B.Sc. I (Sem. II Paper III) Unit 2, 2.1 INDEX NUMBERS : निर्देशांक , देशनांक , सूचकांक
Unit ... 2
The time has come, the Walrus said
To speak of many things,
Of shoes, and ships, and sealing wax,
Of cabbages and kings
- lewis Carroll
2.1 Index Numbers
introduction:
Index
Number is a tool used to measure the changes in prices of commodities,
industrial and agricultural production, sales, imports, exports, etc. It was
first developed by an Italian economist Mr. Carli in 1764 for comparison of
prices of commodities. The fields in which the index numbers are used are
economics, trade, stock market, Government Organizations etc. The popularly
used index numbers are-
i) Bombay
Stock Exchange (BSE) SENSEX Index Number.
ii) NSE index
numbers.
iii) All
India Wholesale Index Price Number.
iv) Consumer
Price index number.
v) Index
number for Industrial production.
vi) Index
number for Agricultural production.
Index
Numbers an economic barometer:
Economic phenomena are dynamic. We observe that the
prices of commodities change from time to time, place to place, wages of
workers, prices of shares exhibit up & down movements, industrial
production also goes changes; in fact they measure pulse of economy like inflationary
or deflationary tendencies. The apparatus barometer reflects the changes in
atmospheric pressure likewise index numbers reflects the changes in economic
activities. Hence they are rightly called as ‘economic barometers’.
Definition:
Index number is a number
designated to measure the average change in the values of a group of related
variable over two different situations.
The group of variables may be prices
of specified commodities, quantities of industrial production, volume of
imports and exports etc. Two different situations maybe two different times or
places.
An index number is a numerical measure of the price
situation at one time on the basis of the price situation at some other
appropriate time in the past. Thus index numbers are always in percentages. We
equate the prices of commodities in the base year to 100 and then express the
prices of commodities in the current year as the percentage of the prices in
the base year.
For example:
|
Commodity |
Price in 1956  |
Price in 1990  |
Index number  |
|
A |
25 |
30 |
120 |
|
B |
18 |
21 |
116.66 |
|
C |
20 |
26 |
130 |
Types of index numbers:
Price index numbers:
i)
Wholesale price index numbers- They reflect the change in the
general price level of a country.
ii)
Retail price index numbers- They reflect the general changes in
the retail prices of the various commodities.
Consumer price index, commonly
known as Cost of Living index number is a special type of retail price index
& enables us to study the effect of changes in the prices of a basket of
goods or commodities on the purchasing power or cost of living of a particular
class or section of the people like industrial or agricultural worker, labor
class, low income or middle income class etc.
1)
Purpose-
There are different index numbers such as of wholesale
prices, of retail prices, of industrial production, of agricultural production
etc. Each index number has its own particular uses and limitations. Hence, it
is necessary at the outset to define the purpose of the index number.
2)
Selection of the base year-
The year with which comparison is made is called the base year or base
period. The following points should be taken into account while selecting the
base year.
i) The base period (year) should be a
period of normal and stable economic activities. The base year should not be
affected by unusual situations like wars, earthquakes, floods, famines etc.
ii) The base year should not be too
distant. The economic activities are always dynamic. A distant period makes the
index number irrelevant for short period comparisons.
iii) Fixed base or chain base-
In the fixed base method, the
comparison is made always with the previous year. Chain base method is superior
since it accounts for all the changes step by step.
3)
Selection of items-
The selection of
items depends upon the purpose of the index number. The items which are
selected for one index number may be irrelevant for the other. For example the
items like scooter, T.V. sets etc. cannot be included in the list for
constructing cost of living index for working classes.
The larger the number of items, the more
representative will be the index number. Also, in order to arrive at meaningful
& valid comparisons, only standard qualities of items are considered.
4) Price quotations
We know
that the prices are different in different cities & even in different shops
in the same city. We cannot make use of the prices collected from all the shops
we select a few standard & reasonable shops & take the average of the
prices supplied by them.
5) Choice of an average-
The price index number is sometimes
computed by averaging the percentage changes in price of each of the
commodities included in the group. The a. mean due to simplicity in calculation
is used in a great majority of cases. But since it is highly affected by
extreme values, geometric mean is preferred in most cases.
