Why are labor wages equal to VMP?

The marginal revenue product of labor (MRPL) is the change in revenue that results from employing an additional unit of labor, holding all other inputs constant. The marginal revenue product of a worker is equal to the product of the marginal product of labor (MPL) and the marginal revenue (MR) of output, given by MR×MP: = MRPL. This can be used to determine the optimal number of workers to employ at an exogenously determined market wage rate. Theory states that a profit maximizing firm will hire workers up to the point where the marginal revenue product is equal to the wage rate, because it is not efficient for a firm to pay its workers more than it will earn in revenues from their labor.

For example, if a firm can sell t-shirts for $10 each and the wage rate is $20/hour, the firm will continue to hire workers until the marginal product of an additional hour of work is two t-shirts. If the MPL is three t-shirts the first will hire more workers until the MPL reaches two; if the MPL is one t-shirt then the firm will remove workers until the MPL reaches two.

Let TR=Total Revenue; L=Labor; Q=Quantity. Mathematically:

• MRPL= ∆TR/∆L
• MR = ∆TR/∆Q
• MPL = ∆Q/∆L
• MR x MPL = (∆TR/∆Q) x (∆Q/∆L) = ∆TR/∆L

Note that the change in output is not limited to that directly attributable to the additional worker. Assuming that the firm is operating with diminishing marginal returns then the addition of an extra worker reduces the average productivity of every other worker (and every other worker affects the marginal productivity of the additional worker) - in other words, everybody is getting in each other's way.

Because the MRPL is equal to the marginal product of labor times the price of output, any variable that affects either MPL or price will affect the MRPL. For example, changes in technology or the quantity of other inputs will change the marginal product of labor, and changes in the product demand or changes in the price of complements or substitutes will affect the price of output. These will all cause shifts in the MRPL.

The marginal revenue productivity theory of wages is a theory in neoclassical economics stating that wages are paid at a level equal to the marginal revenue product of labor, MRP (the value of the marginal product of labor), which is the increment to revenues caused by the increment to output produced by the last laborer employed. This is because no firm would employ additional labor whose cost would exceed the revenue generated for the firm

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