# Deriving the Labor Demand Curve

## Firms will demand labor until the marginal revenue product of labor is equal to the wage rate.

#### Key Points

• The marginal revenue product of labor (MRPL) is the additional amount of revenue a firm can generate by hiring one additional employee. It is found by multiplying the marginal product of labor by the price of output.

• The downward-sloping portion of the marginal revenue product curve gives the firm's demand for labor.

• The marginal revenue product of labor will change when there is a change in the quantities of other factors employed.

• It will also change as a result of a change in technology, a change in the price of the good being produced, or a change in the number of firms hiring the labor.

#### Terms

• The change in total revenue earned by a firm that results from employing one more unit of labor.

• A resource employed to produce goods and services, such as labor, land, and capital.

#### Figures

1. ##### Marginal Product of Labor

The MPL falls as the amount of labor employed increases. The optimum demand for labor falls where the real wage rate (w/P) is equal to the MPL.

A firm must have labor to produce goods and services. But how much labor will the firm employ? A profit-maximizing firm will base its decision to hire additional units of labor on the marginal decision rule: If the extra output that is produced by hiring one more unit of labor adds more to total revenue than it adds to total cost, the firm will increase profit by increasing its use of labor. It will continue to hire more and more labor up to the point that the extra revenue generated by the additional labor no longer exceeds the extra cost of the labor.

The marginal revenue product of labor (MRPL) is the additional amount of revenue a firm can generate by hiring one additional employee.  It is found by multiplying the marginal product of labor (MPL) - the amount of additional output one additional worker can generate - by the price of output.  If an employee of a customer support call center can take eight calls an hour (the MPL) and each call earns the company $3, then the MRPL is$24.

The law of diminishing marginal returns tells us that if the quantity of a factor of production is increased while other inputs are held constant, its marginal product will eventually decline. If marginal product is falling, marginal revenue product must be falling as well. Consider the customer support center. The first employee hired can take eight calls an hour and stays busy. The second employee hired, however, is less busy and only increases the number of calls per hour by six. His MRPL is only $18. Continuing to add labor still increases the total revenue generated by the company, but the MRPL will eventually fall. We can use the MRPL curve to determine the quantity of labor a company will hire. Suppose workers are available at an hourly rate of$10. The amount a factor adds to a firm's total cost per period is the marginal cost of that factor, so in this case the marginal cost of labor is $10. Firms maximize profit when marginal costs equal marginal revenues, and in the labor market this means that firms will hire more employees until the marginal cost of labor equals the MRPL. At a price of$10, the company will hire workers until the last worker hired gives a marginal revenue product of \$10 (Figure 1).

Thus, the downward-sloping portion of the marginal revenue product curve shows the number of employees a company will hire at each price (wage), so we can interpret this part of the curve as the firm's demand for labor. We find the market demand for labor by adding the demand curves for individual firms.

### Shifting the Demand for Labor

The fact that a firm’s demand curve for labor is given by the downward-sloping portion of its marginal revenue product of labor curve provides a guide to the factors that will shift the curve. In perfect competition, marginal revenue product equals the marginal product of labor times the price of the good that the labor is involved in producing; anything that changes either of those two variables will shift the curve. The marginal revenue product of labor will change when there is a change in the quantities of other factors employed. It will also change as a result of a change in technology, a change in the price of the good being produced, or a change in the number of firms hiring the labor.

For example, computer technology has increased the productivity (marginal product) of many types of workers. This has led to an increase in the marginal revenue product of labor for these jobs, shifting firms' demand for labor to the right. This both increases the number of employed workers and increases the wage rate.

#### Key Term Glossary

cost
A negative consequence or loss that occurs or is required to occur.
##### Appears in these related concepts:
demand
The desire to purchase goods and services.
##### Appears in these related concepts:
demand curve
The graph depicting the relationship between the price of a certain commodity and the amount of it that consumers are willing and able to purchase at that given price.
##### 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:
employed
in a job; working
##### Appears in these related concepts:
factor of production
A resource employed to produce goods and services, such as labor, land, and capital.
firm
##### Appears in these related concepts:
goods
That which is produced, then traded, bought, or sold, and finally consumed.
##### Appears in these related concepts:
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:
labor market
A market with labor of workers.
##### 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 cost
The increase in cost that accompanies a unit increase in output; the partial derivative of the cost function with respect to output. Additional cost associated with producing one more unit of output.
##### Appears in these related concepts:
Marginal cost
The additional cost from taking a course of action.
##### 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.
##### Appears in these related concepts:
market demand
the quantity demanded by the cumulation of buyers at the equilibrium price.
##### Appears in these related concepts:
Market demand
The summation of the individual quantities that consumers are willing to purchase at a given price.
##### Appears in these related concepts:
output
Production; quantity produced, created, or completed.
##### Appears in these related concepts:
Output
What is produced in the country, often measured by GDP.
##### Appears in these related concepts:
perfect competition
A type of market with many consumers and producers, all of whom are price takers
##### Appears in these related concepts:
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.
##### Appears in these related concepts:
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.
##### Appears in these related concepts:
revenue
The total income received from a given source.
##### Appears in these related concepts:
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.
##### Appears in these related concepts:
variable
something whose value may be dictated or discovered.