Production refers to the act of transforming the factors of produc­tion into the goods and services that are desired for consumption and investment. The business firm is essentially a producing unit. It is a technical unit in which inputs are converted into output for sale to consumers other business firms, governments and foreign- countries.

The key concept in the theory of production is the production function which shows how inputs are converted into output and the production theory is essentially con­cerned with the nature of the conversion process.

The production function is a mathematical relation between the quantity of output of a good and the quantities of inputs required to make it. It is also an efficiency relation showing the maximum amount of output that can be obtained by the firm from a fixed quantity of resources. The concept of production function refers to the functional relationship between the quan­tities of inputs used and the quantities of outputs obtained.

It is the name for the relation between physical inputs and the physical outputs of a firm.

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The quantity of output which a firm produces during a given period of time depends on:

(i) Its method of production or the state of technology, and

(ii) The quantity of inputs used. Assuming the method of production to remain unchanged, the quantity of output will vary with the change in the inputs.

Such technical relationship between the quantity of inputs used and the quantity of output obtained is described by the economist as the pro­duction function. In the words of Leontief, “A production function is a description of the quantitative relationship between the inputs absorbed and the outputs emerging from a particular production process”.

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Watson defines the production function thus:

“Production means the transforma­tion of inputs into outputs. The production function is the name for the relation between the physical inputs and the physical outputs of a firm. If a small factory produces 100 wooden chairs per eight-hours shift, then its production function consists of the minimum quantities of wood glue, varnish, labour time, machine time, floor space, electricity, etc., that are required to produce the 100 chairs”.

For the sake of convenience we often assume that the firm employs only two factors of production, viz., labour and capital. The film’s output is treated as a flow, i.e., so many units per period of time. The volume of output of the firm’s product, per period of time, depends on the quantities of these factors that are used by the firm.

The production function shows the relationship between the output of a good, and the inputs (factors of production) required to make the same.

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While typically used in the context of the theory of the firm, it is possible to speak of a nation’s output being dependent upon the various resources used to produce that output. Such a production function is termed an aggregate production function, and has the same general form as that indicated above except that Q would now be the gross national (or domestic) product and K, L etc., would refer to the whole capital stock of the nation, the entire work force, etc.

Production functions may take many specific algebraic forms. Typically, economists work with homogeneous production functions.

Production function is essentially concerned with the physical aspects of production. So, it is of more concern to technicians and engineers than to economists. Only a technical person is in a position to say what specific quantity of a commodity can be produced by the use of the various produc­tive resources and their combinations.

Every business firm or its manager has to choose an appropriate produc­tion function on the basis of three things:

(1) Knowledge of industry,

(2) The prices of the various factor inputs, and

(3) Its own capacity to manage the production process.

The production manager has also to select the various factors and combine them properly. These two decisions are interrelated. The basic objective is to choose that particular combination of the factors which minimises cost per unit and gives maximum aggregate profit.

Four aspects:

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There are four points to be noted for understanding the nature of the production function:

1. The production function is essentially a purely technical relationship in the sense that it shows the relation between physical quantities of inputs and the resulting output. It has nothing to do with the price of a factor or price of the commodity the firm produces.

2. Output is the joint contribution of all factors of production. This means that the physical productivity of one factor can be measured only when this factor is used with other factors.

3. How the various factors of production are combined and what type of factors to be used depend on the state of technical knowledge. For example, labour productivity depends not only on the quantity of labour but also on the quality of the labour force which is determined by workers’ education and training. In a like manner, the productivity of capital goods like ma­chines is largely determined by the technical knowledge embodied in them.

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Furthermore, it is on the basis of technical knowledge existing at the time that different factors of production will be suitably combined in the process of production. This means that the state of technical knowledge is to be treated as given (i.e., there is no change in technology) while specifying and choosing a particular production function.

In formal notation, the produc­tion function has the general form:

Q = f (L, K, t, etc.)

where Q is output, L is labour, K is capital, t is ‘technical progress’ and where the ‘etc.’ indicates that other inputs may also be relevant (raw materials, for example). Any technological change will shift the production function and thus alter cost conditions of firms and industry. Any improvement in technology will result in a larger volume of output from a given combina­tion of labour, machines and other factors of production.

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4. Finally, while specifying the production function of a firm it is neces­sary to take into account the fixity or the variability of the factors as also whether they are divisible or indivisible. These two features of the factors of production will largely determine their physical productivities and thus the nature of the firm’s production function.