2. INTRODUCTION
🞆An index number measures the relative change
in price, quantity, value, or some other item of
interest from one time period to another.
🞆A simple index number measures the relative
change in one or more than one variable.
4. DEFINITION
🞆“Index numbers are quantitative measures of
growth of prices, production, inventory and
other quantities of economic interest.”
Ronold
5. Features of Index Numbers
Relative Changes: Index numbers measures relative of percentage changes in
variables over time.
Index numbers of prices, for example is not simply a statement of prices of different
dates, it presents estimates of percentage changes in the prices over years with
reference to some selected base year. If index of price stands at 200 in 2020
compared to 100 in 2011-12 (the base year), it suggest that compared to the base
year, prices have risen by 100 present.
Quantitative expression:- Index numbers offer a precise measurement of the
quantitative change in the concerned variable(s) over time.
The index of prices, for example, will tell us that between the year 2018 and 2019,
prices have risen by 7 present, or that industrial production has declined by 3
percent.
The index numbers are not the qualitative statements like prices are rising or falling.
Averages:- Index numbers shows changes in terms of averages. For example, it is
said that between the years 2018 and 2019 prices have risen by 7 percent, it does
not mean that prices of all goods and services have uniformly risen by 7 present; it
only mean that on an average there has been a 7 present rise in the prices of
various goods and services.
6. Problems in the construction of Index
Numbers
1)Purpose of Index Numbers:- There are various type of index numbers,
contracted with the different objectives. Before constructing an index numbers, one
must define the objective.
• For example if the objective is to study the impact of change in the value of
money on the consumers one should study the impact of change in the value of
money on consumers, one should construct consumer price index.
• If we are to study the impact of change in the purchasing power of money on
the producers, we shall construct index number on the basis of wholesale prices.
2) Selection of base year:- Selection of base year is another problem in the
construction of index numbers.
Base year is the reference year.
It is the year with which prices of current year are compared. As for as possible,
base year should be normal one.
3) Selection of Goods and services:- It is neither possible nor desirable to
include all the goods and services produced in the country. If we have to choose
goods and services which represent most of others in the market.
7. Problems in the construction of Index
Numbers
4) Selection of Prices of the goods and services:- Broadly in the construction
of pirc index, the problem is whether to adopt retail prices or whole sale prices,
controlled or open market prices. The choice would depends upon the objective or
purpose of study.
5) Selection of weights:- While constructing of index number, weights are
accorded to different commodities according to their relative significance.
There are several methods of according weights i.e. Fisher’s methods, Paasche’s
methods, Laspeyre’s method
While constructing weighted index numbers, one must justify his choice of
weighting technique in accordance with the nature and objective his study.
6) Selection of formula:- Index numbers can be constructed with the help of
many formulae, such as, Laspeyre’s method, Paasche’s method, Fisher’s methods.
One has to decide about the method to be used while constructing the index
numbers.
8. Uses of Index Numbers
1)Measurement of change in price level or the value of money:- It measures the
value of money during a different period of time.
We can use the index numbers to know the impact of the change in the value of
money on different section s of society.
2) Knowledge of change in Standard of Living:- It helps to know the standard of
living of people.
Money income may increase but if index numbers show a decrease in the value of
money, living standard may even decline.
Thus index numbers indicate change in real life.
3) Adjustment in salaries and Allowance:- Cost of living index is a useful guide to
the government and private enterprises to make necessary adjustments in the
salaries and allowances of the workers.
Increase in the cost of living index suggests increases in the salaries and allowances.
4) Useful to the business community:- Price index numbers serves a useful guide to
the business community in their planning and decisions
5) Information regarding production:- Index numbers of production shows whether
the level of agricultural and industrial production in the economy is increasing or
decreasing.
Accordingly, agricultural and industrial development policies are framed.
9. Uses of Index Numbers
6) Information regarding foreign trade: Index of exports and imports provides
useful information regarding foreign trade.
Accordingly, export – imports polices are framed.
7) Useful to politician:- Politician come to know of the real economic condition in
the country on the basis of index numbers.
8) Useful to the government:- With the help of index numbers government
formulates appropriate policies to increase investment, output, income,
employment, trade, price level, consumption etc.
12. SIMPLE AGGREGATIVE METHOD
It consists in expressing the aggregate price of all
commodities in the current year as a percentage of the
aggregate price in the base year.
= Total of the current year’s price of all commodities.
= Total of the base year’s price of all commodities.
×10
0
0
∑
1
0
1
P
= ∑ p
p
1
Pp01= Index number of the current year.
p
0
13. EXAMPLE:
FROM THE DATA GIVEN BELOW CONSTRUCT THE INDEX
NUMBER FOR THE YEAR 2007 ON THE BASE YEAR 2008
IN RAJASTHAN STATE.
COMMODITIES UNITS
PRICE (Rs)
2007
PRICE (Rs)
2008
Sugar Quintal 2200 3200
Milk Quintal 18 20
Oil Litre 68 71
Wheat Quintal 900 1000
Clothing Meter 50 60
14. SOLUTION:
COMMODITIES UNITS
PRICE (Rs)
2007
PRICE (Rs)
2008
Sugar Quintal 2200 3200
Milk Quintal 18 20
Oil Litre 68 71
Wheat Quintal 900 1000
Clothing Meter 50 60
∑ p0 = 3236
∑ p1 = 4351
Index Number for 2008-
0
×100 = 4351
×100 =
134.45
3236
01
∑ p
= ∑ p
1
P
It means the prize in 2008 were 34.45% higher than the previous year.
