Meaning of Production Function:

Production function is the name given to the physical relationship between a firm’s physical inputs and outputs depending on a given state of technical knowledge.

Like demand, it refers to a period of time. Accordingly, it refers to a flow of inputs resulting in a flow of outputs over a period of time, leaving prices aside. It shows the maximum amount of output that can be produced from a given set of inputs in the existing state of technology.

The output will change when the quantity of any input is changed.

In real life, a manufacturer wants to know how much of the various factors or inputs, viz., land (i.e. natural resources), labour and capital will be required to produce a unit or a given quantity of a commodity during a given period of time.


It is necessary for him to know this so that he may be able not only to assess his requirements of productive services but also roughly to estimate the probable cost. It will thus indicate the quantities of the productive resources and their possible combinations used for the purposes of production.

Factors Affecting Production Function:

Production function, of course, depends, inter alia, on:

(a) Quantities of resources used,

(b) State of technical knowledge,


(c) Possible processes,

(d) Size of the firms,

(e) Nature of firm’s organisation,

(f) Relative prices of the factors of production and the manner in which the factors of production are combined.


As these things change, production function will change too. For instance, output can be increased by increasing the quantity of factors of production or of some of them. It can also be increased by varying the proportion in which the factors combined. Adoption of more efficient techniques of production, too, will add to the output. The less efficient are the techniques, the smaller will be the output.

Production changes with period of time. In the very long period, it changes altogether because the same inputs produce different outputs. In the long run, the production function depicts the whole set of choices open to the producer, i.e. what inputs will produce what output.

In the short run, the choices open to the producer are restricted, because some of the factors are fixed and cannot be changed in the short period and only some can be varied. In this situation, the producer tries to find out the relation between the variable inputs and the outputs.

Since production function is concerned with the physical aspects of production, it is more a concern of an engineer or a technician than of an economist, only a technician can say what specific quantity of a good can be produced by the use of the various productive resources and their combinations.

Nature of Production Function:

Production function can be expressed as under:

X = f (a, b, c, d …)

Here X is the output of a commodity per unit of time and a, b, c, d, ,,,,,,,,, are the various productive resources which go into the making of the quantity of the commodity. Every management has to make a choice of the- production function depending not only on industrial knowledge and the prices of the various factors of production but also on its own capacity to manage. It has also to select the various factors and knit them together in economical combinations. These two choices are interlinked. The overriding consideration is to seek a combination which gives the minimum average cost and maximum aggregate profit.

For understanding the nature of production function, the following points may be emphasized:

(i) The production function represents a purely technical relationship in physical quantities between the inputs of factors and the output of the products. It has no reference to money price. The price factor is left out altogether.


(ii) The output is the result of a joint use of the facts of production. It is obvious that the physical productivity of one factor can be measured only in the context of this factor being used in conjunction with other factors.

(iii) The nature of the quantity of the various factors and the manner in which they are combined will depend on the state of technical knowledge. For instance, labour productivity will depend on the quality of labour as determined by their education and training. Similarly, the productivity of machines will be determined by the technical advances embodied in them.

Again, it is on the basis of technical knowledge at the time that labour, machines and other factors will be combined in the processes of production. Thus, the state of technical knowledge is treated as given (i.e., as a parameter) for specifying a production function.

A change in technology will mean a shift to another production function. It will alter the cost conditions. Improvement in technology will result in a larger output from a given combination of the factors of production.


(iv) In specifying the production function of a firm, we have to take into account the variability of factors of production and also whether they are divisible or indivisible. These features of the factors of production will determine their physical productivities and hence the nature of the production functions.