It reveals various types of natural resources, land, labor and capital, which will have to be employed in order to produce one unit or a given quantity of certain commodity or service, in a given period of time. In other words, it indicates varieties of resources and their unique combinations that can be transformed into desired quantities of goods and services. It reflects the state of arts technological possibilities of the production processes and the size of the producing units.
Thus, the production function is a symbolical expression of the fact that output of a firm depends on the inputs employed in the production process.
Traditionally, the production function has been called the Law of Diminishing Returns and has been explained by economics in different ways in the last 200 years or so.
We may study the production function as follow:
(a) Will land as fixed factor and labor and capital as variable factors. This is marshal’s version of the law of diminishing returns.
(b) With on factor variable and other factors fixed, this is the modern cession of the law of diminishing returns.
(c) With all factors variable, this is the law of returns to scale.
In traditional production theory resource used for the production of product are known as factors of production. Factors of production are now termed as inputs that may mean the use of the services of land, labor, capital and organization in the process of production. Then term output refers to the commodity produced by the various inputs. Production theory concerns itself with the problems of combining various inputs, given the state of technology, in order to produce a stipulated output. The technological relationships between inputs and outputs are known as production functions.