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indexnumber-100320062600-phpapp01
Transcript of indexnumber-100320062600-phpapp01
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CONTENTS
IntroductionDefinitionCharacteristicsUses
ProblemsClassificationMethods
Value index numbers
Chain index numbers.
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WHA T I S A N I NDEX NUMBER
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DEF I N I T I ON
Index numbers are quantitative measures of growth of prices, production, inventory andother quantities of economic interest .
y
-Ronold
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C HA R A CTER I ST I CS OF I NDEX NUMBERS
Index numbers are specialised averages.
Index numbers measure the change in the level
of a phenomenon.
Index numbers measure the effect of changesover a period of time.
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USES OF I NDEX NUMBERS
o To framing suitable policies.
o They reveal trends and tendencies.
o Index numbers are very useful in deflating.
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P ROBLEMS REL A TED TO I NDEX NUMBERS
Choice of the base period.
Choice of an average.
Choice of index.
Selection of commodities.
Data collection.
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CL A SS I F I C A T I ON OF I NDEX NUMBERS
Price IndexPrice Index
Quantity IndexQuantity Index
Value Index Value Index
Composite IndexComposite Index
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MET H ODS OF CONSTRUCT I NG I NDEX NUMBERS
IndexNumbers
Simple A ggregative
Simple A verage of
Price Relative
Unweighted
Weighted
Weighted A ggregated
Weighted A verage of
Price Relatives
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S I M P LE A GGREG A T IV E MET H OD
It consists in expressing the aggregate price of allcommodities in the current year as a percentage of theaggregate price in the base year.
P 01 = Index number of the current year.= Total of the current years price of all commodities.= Total of the base years price of all commodities.
1000
101 v!
p p
P
1 p0 p
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EX A M P LE: -
F ROM THE D ATA G IV E N B EL OW CONS TRUC T THEIND EX NUMB E R F OR THE YEA R 2007 ON THE B A SE YEA R 2008 IN R AJA STHA N S TATE .
COMMOD I T I ES UN I TSP R I CE (Rs)
2007P R I CE (Rs)
2008
Sugar Quintal 2200 3200
Milk Quintal 18 20
Oil Litre 68 71
Whe at Quintal 900 1000
Clot h ing Meter 50 60
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S I M P LE AV ER A GE OF REL A T IV ESMET H OD .
The current year price is expressed as a pricerelative of the base year price. These price relativesare then averaged to get the index number. Theaverage used could be arithmetic mean, geometricmean or even median.
N
p p
v
!100
0
1
01
W here N is Numb ers Of ite ms .
W hen ge om etric mean is used -
N
p p
v
!100log
log 01
01
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E XA MP LE -
F rom the data given below construct the indexnumber for the year 2008 taking 2007 as byusing arithmetic mean.
Commoditi e s P ric e (2007) P ric e (2008)
P 6 1 0
Q 2 2
R 4 6
S 1 0 1 2
T 8 1 2
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SOLU TION -
Index number using arithmetic mean-
Commoditi e s P ric e (2007) P ric e (2008) P ric e R e lativ e
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 v p
p
v 100
0
1
p
p=6 03.37
63.12 05
37.6 03100
0
1
01 !!
v
!
N
p p
P
1 p0 p
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W E I G H TED I NDEX NUMBERS
These are th ose index numbers in which rati onal wei ghts areassi gned t o vari ous chains in an exp licit fashi on.
( A) Weighted aggregative index numbers-These index numbers are the simple aggregative typewith the fundamental difference that weights areassigned to the various items included in the index.Dorbish and bowleys method.F ishers ideal method.Marshall- E dgeworth method.Laspeyres method.Paasche method.Kellys method.
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L ASPEYRES M ETHOD -This meth od was devised by Laspeyres in 187 1. In this
meth od the wei ghts are determined by quantities in the base .
10000
0101 v!
q p
q p p
Paasches Method.
This meth od was devised by a German statistician Paasche
in 187
4.
The wei ghts of current year are used as base year in c onstructin g the Paasches Index number .
