# Production Function in Economics: Definition, Formula & Example

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Lesson Transcript
Instructor: Lucinda Stanley

Lucinda has taught business and information technology and has a PhD in Education.

In this lesson, you'll learn the definition for the production function and the formula used to calculate a production function. You'll also encounter some examples and see a production function graph.

## Production Function in Economics

How do businesses determine if they're producing goods or services efficiently?

What if a castaway - we'll call him Carl - wanted to see if he was being efficient in his production? Carl is stranded on an island alone, so it makes for a simple economy: one producer and one consumer -- him. His product, in this case, is coconuts that he collects. One thing he can do is calculate a production function.

A production function is a mathematical and sometimes graphical way to measure the efficiency of production by considering the relationships between two or more variables, meaning two or more factors that are relevant when producing a good or service, such as raw materials and labor. Once a business has determined the factors for production, it can begin building the production function. For our castaway Carl, his factors of production would be his labor compared to the number of coconuts he collects.

## Possible Formulas

The basic production function is:

Q = f(KL)

Q = output, or the amount of goods or services produced

f is shorthand for function

K = capital or fixed resources (meaning they don't change)

L = labor, referring to the human resources a business uses to produce its good or service.

Labor can be variable, meaning it's a factor that can be changed by the business (by hiring more people). The actual formula used to calculate production could be any variety of the following:

Q = KL (Output = Capital times Labor)

Q = K + L (Output = Capital plus Labor)

Or output could just be a function of the variable factor, so Q = L (Output = Labor).

Once the function is calculated, it can be graphed, and a company can see where its inefficiencies are and how much the variables can or should be changed to maximize output in relation to the raw materials.

Carl's production function would be Q = L (number of coconuts collected = amount of time Carl labors to collect them). This is a pretty simple example; let's look at some other possible scenarios.

## Examples

There are a couple of different types of production functions a business could calculate, and which one it uses depends on the type of business.

The first, and most simple, is the linear production function, which applies the same amount of output to each input. Here's an example:

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