When most people think of fundamental tasks of a firm, they think first of production. Economists describe this task with the production function, an abstract way of discussing how the firm gets output from its inputs. It describes, in mathematical terms, the technology available to the firm.The technological relationship between inputs and output of a firm is generally referred to as the production function. The production function shows the functional relationship between the physical inputs and the physical output of a firm in the process of production. To quote Samuelson, "The production function is the Technical relationship telling the maximum amount of output capable of being produced by each and every set of specified inputs. It is defined for a given set of technical knowledge."
According to Stigler, "the production function is the name given to the relationship between the rates of input of productive services and the rate of output of product. It is the economist's summary of technical knowledge.
Production is the transformation of inputs into outputs. Inputs are the factors of production -- land, labor, and capital -- plus raw materials and business services.
The transformation of inputs into outputs is determined by the technology in use. Limited quantities of inputs will yield only limited quantities of outputs. The relationship between the quantities of inputs and the maximum quantities of outputs produced is called the "production function."
But how do these outputs change when the input quantities vary? Let's take a look at an example of a production function.
In general, we would allow for varying amounts of land, labor and capital. However, in this example, labor will be the only input, for the sake of simplicity.
The main theme of production function is to get the maximum production with the present given set of variable.
Eg: a firm can use the more labour and less machines OR it can use less labour and more machines to get maximum production. Here which is suited best and how to find the best alternative choice is the main aim of production function.
In a general mathematical form, a production function can be expressed as: Q= f(LB, L, K, M, , t)
LB = Land & Buildings.
L = Labour.
K = capital.
M = raw material.