## Definition and Meaning:

Production of goods requires resources or inputs. These inputs are called factors of production named as land, labor, capital and organization. A rational producer is always interested that he should get the maximum output from the set of resources or inputs available to him. He would like to combine these inputs in a technical and efficient manner so that he obtains maximum desired output of goods. The relationship between the inputs and the resulting outputs are described as *production function.*

“A *production function* shows the relationship between the amounts of factors used (input) and the amounts of output generated per period of time”.

## Formula:

*Production function can be expressed in algebraic formula as under:*

**X = f (a ^{1}, a^{2} ,…….., a^{n})**

**Production function formula (equation)** tells us the quantity of the product X which can be produced by the given quantities of inputs (lands labor, capital) that are used in the process of production. Here it may be noted that production function shows only the maximum amount of output which can be produced from given inputs. It is because *production function* includes only efficient production process.

## Explanation:

**The analysis of production function is generally carried with reference to time period which is called short period and long period.**

**In the short run,** *production function* is explained with one variable factor and other factors of productions are held constant. We have called this production function as the law of variable proportions or the law of diminishing returns.

**In the long run**, *production function* is explained by assuming all the factors of production as variable. There are no fixed inputs in the long run. Here the production function is called the law of returns according to the scale of production.

As it is difficult to handle more than two variables in a graph, we therefore, explain the law of returns according to scale of production by assuming only two inputs i.e., capital and labor and study how output responds to their use.