6) Selection of weights-
All items are not equally important
ex. Sugar is not as important as rice. The weights are assigned in two ways- i)
Quantity weights ii) Value weights.
i) Quantity weights- Actual quantities may be used as
weights, but they are not always appropriate. Also in many cases, the
quantities are not measured in the same unit. They are appropriate where
various commodities are attached importance according to the amount of their
quantities used, purchased or consumed.
ii) Value weights- When units of measurement are different, it is convenient to use value weights.
They
are appropriate if importance is given to the expenditure incurred on them.
7) Selection of formula/ Choice of
method-
There are various formulae available to calculate
index number. The choice depends upon the purpose & the nature of data
collected. Fisher’s formula is ideal; it has also its own limitations.
Methods of constructing Price index numbers:
A
number of formulae have been devised for constructing index numbers. They can
be divided into two types.
i) Unweighted index numbers & ii)
Weighted index numbers.
Each of these
two types may further be divided into two classes as:
i) Aggregative & ii) Average of
price (quantity) relatives.
The methods can be shown by the following chart:
Unweighted Price index numbers:
i) Aggregative method-
In this method
the aggregate of prices of different commodities in the current year is divided
by the aggregate of prices of different commodities in the base year and the
quotient is multiplied by 100.
Ex.: Compute price index
no. by average of price relatives method using a. mean for the following data.
Que : From the following data construct calculate index no. of the types- i) Simple aggregate prices. Ii) weighted aggregate prices iii) simple a. mean of price relatives iv) weighted a. mean of price relatives v) simple g. mean of price relatives vi) weighted g. mean of price relatives.
Item | Base yr. price | Current yr. price | P=price relative | Log p |
A | 120 | 144 | 120 | 2.07918 |
B | 160 | 176 | 110 | 2.04139 |
C | 150 | 195 | 130 | 2.1139 |
D | 130 | 182 | 140 | 2.1461 |
Total | 560 | 697 | 500 | 8.3806 |
Weighted
Price index numbers:
i) Aggregative method-
In this method, appropriate weights are assigned to various commodities to reflect their relative importance in the group. Usually, the quantities consumed, sold or marketed in the base year or current year are used as weights. If W is a weight attached to a commodity, then the price index is given by,
1) Laspeyre’s index number
2) Paasche’s index number
3) Fisher’s index number
Comparison:
1) In Paasche’s index, actual quantities
of every year are required.
2) In Laspeyre’s formula, since the
quantities of base year are used as weights, the influence of price changes on
quantity demanded would not get reflected in index number.
3) Laspeyre’s index has upward bias
& Paasche’s index has downward bias.
3)
Fisher’s ideal index number:
Fisher’s ideal price
index number is given by the geometric
mean of Laspeyre’s & Paasche’s formula. Symbolically,
Merits:
i) It is free from bias since the upward
and downward biases of Laspeyre’s & Paasche’s index are balanced.
ii) It is based on geometric mean,
theoretically which is considered to be the best average for constructing index
numbers.
iii) It confirms to certain tests of
consistency.
iv) It takes into account the influence
of the current as well as the base year.
Demerits:
i) The ideal index is a hybrid of two
index numbers. It is difficult to say what exactly it is supposed to measure.
ii) It requires the quantities of both
base & current years. The determination of these quantities is a difficult
task, involving a lot of labor, expense and time.
ii) Average of price relatives:
If the
weights of all items are given, then the index number by weighted average of
price relatives method is given by,
Note:
i) Sometimes weights are given as
percentages of the total expenditure.
ii) This index is called as cost of
living index.
iii) Index number of the type using
geometric mean will be,
Test of Index Numbers:
We have seen that there are a number
of formulae for constructing index numbers. To select a proper (best) formula
for the following tests are suggested, which compare the adequacy of the
formula.
i)
Unit
test
ii)
Time
reversal test
iii)
Factor
reversal test
i) Unit test:
Index number
which is independent of units in which prices & quantities are expressed is
said to satisfy unit test. All index numbers except the simple aggregative
price (or quantity) index number satisfy this test.
ii) Time reversal test:
According to Fisher a good index
number must maintain time consistency. Index number is said to follow time
reversal test if the product of original index number & the index number
after interchanging the base year and current year, should be equal to unity
(without the factor 100). Thus time reversal test demands that,
For
ex: Suppose the price of commodity in
base year is Rs. 12 per unit & in current year it is Rs. 15 per unit.
