decrease. However, at the point of diminishing returns the MPL is still above the APL and APL will continue to increase until MPL equals APL. When MPL is below APL, APL will decrease.
Graphically, the APL curve can be derived from the total product curve by drawing secants from the origin that intersect (cut) the total product curve. The slope of the secant line equals the average product of labor, where the slope = dQ/dL. The slope of the curve at each intersection marks a point on the average product curve. The slope increases until the line reaches a point of tangency with the total product curve. This point marks the maximum average product of labor. It also marks the point where MPL (which is the slope of the total product curve) equals the APL (the slope of the secant). Beyond this point the slope of the secants become progressively smaller as APL declines. The MPL curve intersects the APL curve from above at the maximum point of the APL curve. Thereafter, the MPL curve is below the APL curve.