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On the basis of time period, production function is of two types-

1. Short-term production function
2. Long-term production function.

Production functions are of two types according to time period. 

These are:

1. Short-term production function
2. Long-term production function.

According to the N Gregory Mankiw, “Relationship between the quantity of factors of production and quantity of production is production function”.

The direct relation of production function is not with economics but with engineering, and to make decisions for optimum production, information about all the alternative production functions of any goods and services is necessary. This comparison only can give us the desired result, since with the comparison of production functions only, the ideal proportion of production means can be properly conceptualized.

Long period or long-term is defined as that period of time in which all factors of production or inputs are variable. Distinction between fixed and variable inputs is obtained only in the short-term. In the long-term, all inputs become variable, i.e. the scale of production itself can be changed by installing new plant and equipment and hiring more labour and other factor inputs.

Five types of Production Function are:

(a) Linear Homogenous Production Function
(b) Cobb-Douglas Production Function
(c) Input-Output Production Function
(d) Activity analysis Production Function
(e) Transcendental – Logarithmic Production Function.

Short-term: Short-term is a period in which some factors are fixed and some factors are variable. Fixed factors have fixed cost and variable factors have variable cost.. Therefore, law of variable proportion applies here. In short-term, output can be increased or decreased by changing variable factors only, but fixed factors cannot be varied.

The distinguishing characteristics of short-term is that certain factor-inputs are fixed in character, while other factor inputs are variable in nature only. The level of production can be changed. The scale of production cannot be changed.

The behavior of output when one output and one input is varied and others are held constant, is studied under the ‘law of variable proportions’. It is also known as the ‘Law of Diminishing Returns’ and the ‘Law of Non-proportional Returns.’

Long-term: Long period or long-term is defined as that period of time in which all factors of production or inputs are variable. Distinction between fixed and variable inputs obtains only in the short-term. In the long-term, all inputs become variable, i.e. the scale of production itself can be changed by installing new plant and equipment and hiring more labour and other factor inputs.

The behaviour of output when all inputs are varied, is studied under the “law of returns to scale”.

The quantity of production of goods and services depends on the following two factors –

1. On cost of production factors.
2. On production function.

Long period or long-term is defined as that period of time in which all the factors of production or inputs are variable.

Short-term is a period in which some factors are fixed and some factors are variable. Fixed factors have fixed cost and variable factors have variable cost. Therefore, law of variable proportions applies here. In short-term, output can be increased or decreased by changing variable factors only, but fixed factors cannot be varied.

The distinguishing characteristics of short-term is that certain factor inputs are fixed in character, while other factor inputs are variable in nature. The level of production can be changed. The scale of production cannot be changed.

In short-term, the supply of fixed means of productionis in elastic.

Short-term: Short-term is a period in which some factors are fixed and some factors are variable. Fixed factors have fixed cost and variable factors have variable cost.

Long-term: Long period or long-term is defined as that period of time in which all factors of production or inputs are variable. In the long-term, all inputs become variable, i.e. the scale of production itself can be changed by installing new plant and equipment and hiring more labour and other factor inputs.

In short-term, the proportion of fixed and variable factors keep on changing along with the change in production. On the contrary, in the long-term, all factor inputs can be varied.

Short term is the time period during which a firm can make changes only in its variable factors but not in its fixed factors.

(b) output or produce

(a) Quantitative

(a) quantitative relation between dependent and independent variables

(d) E.H. Chamberlin

(c) Production function is the subject of Administrative economics.

(c) the relationship between factors and production

Economists like Adam Smith, Prof. Marshall and Ricardo related the law of diminishing marginal production with agriculture. They were of the view that if no improvement is made in agricultural techniques, then by increasing the quantity of labour and capital used on land, there will be less increase in general proportion of total produce. Modern economists do not agree with this concept. According to modem economists, this law applies in the sphere of manufacturing. The supporters of this ideology are economists John Robinson, Benham, Stigler, Bolding, etc.

According to modem economists, this law is ultimately applicable to every field of production. Initially, the production increase law applies, then, the law of equal production, and finally diminishing production law applies. Hence, these economists call this ideology “the law of returns of the variable proportions of means”. This name seems more appropriate, since it explains all the three states of production.

(a) short term

\(O_X=f(i_1,i_2,i_3,.....i_n)\)

Variable factors refer to those factors, which can be changed in the short run.