This document discusses production functions and the factors that influence them. It defines key concepts like total product, average product, marginal product, and different types of production functions. The short-run production function, known as the law of variable proportions, describes how output changes as one input varies while others are held fixed. It outlines the three stages of increasing, decreasing, and negative returns. The long-run production function examines how output changes as all inputs vary, governed by laws of returns to scale. Constant, increasing, and decreasing returns to scale are defined. Isoquants and the marginal rate of technical substitution are also explained. The document concludes by discussing how production functions inform managerial decision making.

1. Pr oduction
Function

2. Fundamental Questions of
Managers
• How can production be optimised or cost minimised
• How does output behave when quantity of input is
increased
• How Technology effects the cost of production
• How can least –cost combination of inputs be achieved.
• What happens to rate of return when the firm expands.

3. Factors of Production
•
Production requires use of factors – agents of production
•
Economic growth is dependent upon the supply and
productivity of factors.
•
The good and services which are used for the production
of goods – Inputs.
•
What they produce – Outputs.
•
The input –output analysis has become an important tool
of modern economic analysis.
•
Classified as
– Land, Labour, Capital, Entrepreneurship

4. Theory of Production
•
Production means creation of a valuable utility.
•
Supply of product refers to the quantity supplied at the
given price.
•
Which depends upon
– Relationship between input and output
– Prices of inputs
– Managerial efficiency
•
Production function:
The functional relationship under given technology between
input and output, per unit of time.
Q = f ( L, K)

5. Theory of Production
• It states the maximum amount of output that can be
produced with any given quantities of various inputs.
• Particular period of time
• Flow concept : Flow of inputs leads to flow of output

6. Types of Production
Function
Types
Short –Run
(Inputs kept constant
One input (Labour) is varied)
Law of variable
proportion
Long – Run
(Varying all inputs)
Law of returns to
scale

7. Concepts Of Product
1)
Total Product:
Total output produced by given amount of factor, other
factor held constant.
As the factor increases the total output increases.
2)
Average Product :
AP =
Total Product
No of Units of a Factor employed
=
Q
L
Avg product first rises and then falls
3)
Marginal Product:
The addition to the total production by the employment
of an extra unit of a factor
MP = ∆Q
∆L

8. Units of
Labour
Marginal
Product
(Quintals)
Average
Product
(Quintals)
L
Total
Product
(Quintals)
Q
1
80
80
80
2
170
90
85
3
270
100
90
4
368
98
92
5
430
62
86
6
480
50
80
7
504
24
72
8
504
0
63
9
495
-9
55
10
480
-15
48
IR
DR
Negative

9. Short – Run Production Function
Law of Variable Proportion
•
One – factor varying, quantities of other factor as fixed
•
Law of variable proportion:
It’s the study of the effect on output of variations in factor
proportion
•
As the proportion of one factor in a combination of factors is
increased after a point, first the marginal and then the
average product of that factor will diminish.
•
It’s a new name for Law of Diminishing returns
– The state of technology is assumed to be given /
unchanged
– Some inputs whose quantities is fixed
– Measured in physical terms.

10. Stages of Law of Variable
proportion
H
TP
Total Product
F
Stage 1
D
Stage 2
Stage 3
S
AP
Amount of Variable Factor
MP

11. Stages
Stage 1.
– TP increases at an increasing rate upto a point.
– MP of variable factor is rising
– Point F (Point of Inflection), TP curve rises but its
slopes decline – TP is increasing at a diminishing
rate. MP starts falling but its positive.
– AP reaches its highest point
– MP of variable factor rises and then falls
– MP of fixed factor is negative
– Quantity of fixed factor is too much to the variable
factor

12. Stages
Stage 2.
– TP increases at a diminishing rate, reaches its
maximum point
– MP, AP are diminishing but positive
– MP becomes Zero
Stage 3.
– TP slopes downwards
– MP of variable factor is Negative

