This document discusses the law of variable proportions, which examines how output changes as the quantity of one input is varied while keeping other inputs fixed. It defines the law, lists its assumptions, and provides an example to explain the three stages of production: increasing returns, diminishing returns, and negative returns. As labor is increased with land held fixed, total output first rises at an increasing rate, then at a diminishing rate, and eventually reaches negative returns if labor is increased too much. The stages are demonstrated through a table and graph of the relationship between labor input and total product.

1. AnuragRoy
AlinaAsghar
Malka Parveen
Farhaj Alam
DiptanilMukherjee
LAW OF VARIABLE PROPORTION
JIS University
Semester - 1st
Course – MBA

2. CONTENTS
1. INTRODUCTION
2. DEFINITION
3. ASSUMPTION
4. EXPLAINATION
I. TABULATION
METHOD
II. GRAPHICAL
METHOD
5. THREE STAGES OF
LAW

3. Introduction
 When producing an economic product, the supplier must decide
how much of each input to use:
◦ Land
◦ Labor
◦ Capital
 In particular, the supplier must examine the relation between input
and output

4. The Law of VariableProportion
This law place a vital role in economic theory.
It examines the production function with one factor variable,
keeping the quantities of other factors fixed.
In other words, it refers to the input-output relation when output is
increased by varying the quantity of one input.

5. Definitions
 By Benham –
“As the proportion of the factor in a combination of factors is
increased after a point, first the marginal and then the average product of
that factor will diminish.”
 By Samuelson –
“An increase in some inputs relative to other fixed inputs will in a
given state of technology cause output to increase, but after a point the extra
output resulting from the same additions of extra inputs will become less and
less.”

6. By Leftwitch –
“The law of variable proportion states that if the inputs of one
resource is increased by equal increment per unit of time while the
inputs of other resources are held constant, total output will increase,
but beyond some point the resulting output increases will become
smaller and smaller.”

7. Assumptions
(i) Constant Technology:
The state of technology is assumed to be given and constant. If there
is an improvement in technology the production function will move
upward.
(ii) Factor Proportions are Variable:
The law assumes that factor proportions are variable. If factors of
production are to be combined in a fixed proportion, the law has no
validity.

8. (iii) Homogeneous Factor Units:
The units of variable factor are homogeneous. Each unit is identical
in quality and amount with every other unit.
(iv) Short-Run:
The law operates in the short-run where it is not possible to vary all
factor inputs.
Assumptions

9. Explanation of thelaw
In order to understand the law of variable proportion, we take the
example of agriculture. Suppose land and labour are the only two
factors of production.
As we can observe from the table (next slide), the output varies with
one of the input is fixed and varying other input.
 The output varies in three different stages.

10. Fixed factor Variabl
e
factor
Total
Product
Margin
al
Produc
t
1 1
1 2
1 3
1 4
1 5
1 6
1 7
1 8

11. Calculationsof TotalProduct,AverageProductand
MarginalProduct
Total Product
The sum total volume of Production or total number of Units produced with the given
fixed and variable inputs.
Average Product
The ratio between total product and number of units of variable factor.
AP = TP / Units of VariableFactor
Marginal Product
The Increment in total output due to the use of an extra unit of labour.
MP = ∆TP/ ∆ L

12. Fixed factor Variabl
e
factor
Total Product Margin
al
Produc
t
1 1 2
1 2 5
1 3 9
1 4 12
1 5 14
1 6 15
1 7 15
1 8 14

13. Fixed factor Variabl
e
factor
Total Product Margin
al
Produc
t
1 1 2 2
1 2 5 3
1 3 9 4
1 4 12 3
1 5 14 2
1 6 15 1
1 7 15 0
1 8 14 -1

14. VARIABLE FACTOR
(LABOUR)
VARIABLE FACTOR
(LABOUR)
TOTAL
PRODUCT
STAG
E I

15. VARIABLE FACTOR
(LABOUR)
VARIABLE FACTOR
(LABOUR)
TOTAL
PRODUCT
STAG
E I
STAGE
II

16. VARIABLE FACTOR
(LABOUR)
VARIABLE FACTOR
(LABOUR)
TOTAL
PRODUCT
STAGE
III
STAGE I
STAGE
II

17. STAGE
III
POINT OF
INFLEXTION
STAGE I
STAGE
II
T
P
A
P
M
P
VARIABLE FACTOR
(LABOUR)
VARIABLE FACTOR
(LABOUR)
TOTAL
PRODUCT

18. Bykeepinglandas afixedfactor,theproduction ofvariablefactor
i.e.,labourcanbeshown withthehelpofthefollowingtable:
Land and Capital
(Units of fixed
factor)
Labour (Units of
variable factor)
Total Product
(TP) (tons of
wheat)
Marginal Product
(MP)
Average Product
(AV)
Stages of Variable
Proportions
10
10
10
10
10
10
10
10
10
10
0
1
2
3
4
5
6
7
8
9
0
20
50
90
120
140
150
150
140
125
-
20
30
40
30
20
10
0
-10
-15
-
20
25
30
30
28
25
21.3
17.5
13.8
Increasing
returns
Decreasing
returns
(negative returns)

19. Graphical Representation
TOTALPRODUCT
AVERAGE PRODUCT
MARGINAL PRODUCT
WORKER
PRODUCT
1st STAGE
Increasing Returns
2ND STAGE
Decreasing Returns
3RD STAGE
Negative
Returns

20. Three Stages ofLaw
 Stage 1 <Increasing Returns>
The output increases in an increasing rate.
 Stage 2 <Diminishing Returns>
The output increases in a diminishing rate
 Stage 3 <Negative Returns>
The output goes in negative value.

21. THANKYOU