Production functions measure the relationship between inputs and outputs in a production process. A *typical production function assumption* is that the only variable input into the production process is labor.

This assumption is made because it is fairly straightforward to measure labor as a variable input, whereas measuring other variables such as capital and energy would be more difficult.

Therefore, the slope of the **production function represents** the increase in output per increase in labor. This is known as the marginal product of labor.

Production functions can be linear or non-linear. If linear, then the marginal product of labor can be measured by finding the change in output per change in labor. If non-linear, then you must find the average effect of *one additional unit* of labor on output.

## Slope

A firm’s variable input is labor, so the slope of the **production function measures** the amount of output per unit of labor. This is also referred to as the marginal product of labor.

In other words, the slope of the *production function shows* how much output a firm gets for ** every additional unit** of labor it employs. The more workers a firm has, the more output it produces.

Production functions can be linear or non-linear. If a production function is linear, then its slope is simply a constant value. If it is non-linear, then its slope changes at different points.

Both cases show how much output an employer gets for every additional unit of labor they employ. Both cases show the same thing: The more workers an employer has, the more output they have.

## Slope and marginal revenue product

As mentioned before, the marginal revenue product of labor is the increase in revenue generated by *one additional unit* of labor.

The slope of the production function represents the marginal product of labor, which is also called the wage. It is the increase in output due to an increase in input, in this case labor.

The relation between wages and the production function can be explained with a simple example. Consider a factory that *produces computers using two inputs*: computer chips and labor.

If there were no computer chips, then the *factory would need* to hire more workers to produce the same number of computers. Hence, computer chips are a constant input that cannot be reduced unless there are no computers to produce.

Assuming that there are enough workers available at reasonable prices, then reducing the number of workers will lead to *less output due* to lack of production inputs such as computers or machinery.

## Examples

Consider the example of a bakery that can only add bags of flour to produce more bread. The more bags of flour it adds, the more bread it can produce.

The number of loaves of bread the **bakery produces per hour** is the output and depends on the number of hours worked. The number of **hours workers work** is the input and only variable input into making bread.

The slope of the production function for baking bread is therefore the ratio of inputs: how many bags of **flour per loaf** and how **many hours** to make it.

## In practice

A firm’s production function is a representation of the inputs required to produce a certain output.

Inputs can be labor, capital, technology, and other factors that contribute to the production of a good or service. In economics, the term “factor” refers to any of these inputs.

The output level that a firm can achieve depends on the levels of all its inputs. A higher level of any input will lead to a **higher output level**. But what if one of the inputs is the only variable input?

If labor is the only variable input in producing a good or service, then the slope of the production function will determine the quantity of *output produced per unit* of labor. This concept is known as Baer’s law, named after economist Fredrick C. Baer.

## Implications for firms

As shown in the above graphs, when *output increases due* to an increase in input only of labor, then the slope of the production function is the wage.

This is an important factor to consider when deciding how to organize production processes. When production processes are organized in a way that minimizes the need for additional labor, then production will be most efficient.

For example, if it *takes one hour* to produce one unit of a product and then it *takes two hours* to produce another unit of that product, then the wage per hour is one unit.

The above *explanation may seem simple*, but it is an important concept in economics and organizational sociology. It shows how organizations can be most efficient when they use the least amount of labor necessary for production.

It also shows how organizations can leverage what they pay their workers by finding ways to reduce the number of workers needed for production.

## Implications for consumers

As explained above, firms will produce the level of output that maximizes their profits. As a result, more expensive inputs will lead to higher output levels.

This is important to know as a consumer because it means that prices are set at a level where suppliers can guarantee a minimum profit. If prices were set below this point, then suppliers would make no profit and **would likely stop producing** that good or service.

Prices are not arbitrary and are not dictated by consumers. In fact, if consumers were to demand lower prices, then producers would have to reduce their production levels in order to stay in business. This would lead to a lower supply and *likely higher consumer prices due* to lack of supply.

Also, as *production levels increase due* to increased input costs, then there will be more production units of the good or service. This will lead to more supply and **possibly lower prices due** to competition.