13. In which stage the
Producer should Produce
•
Stage 3 – No
MP of variable factor is negative
•
Stage 1 – No
MP of fixed factor is negative
Full utilisation is not there
Stages of
Economic absurdity / Economic non-sense /
Non- economic regions
•
Stage 2 – Yes
MP and AP are positive but diminishing

14. Causes
•
Increasing Returns
– Quantity of fixed factor is abundant than variable factor
– Fixed factor are indivisible
– With addition of variable factor , fixed factor is more
effectively and intensively utilised.
– More units of variable factor are employed , the
efficiency of variable factor increases –
“specialisation of labour”.
•
Diminishing Returns
– The maximum point has reached.
– The amount of the variable factor is sufficient to ensure
the efficient utilisation of fixed factor.
– The contribution to the production made by the variable
factor after a point become less as the additional units
of the variable factor have less of fixed factor.

15. Causes
•
Negative Returns
Number of variable factor become too excessive to the fixed
factor Marginal Product of variable factor is negative.
•
Diminishing returns occur because the factors of production
are Imperfect substitutes for one another.
There is a limit to which one factor of production can be
substituted for another.
Elasticity of substitution between factors is not infinite.

16. Technological Progress and
Diminishing Returns
• In today’s scenario the Technological progress can
suspend the operation of diminishing returns by
continually improving the techniques of production.
AP4
AP3
Output
AP2
AP1
Labour Force

17. Long Run –
Laws of Return to
Scale
•
Both the factors are taken as variables
•
Isoquant : is a curve representing the various combinations
of two inputs that produce the same amount of output
Also called as equal product curve
Factor
Production
Labour Capital
A
1
12
B
2
8
C
3
5
D
4
3
E
5
2
Isoquant
K
L

18. General Properties of
Isoquant
•
An Isoquant is downward sloping to the right:
If more of one factor is used then less of the other factor
is needed for producing same level of output
•
Higher Isoquant represents larger output
•
No two isoquants can intersect each other
Same amount of factors can produce two levels of output
•
Isoquants are convex to the origin
Slope of isoquants diminishes from left to right, Marginal rate of technical substitution

19. Types of Isoquant
The shapes depends upon degree of substitutability of inputs
1)
2)
Linear Isoquant:
Perfect substitutability between
factors of production.
An output can be produced by
either using one or both
Input- Output Isoquant
Strict complementarity's between
inputs. One method of
production. If a quantity
of one input is
increased there will be
no change in output.
Q3
Q2
Q1
Q2
Q1

20. Marginal Rate of Technical
Substitution
•
•
MRTS = The rate at which the factors can be
substituted at a margin without altering the level of
output.
MRTS L for K = No of units of capital which can be
replaced by one unit of labour
Factor
Combination
Units of
Labour
Units of
Capital
MRTS of
L for K
A
1
12
B
2
8
4
C
3
5
3
D
4
3
2
E
5
2
1
MRTS L for K = Slope = ∆K = MPL
∆L
MPK

21. Marginal Rate of Technical
Substitution
•
•
As the output remains constant
When labour and capital are substituted for each other,
the change in output due to decrease in the amount of
capital is equal to increase in output due to increase in
amount of labour.
– ∆K. MPK = ∆ L.MPL
MRTS L for K = ∆K =
∆L
MPL
MPK
– MP = Marginal productivities of labour and capital

22. Why Diminishing MRTS
•
MRTS diminishes as more and more of labour is
substituted for capital.
•
Less of capital is required to be substituted by an
additional unit of labour so as maintain the same level
of output.

