# Marginal Product of Labor (Revenue)

## The marginal revenue product of labor is the change in revenue that results from employing an additional unit of labor.

#### Key Points

• The marginal revenue product of a worker is equal to the product of the marginal product of labor (MP:) and the marginal revenue (MR) of output.

• The marginal revenue productivity 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.

• The change in output from hiring one more employee is not limited to that directly attributable to the additional worker.

#### Terms

• The extra output that can be produced by using one more unit of the input.

• The decrease in the per-unit output of a production process as the amount of a single factor of production is increased.

#### Figures

1. ##### Factory at Capacity

Without any additional space and machinery, adding more employees is unlikely to increase output by very much. The marginal revenue product of labor is relatively low.

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. Figure 1

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.

#### Key Term Glossary

Complement
A good with a negative cross elasticity of demand, meaning the good's demand is increased when the price of another good is decreased.
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demand
The desire to purchase goods and services.
##### Appears in these related concepts:
diminishing marginal returns
The decrease in the per-unit output of a production process as the amount of a single factor of production is increased.
##### Appears in these related concepts:
efficient
Making good, thorough, or careful use of resources; not consuming extra. Especially, making good use of time or energy.
firm
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input
Something fed into a process with the intention of it shaping or affecting the outputs of that process.
##### Appears in these related concepts:
labor
The workers used to manufacture the output.
##### Appears in these related concepts:
marginal
Of, relating to, or located at or near a margin or edge; also figurative usages of location and margin (edge).
##### Appears in these related concepts:
marginal product
The extra output that can be produced by using one more unit of the input.
##### Appears in these related concepts:
marginal revenue
The additional profit that will be generated by increasing product sales by one unit.
##### Appears in these related concepts:
marginal revenue product
The change in total revenue earned by a firm that results from employing one more unit of labor.
##### Appears in these related concepts:
market
one of many varieties of systems, institutions, procedures, social relations and infrastructures whereby parties engage in exchange. While parties may exchange goods and services by barter, most markets rely on sellers offering their goods or services (including labor) in exchange for money from buyers.
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output
Production; quantity produced, created, or completed.
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Output
What is produced in the country, often measured by GDP.
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price
The cost required to gain possession of something.
##### Appears in these related concepts:
Price
The quantity of payment or compensation given by one party to another in return for goods or services.
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productivity
A ratio of production output to what is required to produce it (inputs).
##### Appears in these related concepts:
Productivity
the rate at which goods or services are produced by a standard population of workers.
##### Appears in these related concepts:
profit
Total income or cash flow minus expenditures. The money or other benefit a non-governmental organization or individual receives in exchange for products and services sold at an advertised price.
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revenue
The total income received from a given source.
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Substitute
A good with a positive cross elasticity of demand, meaning the good's demand is increased when the price of another is increased.
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technology
The study of or a collection of techniques.
##### Appears in these related concepts:
total revenue
The profit from each item multiplied by the number of items sold.
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variable
something whose value may be dictated or discovered.