Production Function

What is Production Function?

Production function can be defined as a technological relationship between the physical inputs and physical output of the organisation.

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.

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.

• 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 function. 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 inputs used are labour and capital.

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

where ‘Q’ is output, ‘L’ the quantity of labour and ‘C’ 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 the manufacturing production. Although, the Cobb-Douglas production function suffers from many shortcomings, it is extensively used in Economics as an approximation.

Reference
1. D N Dwivedi, Managerial Economics, 8th ed, Vikas Publishing House

2. Petersen, Lewis & Jain, Managerial Economics, 4e, Pearson Education India

3. Brigham, & Pappas, (1972). Managerial economics, 13ed. Hinsdale, Ill.: Dryden Press.

4. Dean, J. (1951). Managerial economics (1st ed.). New York: Prentice-Hall.

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