Weighted Average of Price Relatives Method, Practical Problem | Index Numbers
🚩Timestamps:-
00:31 previously
00:51 Session Agenda
01:57 Construction of Weighted Index Numbers (There are two methods)
02:12 WEIGHTED AVERAGE OF PRICE RELATIVES METHOD
04:11 not all commodities are ever included
05:55 Practical Problem 1 (Weighted Average of Price Relatives Method)
11:33 Concluding Remarks (upcoming sessions…)
Learning Outcomes:-
Through this module, you will gain understanding
on:-
1.
Construction
of Weighted Index Numbers (There are two methods)
2.
WEIGHTED
AVERAGE OF PRICE RELATIVES METHOD
3.
Practical
Problem 1 (Weighted Average of Price Relatives Method)
4.
WEIGHTED
AGGREGATIVE METHOD
5.
Laspeyre's
Method
6.
Paasche's
Method
7.
Fisher's
Method
8.
Fisher's
Index Number as an Ideal Method
9.
Time
Reversal test (TRT)
10.
Factor
Reversal Test (FRT)
11.
Practical
Problem 2 (Laspeyre, Paasche & Fisher Methods)
Construction
of Weighted Index Numbers (There are
two methods)
WEIGHTED AVERAGE OF PRICE RELATIVES METHOD
According to this method,
weighted sum of the price relatives is divided by the sum total of the weights.
In this method, goods are given weight according to their quantity.
Not all Commodities are Ever Included
Not all commodities are
ever included in the construction of an Index Number. Only a sample of
commodities is taken which represents characteristics of commodities under
study
|
Goods |
weight |
2004 price Rs (0) |
2014 price Rs (1) |
|
wheat |
40 |
100 per qt |
200 per qt |
|
Rice |
30 |
200 per qt |
800 per qt |
|
Milk |
15 |
2 per L |
16 per L |
|
Ghee |
10 |
8 per kg |
40 per kg |
|
sugar |
5 |
1 per kg |
6 per kg |
WEIGHTED AGGREGATIVE METHOD
·
Under this
method, different goods are accorded weight according to the quantity bought.
·
Economists have
different views in this respect. Should the weight be given
(i)
on the basis of the quantity bought in the current year or
(ii)
on the basis of the quantity bought in the base year or
(iii)
on the basis of the quantities bought in both the years?
Different economists have,
therefore, suggested different techniques of weighting. Some of the well known
methods are as under:
(1) Laspeyre's
Method:
Laspeyre's uses base year
quantities (q0) as weights of different items. His formula for estimating Index
values is:
(2) Paasche's Method:
Paasche's on the other hand
uses current year's quantities (q1) as weight. His formula to construct the
Index value is:
What is the basic difference between Laspeyre's and
Paasche's methods of construction of Weighted index Numbers?
Laspeyre uses base year
quantities as the weights of different items. Paasche on the other hand, uses
current year quantities as weights.
(3) Fisher's Method:
Fisher has combined the
techniques of Laspeyre's and Paasche's method. He used both base year as well
as current year quantities (q0, q1) as weight. His formula to construct Index
Number is:
Fisher's Index Number as an Ideal Method
The choice of method for
the construction of an index number will depend upon the object with which a
particular index number is constructed. Many formulae may be used for the
construction of index numbers but all may not be suitable for the specific purpose
in hand. Some of the important formulae do not conform to certain appropriate
test of consistent behaviour; it implies that these formulae give us biased
results. However, Fisher's Method is considered as an 'ideal' method for
constructing index numbers:
Fisher's Method is
considered as 'ideal' because
(1) It is based on variable weights.
(2) It takes into consideration the price and
quantities of both the base year and current year.
(3) It is based on geometric mean (GM) which is regarded
as the best mean for calculating index number.
(4) Fisher's index number satisfies both the
Time Reversal Test and Factor Reversal Test.
·
The time reversal test implies that the
formula for calculating an Index Number should be such that will give the same
ratio between one point of comparison and the other, no matter which of the two
is taken as base. Time Reversal means that if we change base year to current
year and vice versa then the product of two indexes should be equal to unity.
Thus, an index number should work both ways, i.e., forward as well as backward.
·
On the other hand,
Factor Reversal Test implies, just as our formula should permit the
interchange of two items without giving inconsistent results, so it ought to
permit interchange of prices and quantities without giving inconsistent
results, i.e., the two results multiplied together should be equal to value
ratio.
|
Items |
2004
Base Year (0) |
2014
Current Yr (1) |
||
|
|
Price |
Quantity |
P |
Q |
|
A |
10 |
10 |
20 |
25 |
|
B |
35 |
3 |
40 |
10 |
|
C |
30 |
5 |
20 |
15 |
|
D |
10 |
20 |
8 |
20 |
|
E |
40 |
2 |
40 |
5 |
Introduction to Time
reversal test|Factor reversal test|Circular test|Index numbers|BBA|BCA|B.COM
https://www.youtube.com/watch?v=fh7kDWCowXQ
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Construction of Weighted Index Numbers (There are two methods), WEIGHTED AVERAGE OF PRICE RELATIVES METHOD, not all commodities are ever included, Practical Problem 1 (Weighted Average of Price Relatives Method) | Index Numbers | 11th Commerce | by @statomics11comm
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