# Nature of Production Function

Production changes with period of time. In long run, there are various choices available with the producer to make required changes. However, in short run, the choices open to the producer are restricted because some factors are fixed and they can not be changed in the short period. In this situation, production function helps the producer to find out the relations between the variable inputs and the outputs.

X =f(a, b, Here X is the output of a commodity per unit of time and a, b, c, d….. are the various productive resources which go into the making of the quantity. Every manage- ment is required to make a choice of the production function which depends on the prices of the various factor of production but also on the capacity to manage.

Characteristics of Production Function

Important Characteristics of Production Function can be explained as under

1.Production Function explains the relationship be- tween physical quantity of the factors of production and the physical quantity of production.

2.Production Function is related with a given state of technological knowledge.

3.Production is completely free from the price of products and the prices of the factors of production.

4.Production Function is always related with a certain period of time.

5.Production Function can be divided into two parts on the basis of variability of factors of production: 1. Production Fünction in which the quantity of some factors of production remains fixed and the quantity of other factors of production varies, (i) Production
Function in which the quantity of all the factors of production varies.

6.Law of variable production is a stage of Production Function.

7.Production Function in which the quantity of all the factors of production remains variable is called long- term Production Function.

8.When the factors of production are increased in a certain ratio, there may be three situations with re- gards to the quantity of production

(i) Stage of Law of Increasing Returns,

(ii) Stage of Law of Constant
Returns,

(ii) Stage of Law of Decreasing Returns.

Mathematical Equation

Production Function of can be, expressed in the form of a mathenmatically equation as under:

p=Total Production of a Commodity

a=Quantity of One Factor of Production (Let it be Land)

b= Quantity of Another Factor of Production (Let it be Labour)

c=Quantity of Another Factor of Production (Let it be Capital)

f = Function of (is dependent of) Quantity of
Other factors of Production.

Above equation makes it clear that the quantity of production (P) depends upon the quantity of factors of pro- duction (a, b, c etc.), if any of a, b, c is changed, ‘p? will also change.

If a small textile factory produces 5,000 meters of cloth per 8-hour shift, then its productive function consists of the minimum quantities of raw cotton, power, labour, dyestuffs,floor space, machine time, etc. that are required to produce 5.000 meters of cloth. Putting it differently, the production function of the same textile factory consist of the maximum number of meters of cloth that can be produced with given quantities of raw cotton, power, labour, dyestuffis, etc. The production function is always specified for a period oftime.It is a flow of inputs, resulting in a flow of output during a specified period of time.