15. SIMPLE AVERAGE OF RELATIVES
METHOD.
🞆The current year price is expressed as a price
relative of the base year price. These price relatives
are then averaged to get the index number. The
average used could be arithmetic mean, geometric
mean or even median.
∑⎜ p
P
×100⎟
= ⎝ 0
⎠
N
⎛ p1 ⎞
01
Where N is Numbers Of items.
When geometric mean is used-
∑log⎜
p
×100⎟
= ⎝ 0
⎠
⎛ p1 ⎞
log
P
01
16. EXAMPLE
From the data given below construct the index
number for the year 2008 taking 2007 as by using
arithmetic mean.
Commodities Price (2007) Price (2008)
P 6 10
Q 2 2
R 4 6
S 10 12
T 8 12
17. SOLUTION
Index number using arithmetic mean
∑
⎠
⎞
⎜
⎝
0
p
⎛ p1
×100⎟
=603.37
Commodities Price (2007)
p0
Price (2008)
p Price Relative
p1
×100
p0
1
P 6 10 166.7
Q 12 2 16.67
R 4 6 150.0
S 10 12 120.0
T 8 12 150.0
= 120.63
5
603.37
01
⎞
×100⎟
= ⎝ 0
⎠ =
∑⎜ p
⎛ p1
P
18. WEIGHTED INDEX NUMBERS
🞆These are those index numbers in which rational weights are
assigned to various chains in an explicit fashion.
• Weighted aggregative index numbers
These index numbers are the simple
aggregative type with the fundamental difference that
weights are assigned to the various items included in
the index.
⮚ Fisher’s ideal method..
⮚
⮚ Laspeyres method.
⮚ Paasche method.
19. LASPEYRES METHOD-
This method was devised by Laspeyres in 1871. In this
method the weights are determined by quantities in
the base.
×100
0
0
01
∑ p q
= ∑ p
1
q
0
p
Paasche’s Method.
This method was devised by a German statistician Paasche
in 1874. The weights of current year are used as base year
in constructing the Paasche’s Index number.
×100
0
01
p q
= ∑ p
1
q
1
p
20. Fisher’s Ideal Index.
Fisher’s deal index number is the geometric mean of the
Laspeyre’s and Paasche’s index numbers.
0
1
0
0 ∑ p q
∑ p q
∑ p
1
q
0
× ∑ p1
q1
×100
P
=
21. EXAMPLE
Given below are the price quantity data,with price
quoted in Rs. per kg and production in qtls.
Find(1) Laspeyers Index (2) Paasche’s Index
(3)Fisher Ideal Index.
ITEMS PRICE PRODUCTION PRICE PRODUCTION
BEEF 15 500 20 600
MUTTON 18 590 23 640
CHICKEN 22 450 24 500
2002 2007
23. ×100 = 34370
×100 = 122.66
28020
0
0
01
∑ p q
= ∑ p
1
q
0
SOLUTION
1.Laspeyres index:
p
2. Paasche’s Index :
×100 = 38720
×100 = 122.84
31520
0
1
01
∑ p q
= ∑ p
1
q
1
p
3. Fisher Ideal Index
0
1
0
0 ∑ p q
× ∑ p1
q1
×100
= 34370
× 38720
×100 = 122.69
28020 31520
∑ p q
∑ p
1
q
0
01
P
=
24. WEIGHTED AVERAGE OF PRICE
RELATIVE
In weighted Average of relative, the price relatives for
the current year are calculated on the basis of the
base year price. These price relatives are multiplied by
the respective weight of items. These products are
added up and divided by the sum of weights.
Weighted arithmetic mean of price relative
∑V
= ∑ PV
P01
P0
P = P1
×100
Where-
P=Price relative
V=Value weights= 0
p q
25. VALUE INDEX NUMBERS
Value is the product of price and quantity. A simple
ratio is equal to the value of the current year
divided by the value of base year. If the ratio is
multiplied by 100 we get the value index number.
×100
∑ p
0
q
0
V =
∑ p
1
q
1
26. Some Important Index Numbers
1) Consumer Price Index:- Consumer price index (CPI), also known as cost of living
index, measures the average change in the retail price.
2) Whole sale Price Index:- Whole sale price Index number indicates the change in
the general price level. Unlike the CPI, it does not have any reference consumer
category.
The wholesale price index is now being prepared with the base 2011-12=100.
Usually the data on WPI is available quickly The ‘All Commodities Inflation Rate’ is
often referred to ‘Headline Inflation’
3) Index Of Industrial Production:- Unlike the CPI or the WPI, this is an index which
tries to measures quantities. With effect from April 2017, the base year has been
fixed at 2011-2012 = 100.
4) Human Development Index:- Another useful index widely used to knoe the
development of a country is Human Development Index (HDI) about which you
might have studied in class X.
5) Sensex:- Sensex is the short form of Bombay Stock Exchange Sensitive Index with
1978-79 as a base.
It is benchmark index for Indian stock market.
It consist of 30 stocks which represent 13 sectors of the economy and companies
listed are leaders in their respective industries.
27. Conclusion
Estimating Index Numbers Enables you to calculate a single measures of change of
a large numbers of items.
Index Numbers can be calculated for price, quantity. Volume etc.
