Index Numbers Jasvinder

8/3/2019 Index Numbers Jasvinder

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BY: JASVINDER SINGH

MBA -1(C)

MB-134

To: Dr. Sonia


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Introduction

Definition

Characteristics

Uses

Problems

Classifications

Methods Value index numbers

Chain index numbers


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An index number measures the relative

change in price, quantity, value,or some

other item of interest from time period to

another.

A simple index number measures the relative

change in one or more than one variable.


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An index number measures how much a

variable changes over time.

We Calculate the index number by findingthe ratio of the current value to a base

value.


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Index numbers are quantitative measures of

growth of prices, production, inventory and

other quantities of economic interest.

Ronald


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Index numbers are specialized averages

.

Index numbers measure the change in the

level.

Index number measure the effect of changes

over a period of time.


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To framing suitable policies.

They reveal trends and tendencies.

Index numbers are useful in deflating.


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Choice of the base period.

Choice of an average.

Choice of index.

Selection of Commodities.

Data collection.


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Price Index.

Quantity Index.

Value Index.

Composite Index.


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UNWEIGHTED

a) Simple Aggregative.

b) Simple average of price relative

WEIGHTED

a) Weighted aggregated.b) Weighted average of price relative


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It consists in expressing the aggregate price ofall commodities in the current year as apercentage of the aggregate price in the baseyear.

P=pp100

P=Index number of current year

p=Total of current years price of all the

commodities. p=Total of the base years price of all

commodities


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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


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Commoditi

es

Units Price(Rs)

2007

Price(Rs)2

008

Sugar Quintal 2200 3200

Milk Quintal 18 20

oil Litre 68 71

Wheat Quintal 900 1000

Clothing meter 50

p=3236

60

p=4351

Index number for 2008-P=p100= 4351 3236 100 = 134.45


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The current year price is expressed as a price

relative of the base year price. These price

relative a re then averaged to get the index

no. The average used could be arithmeticmean or even median.

P=(p/p100)N

When geometric mean is used:

log P=log (p/p100)N


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From the data given below construct the index

number for year 2008 taking 2007as by using

arithmetic mean.

COMMODITIES PRICE

(2007)

PRICE

(2008)

P 6 10

Q 2 2

R 4 6

S 10 12

T 8 12


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Index number using arthmetic mean-

Commodities Price

(2007)

Price

(2008)

Price

relative

P 6 10 166.7Q 12 2 16.67

R 4 6 150.0

S 10 12 120.0T 8 12 150.0

P=(p100)/ N= 603.37/5=120.63


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These are those index number in whichrational weights are assigned to variouschains in an explicit fashion.

Weighted aggregative aggregative indexnumbers, these index numbers are thesimple aggregative type with thefundamental difference that weights areassigned to the various items included in theindex.

Dorbish and Bowleys method.

Fishers method.Marshall-Edgeworth method. Laspeyres method. Paasche method. Kellys method.


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This method was devised by Laspeyres in1871.in this method the weights aredetermined by quantities in the base.

p= pq pq 100

PAASCHES METHOD. This method was devised by a German

sttistician Paasche in 1874.The weights ofcurrent year are used as base year inconstructing the Paasches index number.

p=pq pq 100


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This method is a combination of laspeyres andPaasches methods.If we find out the arithmetic averageof Laspeyres and paasches index we get the indexsuggested by Dorbish &Bowley.

p=(pq pq) + (pq pq) /2100

FISHERS IDEAL INDEX .

It is the geometric mean of the Laspeyres andPaasches index numbers.

p=(pq pq) (pq pq) 100


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In this index number the numerator consist of anaverage of the current years price multiplied bythe weights of both the base year as well as thecurrent year.

p=(pq + pq) (pq + pq) 100

KELLYS METHOD.Kelly thinks that a ratio of aggregates with

selected weights (not necessarily of base or

current year) gives base index number.p = pq pq 100

q refers to quantites of the year which isselected as the base.i may be any year, eitherbase or current year.


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Given below are the price quantity data,with

price quoted in Rs. And production in qtls.Find -

Laspeyers Index, Paasches Index, Fisher Ideal

Index.Items Price

(2002)

Production

(2002)

Price

(2007)

Production

(2007)

Beef 15 500 20 600

Mutton 18 590 23 640

Chicken 22 450 24 500


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ITEM PRICE

(p)

PROD

UCTION(q)

PRICE

(p)

PROD

UCTION(q)

(pq) (pq) (pq) (pq)

Beef

15 500 20 600 10000 7500 12000 9000

Mutton

18 590 23 640 13570 10620 14720 11520

Chicke

n 22 450 24 500 10800 9900 12000 11000

TOTAL

34370 28020 38720 31520


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1.Laspeyres index;p=pq pq 100

=34370/28020 100 = 122.66

2.Paasches index;

p=pq pq 100= 38720/31520 100 = 122.84

3.Fisher Ideal indexp= (pq pq) (pq pq) 100

= 34370/ 28020 38720/ 31520 100 = 122.69


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In weighted Average of relative, the price

relative for the current year are calculated

on the basis of the base year price. These

price relative are multiplied by therespective weight of items. These products

are added up and divided by sum of weights.

Weighted arithmetic mean of price

relative-P=PV/ V, Where P= p100

P=Price relative and V= Value weights= pq


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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 the base

year. If the ratio is multiplied by 100 we getthe value index number.

V=pq pq 100


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When this method is used the comparisons

are not made with a fixed base, rather the

base changes from year to year. For example,

for 2007,2006 will be the same and so on.

Chain Index for current year

Average link relative of current year Chain

index of previous year /100


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From the data given below construct an

index number by chain base method.

Price of commodity from 2006 to 2008

YEAR PRICE

2006 50

2007 602008 65


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YEAR PRICE LINKRELATIVE CHAIN INDEX(BASE 2006)

2006 50 100 100

2007 60 6050100=120 1201001OO=12

0

2008 65 6560100=108 108120100=

129.60

SOLUTION


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THANK YOU

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Index Numbers Jasvinder