10010
1101 v!
q p
q p p
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DORBISH & B OWLEYS M ETHOD .
This meth od is a c ombinati on of Laspeyres and Paaschesmeth ods . If we find out the arithmetic avera ge of Laspeyres and Paasches index we get the index su ggested
by D orbish & B owley.
Fishers Ideal Index.F ishers dea l index number is the geometric mean of the
Laspeyres and Paasches index numbers .
1002
10
11
00
01
01v!
q p
q p
q p
q p
p
v!
10
11
00
01
01 q p
q p
q p
q p P 100v
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M ARSHALL -E DGEWORTH M ETHOD .In this index the numerat or consists of an a ggregate of the
current years price mu ltiplied by the wei ghts of both the baseyear as we ll as the current year .
Kellys Method.K elly thinks that a rati o of aggregates with se lected wei ghts
(not necessari ly of base year or current year) gives the base
index number .
1001000
110101
v!
q pq p
q pq p p
1000
101 v!
q p
q p p
q refers t o the quantities of the year which is se lected as the base .
It may be any year, either base year or current year .
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E XA MP LE -Given below are the price quantity data,with price
quoted in Rs. per kg and production in qtls.F ind- (1) Laspeyers Index (2) Paasches Index(3)F isher Ideal Index.
I TEMS P R I CE P RODUCT I ON P R I CE P RODUCT I ON
BEEF 15 500 20 600
MU TT ON 18 590 23 640
CH ICK E N 22 450 24 500
2002 2007
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SOLU TION -
I TEMS P R I CE P RODUCT I ON
P R I CE P RODUCT I ON
BEEF 15 500 20 600 10000 7500 12000 9000
MU TT ON 18 590 23 640 13570 10620 14720 11520
CH ICK E N 22 450 24 500 10800 9900 12000 11000
TOTAL 34370 28020 38720 31520
0 p 0q 1q 1 p 01q p 00q p 11q p 10q p
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S OLU TION -
66.1221002 802 03 437 0100
00
0101 !v!v!
q pq p p
2. P aasches Index :
84.1221003 152 0
3 872 0100
10
1101
!v!v!
q p
q p p
3. F isher Ideal Index
100v 69.1221003 152 0
3 872 02 802 0
3 437 0 !vv!
v!
10
11
00
01
01q p
q p
q p
q p
1 .Las pe yres index :
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W E I G H TED AV ER A GE OF P R I CE REL A T IV E
In weighted A verage of relative, the price relativesfor the current year are calculated on the basis of the base year price. These price relatives aremultiplied by the respective weight of items. Theseproducts are added up and divided by the sum of
weights.Weighted arithmetic mean of price relative-
!
V
P V P 01
1000
1 v! P P
P W here -
P = P rice relative
V= Value weights = 00q p
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V A LUE I NDEX NUMBERS
Value is the product of price and quantity. A simpleratio is equal to the value of the current yeardivided by the value of base year. If the ratio ismultiplied by 100 we get the value index number.
10000
11 v!
q p
q pV
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C HAI N I NDEX NUMBERS
When this method is used the comparisons are notmade with a fixed base, rather the base changesfrom year to year. F or example, for 2007,2006 willbe the base; for 2006, 2005 will be the same and soon.
Chain index for current year-
100year previ ousof indexChainyear currentof relativelink Avera ge v!
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E XA MP LE -
F rom the data given below construct an index
number by chain base method.Price of a commodity from 2006 to 2008.
Y E A R P R I CE
2006 50
2007 60
2008 65
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SO LU TION -
Y E A R P R I CE L I NKREL A T IV E
C HAI N I NDEX (B A SE 200 6 )
2006 50 100 100
2007 60
2008 65
12 01005 0
6 0!v
1081006 065 !v
12 0100
10012 0 !v
6 0.129100
12 0108 !v
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R EFERENCES1. Statistics for management.
Richard i. Levin & David S. Rubin.
2. Statistics for Business and economics.R.P. H ooda.
3. Business Statistics.B.M. A garwal.
4. Business statistics.S.P. Gupta.
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