#### CA Foundation Business Economics Study Material Chapter 3 Theory of Production and Cost – Production Function

Production Function

• Output is a function of inputs i.e. factor services such as land, labour and capital which are used in production. In other words, production is a transformation of PHYSICAL INPUTS into PHYSICAL OUTPUT.
• The functional relationship between physical inputs and physical output, per unit of time under a given state of technology is called production function.
• It can also be expressed in the form of a mathematical equation in which output is the dependent variable and inputs are the independent variables.
Q = f (a, b, c ………… n)
Where –
Q denotes quantity of output of a commodity per unit of time
f stands for function of i.e. depends on a, b, c,… n denotes quantity of various inputs.

Assumptions of Production Function:
The production function is based on the following assumptions:

1. It is specified with reference to a specified period of time.
2. It is assumed that the state of technology remains the same, during the period of time.
3. It is assumed that the firm uses best and most efficient technique available in production.
4. It is assumed that the factors of production are divisible into viable units.

The production function can be explained under two heads:
1. The short run production function in which input – output relations are analysed where –

• One input is variable, all other inputs are fixed, (described as the Law of Variable Proportions) OR
• Two inputs are variable, all other factors are fixed (explained with the help of isoquants)

2. The long run production function in which input- output relations are analysed where all the inputs are variable (described as the Law of Returns to Scale).

Cobb-Douglas Production Function
Q = f (L, K).
Where –
Q = Output; L = Labour; K = Capital

Paul H. Douglas and C.W. Cobb of the U.S.A. studied the production function of the American manufacturing industries. This production function applies to the whole of manufacturing in U.S.A. rather than to an individual firm. In this case, output is manufacturing production and inputs used are labour and capital.

The conclusion of study is that labour contributed 3 /4th and capital about 1 /4th in the manufacturing production.