The act of production involves the transformation of inputs into output. Production is a transformation of physical inputs into physical inputs into physical output. The output is thus a function of factors which are also called inputs. The functional relationship between physical and physical output and physical output of a firm is known as production function. Algebraically production function can be written as
Q = f (L, K, M)
where, Q stands for the quality of output L, K, and M stand for the quantities of factors labour capital and new raw materials respectively.
The above equation shows that the quantity (Q) of output produced depends upon the quantities of the factors used. The production function expresses the relationship between the quantity of output and the quantities of the various inputs used of the production. More precisely the production function sates the maximum quantity of output that can be produced with any given quantities of various inputs. If a small firm produces wooden tables in a day its production function will consists of the maximum number of tables that can be produced form a given quantities of various inputs such as wood varnish labour time machine time floor space.
Two things must be noted in respect of production function. First production function like the demand function must be considered with reference to a particular period of time production function expresses a flow of inputs resulting in a flow of output in a specific period of time secondly production function of a firm is determined by the state of technology. When the technology advances the production function changes with the result that greater flow of output can be obtained from the given inputs or smaller quantities of inputs can bemused for producing a given quantity of output.
In economic theory we are interested in two types of production functions. Rest we study the production function when the quantities of some inputs such as capital and land are kept constant and the quantity of one input such as labour (or quantities of few inputs) is varied. This kind of production function [Q = f(L,K)]is called short-run production function. The study of short –run production is the subject matter of the law of diminishing returns which is also called the law of variable proportions secondly we study production funk in (input-output relation) by varying all inputs and this is called long-run production function and can be expressed as Q = f (L, K, M) this forms the subject matter of the law of returns to scale generally the terms constant and increasing returns are used with reference to constant and increasing returns to scale.