Production Function

The production function is an equation that describes the relationship between the amount of productive factors (like capital and labour) needed and the amount of output produced. It specifies the quantity of inventory that may be obtained from any given set of circumstances, providing that the most efficient methods are applied.

Definition: – production function studies the functional relationship between physical inputs and physical output. It is expressed as under: –

Qx = f (L, K)

Here, Q = production of the commodity X;

           L = units of labour;

            K = units of capital

Output needs input. Land, capital and labour are the common inputs for the production of goods and services. As the producer, you would always be interested to know how much labour and capital (and other inputs) are needed to make a given amount of a commodity. You may find, for example, that 10 units of capital and 5 units of labour are required to produce 100 units of the commodity. It is this relationship between physical inputs (i.e., 10 units of capital and 5 units of labour) and physical output (100 units of the commodity) which is known as production function.

Production function, thus, studies the functional relationship between physical inputs and output of the commodity. It’s a technical relationship between material output on the one hand and material input on the other. Usually, it is expressed in terms of the following equation:

QX = f (L, K)

Here, Q = production of the commodity X; L = units of labour; K = units of capital

It is important to note that the production function does not establish an economic relation between outputs and inputs. It is the engineers (not the economics) who tell us that 10 workers working on 2 machines will yield the maximum output of 100 units of commodity X.

It is highly essential  to observe that a manufacturing function is represented with respect to a given technology or a given technical know – how. With time, technical know-how may improve, it may become possible to produce 110 units of commodity X (instead of 100 units) with the same inputs. It is a situation of shift (or change) in production function.

Factors of production are classified as: –

1. Fixed factors, and
2. Variable factor.

Fixed factors: –

Fixed factors are those the application of which does not change with the change in output. In fact, fixed factors like machines, land etc., are established before output actually commences. Thus, a machine is there even when output is zero. Let us assume that machine can produce a maximum of 1,000 units of commodity X. It means that for any change in output between 0-1,000 units: input of the machine (fixed factor) remains constant.

Variable factors: –

Variable factors are those the application of which varies (or change) with the change in output. For example- labour. You need more labour to produce more units of a commodity, other things remain constant. Thus, use of a variable factor is zero when output is zero; it increases as output increases.

TP (Total product), MP (Marginal product) and AP (Average product) of the variable factor: –

TP (total product): – TP is the total of the output produced by all units of a variable factor, with a constant amount of the fixed factors used in the process of production L consider L (Labour) as the variable factor and K (Capital) as the fixed factor Assume also that along with some constant application of the fixed-factor (say one machine), the producer is using 1 through 6 units of the variable factor. The resultant output is 10, 12, 15, 12, 10, 6 units of the commodity corresponding to each unit of Labour used. In such a situation,

                                                TP = 10 + 12 + 15 + 12 + 10 + 6

                                                     = 65 units of the commodity

MP (marginal product): – MP refers to change in TP when an additional unit of the variable factor is used (fixed actor remaining constant). Example: If output increases from 40 to 45 units when the put of labour is increased from 5 to 6 units (input of capital remaining constant), then

MP =45 – 40 = 5

45 = TP when 6 units of labour are used;

40 = TP when 5 units of labour are used;

5 = Increase in TP when 1 more unit of labour is used.

AP (Average Product): – Average product refers to physical output per unit of the variable factor used in the process of production. It is estimated as under:

AP=TP/L

TP = Total product/output

 L-Units of the variable factor

Conclusion

Production function is the relationship between the output and input of a firm. Factor of production involves variable factors and fixed factors. Fixed factors of production are those the application of which does not change with the change in output. On the other hand, variable factors of production are those factors of production the application of which changes with the change in output.