# Marginal Revenue Product

The marginal revenue product of labor is the incremental revenue generated by one additional unit of labor. The marginal revenue product of labor generally has the same characteristics as the marginal product of labor.
When discussing production (creating output) and the production function (the relationship of output to input), economists introduce the concept of marginal product of labor (MPL)—that is, the incremental output produced by hiring an additional unit of labor while keeping all other inputs to production the same. Units of labor can be workers, worker-hours, worker-days, etc., depending on context. Mathematically, marginal product of labor is given by:
$\text{MP}_{\text{L}}=\frac{\Delta \text{Q}}{\Delta \text{L}}$
Q is the quantity of output and L is the quantity of labor. Quantity of labor refers to the number of worker-hours, worker-days, etc., supplied or demanded in a labor market. Marginal revenue product of labor (MRPL), on the other hand, represents the amount of incremental revenue generated by hiring an additional unit of labor. In general, the marginal revenue product of labor can be calculated as the change in total revenue for a change in labor.
$\text{MRP}_{\text{L}}=\frac{\Delta \text{TR}}{\Delta \text{L}}$
TR is total revenue (i.e., price times quantity of output) and L is the quantity of labor. The marginal revenue product of labor is also referred to as the value of the marginal product of labor.

### Marginal Revenue Product of a Second Worker

Quantity of Labor (L) Output (Q) Price (P) Total Revenue (TR) Marginal Revenue Product (MRPL)
1 5 10 50 50
2 8 9 72 22

In this example, a monopolistic firm hires from a competitive labor market where the marginal revenue product of the second worker is 22.

$22=(72-50)/(2-1)$

In another example, if it is assumed that if a firm is operating in a competitive market (a market with a large amount of sellers and consumers) for its output, the firm can sell as much output as it wants at the prevailing market price.
$\text{MRP}_{\text{L}}=\text{P}\times\text{MP}_{\text{L}}$
The marginal revenue product of labor (MRPL) is equal to the marginal revenue from the product (P) multiplied by the marginal product labor (MPL). If one worker in a factory can produce 10 televisions that sell for $1,000 each, the MRPL would be 10 multiplied by$1,000, or \$10,000. The marginal revenue product of labor generally has the same properties as the marginal product of labor: diminishing marginal product (the principle that as one unit of input increases, output will first grow, then eventually will lessen over time).