What is Production Function? Formula, Uses, Assumption

What is Production Function?

Production function can be defined as a technological relationship between the physical inputs (i.e., factors of production) and the physical output of the organisation.

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Meaning of Production Function

The production function is a statement of the relationship between a firm’s scarce resources (i.e. its inputs) and the output that results from the use of these resources.

Inputs include the factors of production, such as land, labour, capital, whereas physical output includes quantities of finished products produced. The long-run production function (Q) is usually expressed as follows:

Q= f (LB, L, K, M, T, t)

Where, LB= land and building
L = labour
K = capital
M = raw material
T = technology
t = time

Production Function Definition

Production function is the name given to the relationship between the rates of input of productive services and the rate of output.Stigler

Production Function is the technological relationship, which explains the quantity of production that can be produced by a certain group of inputs. It is related with a given state of technological change.Samuelson

The relation between a firm’s physical production (output) and the material factors of production (input) is referred to as production function.Watson

Uses of Production Function

In economics, the uses of production function are as follows:

Helps in making short-term decisions, such as optimum level of output.
Helps in making long-term decisions, such as deciding the production level.
Helps in calculating the least cost combination of various factor inputs at a given level of output.
Gives logical reasons for making decisions. For example, if price of one input falls, one can easily shift to other inputs.

Also Read: Types of Production Functions

Nature of Production Function

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.
The output is the result of a joint use of the factors 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.
The nature or 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.
In specifying the production function of a firm, we have to take into account the variability of the factors of production and also whether they are divisible or indivisible: These features of the factors of production will determine their productivities and hence, the nature of the production function.

Assumptions of Production Function

Assumptions of production function are as follow:

Production function is related to a specific time period.
The state of technology is fixed during this period of time.
The factors of production are divisible into the most viable units.
There are only two factors of production, labour and capital.
Inelastic supply of factors in the short-run period.

Limitations of Production Function

Apart from the advantages, production function also suffers from some limitations.

Limitations of Production Function are:

Restricts itself to the case of two inputs and one output.
Assumes a smooth and continuous curve, which is not possible in the real world, as there are always discontinuities in production.
Assumes technology as fixed, which is not possible in the real world.
Assumes a perfectly competitive market, which is rare in the real world.

Cobb-Douglas Production Function

A cobb-douglas production function is one of the famous statistical production functions. In its original form, this production function applies not to an individual firm but to the whole of manufacturing in the United States. In this case, the output is manufacturing production and the inputs used are labour and capital.

A cobb-Douglas production function is stated as: Q = KLa C (1-a)

where ‘Q’ is output, ‘L’ is the quantity of labour and ‘C’ is the quantity of capital. ‘K’ and ‘a’ are positive constants.

The conclusion drawn from this famous statistical study is that labour contributed about 3/4th and capital about 1/4th of the increase in manufacturing production. Although the Cobb-Douglas production function suffers from many shortcomings, it is extensively used in Economics as an approximation.

What is Production Function? Formula, Uses, Assumption