Here
(without the factor 100)
(without the factor 100)
Note: Fisher index number, Simple aggregative price index number, Simple
G.M. of price relative index number, weighted G.M. of price relative index
number with fixed weights satisfies this test. While Laspeyre’s & Paasche’s
index number, simple average of price relatives does not satisfy this test.
iii) Factor reversal test:
Index
number is said to satisfy the factor reversal test if the product of price
index number & the quantity index number is equal to the value index number
(without the factor 100).
Thus this test demands that,
This test is satisfied by only Fisher index number.
Consider
Hence, Fisher’s index number satisfies the factor reversal test.
Fisher’s index number satisfies the time reversal test and factor reversal test. So it is called as Fisher’s ideal index number.
Cost of Living index number Or Consumer
price index number:
This
is a number which measures the average change in the retail prices paid by a
particular class or section of the people at a particular place for a basket of
specified goods or commodities & services over two different time periods.
Problems (Steps) in the construction of
cost of living index number:
1)
Purpose (Scope)-
The first step in the construction of Cost of Living
index no. is to decide the particular class of people for whom the index number
is intended. ( It must be a homogenous group).
2)
To conduct a family budget survey
(inquiry):
This would give us information about the amount; an
average family spends on different items of consumption. This also enables in
determination of weights.
The commodities are broadly classified into the
following five major groups.
i) Food
ii) clothing iii) Fuel & Lighting iv) House rent v) Miscellaneous (Others).
Each of these groups is subdivided into subgroups. For
ex. Food is further subdivided into cereals, pulses, sugar, oils, milk products
etc. Selected commodities should represent the tastes, habits & preference
of people.
3) To obtain price quotations- (To
collect price data):
The prices ( for the base & current year ) should
be obtained from the localities where the people live & from the shops
where they usually buy. Prices are taken from representative & reliable shops
by trained agency. ( Cash prices only, discounts should not taken into
account). Average of prices should be taken for different shops & time.
4) Weights:
The
weights are determined either from the quantity consumed or from the proportion
of the expenditure on the item.
5) Choice of the formula:
Generally
the following two formulae are used for cost of living index. i) Aggregate
method (Aggregate expenditure method). ii) Family budget method (Weighted
average of price relatives).
i) Aggregate method:
In
this method the quantities in the base year are used as weights. Thus,
ii) Family budget method:
In this method, the weighted average of price relatives is taken, the weights being the percentage expenditure on each item. Thus,
Sometimes the price relative of an item is referred as index number. Thus,
Uses of Cost of Living Index number:
i) Mainly
they are used to fix the dearness allowances of employees for adjusting the
inflations.
ii) They
are useful in obtaining real income or deflating income.
iii) They
are also used to study the purchasing power of money. Purchasing power
decreases as the price index increases.
Deflating
It is
everybody’s experience that, as prices increases the purchasing power of a man
in fixed income group decreases. i.e. As the cost of living index rises, the
purchasing power falls. Symbolically,
Purchasing power of
money =
The process of removing the effect of
price changes from the current money values is called deflation. Deflating the
money index means, making allowance in indices for the effect of changes in
price levels.
If
the present price of a commodity is doubled as compared to base year, the
purchasing power for that commodity is reduced to half. Thus money value of our
earnings changes with the rise or fall in prices of commodities or consumer
price index.
Hence using deflation
technique the real wages, money income index number can be calculated by the
following formula.
Real wage or Real income or deflated income =
The
main purpose of Index number is to measure the relative, temporal or cross
sectional changes.
i)
Index number as a Economic barometer- Index numbers are useful in measuring the
changes in economic activities.
ii)
Index number helps in comparison- They help in comparing the economic and
business activities for two different locations or periods. For ex., changes in
prices in two different countries.
iii)
Index number helps in planning & policy making- Index numbers give the
basis for planning for future, accordingly it helps in policy making.
iv)
To find trend- Index number measures the changes from time to time which
enables us to study the general trend of the economic activity under
consideration.
v)
To find real income or purchasing power of money.
vi)
Dearness allowances- Index numbers are
used to fix the dearness allowances of employees for adjusting the inflations.
vii)
For adjusting national income- Index numbers are used for deflating the net
national income converted at current prices.
viii)
Measure of inflation-
Inflation=
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