## Lesson 13. PRODUCTION FUNCTION FOR A SINGLE PRODUCT

Module 3. Theory of production

Lesson 13
PRODUCTION FUNCTION FOR A SINGLE PRODUCT

13.1 Introduction

Resources used in production are called factors of production or inputs. These are classified as labour, land and capital. The relationship between the inputs to the production process and the resulting output is explained by production function.

13.2 Production Function

The inputs to the production function are classified as fixed and variable. Production is generally carried out based upon market demand. Based upon market demand it is possible to change some of the inputs (either increase or decrees) whereas it is not possible to change some of the inputs immediately. The former are called variable inputs and later, the fixed inputs. The labour and raw material are examples of variable input whereas buildings, major capital equipment are examples of fixed input.

The mathematical relationship between input and output can be given by

P = f (a, b, c,...n)

Where P is dependent variable and represent rate of output.

a, b, c.........n are independent variables represents inputs employed by the firm.

An organization can combine different independent inputs in different ways. For example agricultural university has vast stretch of land at its disposal. This land can be used for either crop production of different variety or even for constructing colleges, hostels etc. The mode of use of land will thus decide the quantum and type of output. Thus according to professor Samuelson production function exhibit technical relationship between the maximum output by using each and every set of specified inputs.

13.2.1 Assumptions of production function

Following are the assumptions of production function

a) Production function is for a particular specified time frame.

b) A given state of technology which remains same during the specified time period.

c) The organization employs best available technology

d) Factors of production are subdivided into small viable units.

13.2.2 Characteristics of production function

Important characteristics of production function are given below.

1. Flow concept: Production function exhibits flow concept. It represents flow of inputs and the resulting output flow for a specified time period.

2. Physical concept: It exhibit technical relationship between physical input and physical output only and not in any other firm.

3. Complementary: Input show complementary characteristics. For example if man and machine combination produces 5 units of a commodity per day. By employing 2 man and 2 machines, 10 units of that commodity can be produced.

4. Substitutability: Some factors may be substitutable. For example X and Y are substitutable factor, X may be increased instead of Y. X is fixed while Y is variable. one can use less capital and more labour and vice versa for obtaining same output. For example, if agricultural university wants more agricultural produce, it can use more land or can adopt new improved varieties of seeds, fertilizers and other inputs to get more produce from the same land.

5. Specificity and versatility: If a factor of production can be used for only one purpose, it is considered as specific on the other hand if it can be used for more than one purpose it is referred to as versatile. In production some factors are specific and some are versatile. A thrasher and tractor are versatile farm equipment whereas chemical spraying pump is specific.

Short run and long run production function: Short run production function represents a time period in which the inputs of some factors of production cannot be changed. They are referred to as fixed factors e.g. plant, machinery and equipment. Long run production function represents time period which allows change in the input of all factors of production used by the organization.