23. The Law of Returns to Scale
• Return to Scale:
The resultant increase in total output as the two inputs
increases.
Total output may increase proportionately
Total output may increase more than proportionately
Total output may increase less than proportionately
• Three types:
– Constant
– Increasing
– Decreasing

24. Constant Return to Scale
• Percentage change in factor inputs leads to equal
percentage change in output.
• Factors of production are perfectly Divisible, production
function must exhibit constant returns to scale
• In some industry it is not possible to increase or diminish
factors in exactly the same proportion
• Some factors supplies are scarce
• Factors are indivisible, full utilisation is done only
when production happens in large scale

25. Constant Return to Scale
IQ3
R
IQ2
IQ1
c
Units of Capital
b
QX3 = 300
a
QX2= 200
QX1= 100
O
Units of Labour
oa = ab = bc

26. Increasing Returns to Scale
• Output increases in a greater proportion than the
increase in the inputs
• Expanding firms experience this factor
– Indivisibility of the factors:
Some factors are better utilised at large scale of
output
– Greater possibility of specialisation of labour and
machinery
– Integration of processes
– Dimensional Advantage

27. Increasing Return to Scale
IQ
IQ2
R
IQ3
c
Units of Capital
b
a
QX3 = 300
QX2= 200
QX1= 100
O
Units of Labour
oa > ab> bc

28. Decreasing Returns to Scale
• When output increases in a smaller proportion then the
increase in all inputs.
– Diseconomies outnumber economies of scale:
When the firm expands beyond a point of constant
return, the diseconomies outnumber
( increasing difficulties of management, co-ordination
and control with the expansion in scale and output)
– Limited reserves of natural resources

29. Decreasing Return to Scale
IQ3
IQ2
R
c
IQ1
Units of Capital
b
QX3 = 300
a
QX2= 200
QX1= 100
O
Units of Labour
oa < ab < bc

30. Returns of Scale in a
production process
•
There are three phases in production
– First Stage:
Increasing returns to scale because of a greater
possibility of specialisation of labour and machinery
– Second stage
Constant returns to scale
– Third stage:
Firms continue to expand – decreasing returns to
scale due to difficulty of co-ordination and control.

31. Importance of Production
functions in Managerial Decision
Making
•
Serve as the foundation for the analysis of cost
•
Optimal allocation of firms resources in
short-run and long-run
•
Capacity Planning
• Accurate forecasts of demand
• Effective communication between the production and
marketing functions

32. Case Study –Vandana
Enterprises
Owners:
Kumars ( Mr Ramesh Kumar(MD) /
Vandana(daughter)
No of employees:
300
No of years in Business :25
Business:
Textile (Spinning and weaving of
white linen)
Target: To expand in Domestic and Export market
When the company was started, they had 350 workers, the
company used old technology to produce clothes. Labour
was mainly used, while machine was minimally used.
The plant was modernised and mechanized over the years
Production: 15000 m to 60,000m everyday (maximum
technical efficiency)
What should the company be doing in order to
increase Sales and increase their impact in the
international market.

33. Case Study –
Vandana Enterprises
Solution:
1)
2)
3)
4)
To produce Bed sheets, pillow covers etc
To improve market Information
Machinizing the plant further
Retrench labour
Import machines
Hire specialised labour

34. Case Study
Pearl Diving Operation
•
•
•
•
•
•
Company: Peter F. Smithson
Product:
Pearl
No of Years : 28
Area of Operation: North Pacific ocean
Offices: Japan and Canada
Mode of Operation
– 3 Trawlers
– Hired local Japanese and Canadian divers
– Coast of Japan more profitable ( Time / efficiency of
Japanese divers)
– Divers intensively pearled the Japan coast ( 9 times in
the same area)

35. Case Study
Pearl Diving Operation
•
•
Sept –Oct data
Peter not happy with
results
Not been able to
compensate for nonoperation of Canada
Q. How many divers seem
to be efficient
Q. How can he modify his
present plan in terms of
return to scale?
Divers
Employ
ed
Oyster
recovered
(Kg)
1
5
25
2
12
70
3
•
Trip
No
9
52
4
6
30
5
13
75
6
4
18
7
13
78
8
16
76
9
12
76