Index Numbers

Abhishek DixitNirbhay KumarRajan DasguptaPrerna TiwaryRashmi Yadav

Iti ShreeBindu Singh

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 just one variable.

CHARACTERISTICS

Specialized averages

Measure the change in the level of a phenomenon

Measure the effect of changes over a period of time

USES

Help in framing suitable policies

Reveal trends and tendencies

Very useful in deflating

CLASSIFICATION

SpecialPurposeValueQuantityPrice

METHODS OF CONSTRUCTING INDEX NUMBERS

IndexNumbers

Un-weighted

Simple Aggregative

Simple Average of

Price Relatives

Weighted

WeightedAggregative

Weighted Average of

Price Relatives

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.

1000

101

p

pP

P01= Index number of the current year.

= Total of the current year’s price of all commodities.

= Total of the base year’s price of all commodities

1p

0p

EXAMPLE:-

From the data given below construct the index number for the year 2007 on the base year 2008 in Rajasthan state.

COMMODITIES UNITSPRICE (Rs)

2007PRICE (Rs)

2008

Sugar Quintal 2200 3200

Milk Quintal 18 20

Oil Litre 68 71

Wheat Quintal 900 1000

Clothing Meter 50 60

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

32360 p 43511 p

Index Number for 2008-

45.1341003236

4351100

0

101

p

pP

It means the prize in 2008 were 34.45% higher than the previous year.

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.

N

pp

P

100

0

1

01

Where N is Numbers Of items.

When geometric mean is used-

N

pp

P

100log

log 0

1

01

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

Solution:- Index number using arithmetic mean-

Commodities Price (2007) Price (2008) Price Relative

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

1000

1 p

p

100

0

1

p

p=603.37

63.1205

37.603100

0

1

01

N

pp

P

1p0p

Weighted index numbers

These are those index numbers in which rational weights are assigned to various chains in an explicit fashion.

(A) 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.

Laspeyres method. Paasche method. Dorbish and bowley’s method. Fisher’s ideal method. Marshall-Edgeworth method. Kelly’s method.

Laspeyres Method.This method was devised by Laspeyres in 1871. In this

method the weights are determined by quantities in the

base.100

00

0101

qp

qpp

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.

10010

1101

qp

qpp

Formula For Calculating Index Numbers

Dorbish & Bowleys Method:This method is a combination of Laspeyre’s and Paasche’s methods. If

we find out the arithmetic average of Laspeyre’s and Paasche’s index we get the index suggested by Dorbish & Bowley.

Fisher’s Ideal Index: Fisher’s deal index number is the geometric mean of the Laspeyre’s and

Paasche’s index numbers.

1002

10

11

00

01

01

qpqp

qpqp

P

10

11

00

01

01 qp

qp

qp

qpP 100

Marshall-Edgeworth Method.In this index the numerator consists of an aggregate of the current years

price multiplied by the weights of both the base year as well as the

current year.

Kelly’s Method.Kelly thinks that a ratio of aggregates with selected weights (not

necessarily of base year or current year) gives the base index number.

1001000

110101

qpqp

qpqpp

1000

101

qp

qpp

q refers to the quantities of the year which is selected as the base. It may be any

year, either base year or current year.

Weighted average of price relative index numbers

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

PVP01

1000

1 P

PPWhere-

P=Price relativeV=Value weights= 00qp

10000

01

pq

pqL

Q = L P

10000

11

pq

pqV

10010

11

00

0101

pq

pq

pq

pqQ

Quantity Index Number

What is Quantity Index Numbers?Measure and permit comparison of the physical volume of goods produced or distributed or consumed.

Where Q=Quantity Index Number

Volume Index Number

The Value of Single Commodity is the product of price and Quantity.

10000

11

qp

qpV

OR

1000

1 V

VV

CONSUMER PRICE INDEX NUMBERS

Meaning The consumer price index numbers, also known as cost of living index numbers, are generally intended to represent the average change over time in the prices paid by the ultimate consumer of a specified basket of goods and services.Need The need for constructing consumer price indices arises because the general index numbers fail to give an exact idea of the effect of the change in the general price level on the cost of different classes of people in different manners.

At present, the three terms, viz. cost of living index, consumer price index and retail price index are used in different countries with practically no difference in their connotation.

.

UTILITY OF CONSUMER PRICE INDICES

Wage negotiations & wage contracts.At Govt. level, mainly used for wage policy,

price policy, rent control, taxation & general economic policies.

To measure changing purchasing power of the currency, real income etc.

Analyzing markets for particular goods and services.