Production is the process of transforming physical inputs into physical outputs. Physical inputs are the factors of production such as land, labor, capital and organization. Physical outputs are the quantity of goods produced. The output is thus a function of factors called inputs. Production may be defined as the functional relationship between physical inputs and physical outputs. The quantity of output of a commodity depends upon the quantity of input used for the production. Thus, the production function summarizes the relationship between labor, capital and land outputs and the maximum output these inputs can produce. It also tells how much output can be produced from a given combination of inputs and tells by how much output will increase if one or all input is increased.
The main assumptions of production function are that it has reference to a particular time period. It expresses the relation between inputs and outputs over a period of time. As the time period changes the production function also changes. The same inputs can produce different inputs can produce different outputs both in the short run and long run. In the long run a producer has more choices than in the short run because all the inputs can be varied in the long run.
The next assumption is that it is a state of technology which does not change. The state of technical knowledge is assumed to be constant for specifying a production function. If the technology advances production function also changes because now it is possible to produce more output from a given set of inputs with the advanced technology or lesser quantities of inputs can be used for producing a given quantity of output. For instance, if laborers are given more education and training labor productivity will improve. Likewise, technological advancement leads to increased productivity of machines.