‘Q’ stands for the quantity of output, ‘K’, ‘L’, ‘1’ and ‘O’ stand for the quantities of capital, labour, land and organization (factors of production) respectively used in producing output. Output quantity, thus, depends on the quantities of these inputs. The above production function describes the technological or engineering relationships involved between the factors of production and the resultant output of a commodity.

The production function of a firm shows the technical methods available to produce a given output of a commodity by combining the factors of production in various possible ways. A rational producer always uses technically most efficient method of production.

A method of production is said to be technically more efficient than other methods, if it uses less of at least one factor input and no more of the other factor inputs to produce one unit of the commodity.

Suppose the two methods of production P1 and P2 require 2 and 2 units of labour, while 3 and 4 units of capital respectively. Here, the rational producer will choose method P1 to produce the commodity, since it saves one unit of capital without using more amount of labour. Hence, this method is economical and more efficient. The theory of production considers only on efficient methods.

However, it is often not possible to directly compare the production processes, when production of a commodity requires more of some factor and less of some other factor (s) as compared with any other production process.

Suppose, the production method P3 requires 3 units of labour and 4 units of capital, while production method P4 require 4 units of labour and 3 units of capital. Here, neither of the two production methods is more efficient than the other.

Since the two methods are not directly comparable, they are considered as technically efficient and included in the production function. The choice of a particular method will depend on the prices of factors.

This choice of a particular production method among several technically efficient methods for decision making at the firm level is an economic one rather than technical. Therefore, a technically efficient production method need not be an economically efficient method.

Derivation of one economically efficient process (given the prices of the inputs) is discussed in this chapter under the heading ‘optimum combination of factors’. This derivation will make the difference between technical efficiency and economic efficiency more clear.

The production function expresses the way output is produced by inputs and the way inputs cooperate with each other in varying proportions to produce any given output. These relations between inputs and outputs and inputs themselves are determined by technology that rules at any given time.

The technology is embedded in the production function, which acts as a constraint on decision making. Thus, production function depicts the present limits of the firm. A firm can produce higher output only by using more inputs or with advanced technology.

At the same time, production function indicates the manner in which a firm can substitute one input or output (as the case may be) for the other without altering their total amounts respectively.

Production function differs from firm to firm, industry to industry. Any change in the state of technology or managerial ability disturbs the original production function. New production function may have a smaller or larger flow of output for a given quantity of inputs in case of deterioration or improvement in the state of firm respectively. The production function shifts downwards/upwards in the two cases respectively.

An estimated production function is a statement of technological specification. Production function can be estimated by statistical techniques using historical data on inputs and output. Estimation of the production function can help business firm in taking correct long-run decision such as capital expenditure. Further, the short-run production estimates at firm level are helpful in arriving at the optimal mix of inputs to achieve a particular output target, i.e., least cost combination of inputs.

Production function can be represented in various forms. It can be represented by schedules, tables, input-output tables, graphs, mathematical equations, total, average and marginal product curves, isoquants (equal product curves) and so on.