Marginal product of labor
In economics, the marginal product of labor (MPL) is the change in output that results from employing an added unit of labor.
The marginal product of a factor of production is generally defined as the change in output associated with a change in that factor, holding other inputs into production 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.
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.
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
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