An index number measures changes in a variable over time by comparing values in one period to another. There are different types of index numbers including price, quantity, and value indexes. Price indexes compare price levels over time, quantity indexes measure changes in quantity, and value indexes combine price and quantity changes to measure total monetary worth. Index numbers are used for various purposes such as measuring inflation, forecasting economic trends, and analyzing trade balances. They are constructed by selecting representative commodities, collecting price data, choosing a base period for comparison, and determining appropriate weights and averages.

2. INDEX NUMBER
Introduction:
Everyone faces the question of how much something has
changed over a period of time. We may want to know how
much the price of groceries has increased so we can adjust our
budget accordingly. In this situation the degree of change
must be determined and defined, we use index numbers to
measure such differences.
Definition:
An index number measure the changes in a variable or a group
of variable with respect to time.
Example–1:
The price of rice in Karachi per kg is Rs. 150 in the year 2013
and the price of rice per kg was 120 in the year 2012.
Find index number for the year 2013 and comment.
Solution:
Price in 2012 = Rs. 120
Price in 2013 = Rs. 150
Price Index =
Price Index =
Price Index = 125 %
The index number 125% means that the price of rice per kg
has increased by 25% in 2013 as compared to 2012.
100
2012inicePr
2013inicePr

100
120
150


3. Simple Index Number:
A simple index is based on a single commodity.
Composite Index Number:
A composite index is based on several commodities.
Types of Index Numbers:
There are three types of index numbers.
(i) Price Index Number:
It compares levels of prices from one period to another.
(ii) Quantity Index Number:
A quantity index measures how much quantity of a
variable changes over time.
(iii) Value Index Number:
The value index measures changes in total monetary
worth. It measures changes in rupee value of a variable.
In effect, the value index combines price and quantity
changes to present a more informative index.
Uses of Index Numbers:
1. The index numbers measure fluctuations during intervals
of time.
2. They measure the purchasing power of money.
3. They are helpful in forecasting the future economic
trends.
4. Index numbers of import prices and export prices are
used to measure the changes in the trade of a country.
5. Index numbers of industrial production are used to
measure the changes in the level of industrial production
in the country.

4. Main Steps to Construct Price Index Numbers:
The following steps are considered for the construction of
price index numbers.
(i) Object:
First of all we decide the purpose of making the index
numbers. Once the purpose is decided, then we decide
about the scope and the area or the people who are to be
considered.
(ii) Selection of Commodities:
The commodities which are representative of the tastes
and customs of the people are taken in the list.
(iii) Collection of Price Data:
Usually some representative shops from where the
consumers mostly purchase their items are selected and
the prices are taken from those shops.
(iv) Selection of Base Period:
(a) Fixed Base Method:
In fixed base method a single year or average price of
several years is taken as the base year. The year which
is selected as base should be a normal year and free
from any economical crises.
Price relative for current year =
OR
100
YearBaseoficePr
YearCurrentoficePr

100
P
P
P
o
n
n,o =

5. (b) Chain Base Method:
In this method, there is no fixed base period. The year
immediately preceding the one for which price index
have to be calculated is assumed as the base year.
Link relative for current year =
OR
(v) Selection of the Suitable Average::
Geometric mean should be calculated for averaging the
relatives. But as the calculation of the geometric mean is
difficult, it is mostly avoided and the arithmetic mean is
commonly used.
(vi) Selection of Suitable Weights:
In calculation of price index numbers all commodities
are not of equal importance. In order to give them their
due importance, commodities are given due weights.
SIMPLE AGGREGATIVE METHOD :-
𝐼 𝑜,𝑛 =
ΣPn
ΣPo
𝑥 100
100
YearecedingPrtheinicePr
YearCurrenttheinicePr

100
P
P
P
1n
n
n,1n =
−
−

6. WEIGHTED AGGREGATIVE PRICE INDEX NUMBER
:-
1) 𝐿𝑎𝑠𝑝𝑒𝑦𝑟𝑒′
𝑠 = 𝐿 =
Σ𝑃𝑛𝑄𝑜
Σ𝑃𝑜𝑄𝑜
𝑥 100
2) 𝑃𝑎𝑎𝑠𝑐ℎ𝑒′
𝑠 = 𝑃 =
Σ𝑃𝑛𝑄𝑛
Σ𝑃𝑜𝑄𝑛
𝑥 100
3) 𝐹𝑖𝑠ℎ𝑒𝑟′
𝑠 = 𝐹 = √
Σ𝑃𝑛𝑄𝑜
Σ𝑃𝑜𝑄𝑜
𝑥
Σ𝑃𝑛𝑄𝑛
Σ𝑃𝑜𝑄𝑛
𝑥100
Or 𝐹𝑖𝑠ℎ𝑒𝑟′
𝑠 = 𝐹 = √ 𝐿𝑥𝑃
4) 𝑀𝑎𝑟𝑠ℎ𝑎𝑙𝑙 = 𝑀 =
Σ𝑃𝑛( 𝑄𝑜 + 𝑄𝑜)
Σ𝑃𝑜( 𝑄𝑜 + 𝑄𝑛)
𝑥 100
COST OF LIVING INDEX NUMBER = C P I :-
1) AGGREGATE EXPENDITURE METHOD.
𝐶𝑃𝐼 =
Σ𝑃𝑛𝑄𝑜
Σ𝑃𝑜𝑄𝑜
𝑥 100
2) FAMILY BUDGET METHOD
𝐶𝑃𝐼 =
Σ IW
Σ W
Where W = Po Qo ; 𝐼 =
𝑃𝑛
𝑃𝑜
𝑥 100

7. PURCHASING POWER
𝑃𝑢𝑟𝑐ℎ𝑎𝑠𝑖𝑛𝑔𝑃𝑜𝑤𝑒𝑟 =
1
𝐶𝑃𝐼
𝑥 100
REAL INCOME
𝑅𝑒𝑎𝑙𝐼𝑛𝑐𝑜𝑚𝑒 =
current Income
C P I
𝑥 100
POTENTIAL SALE
𝑃𝑜𝑡𝑒𝑛𝑡𝑖𝑎𝑙𝑆𝑎𝑙𝑒 =
current sale
l + r
VALUE INDEX
𝑉𝑎𝑙𝑢𝑒𝐼𝑛𝑑𝑒𝑥 =
Σ𝑃𝑛𝑄𝑛
Σ𝑃𝑜𝑄𝑜
𝑥 100