Definition Unweighted and Weighted Index Numbers ( Simple Index Numbers, Laspeyre’s, Paasche’s...
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Transcript of Definition Unweighted and Weighted Index Numbers ( Simple Index Numbers, Laspeyre’s, Paasche’s...
![Page 1: Definition Unweighted and Weighted Index Numbers ( Simple Index Numbers, Laspeyre’s, Paasche’s Index, Fisher’s “Ideal” Index) CPI ( Consumer Price.](https://reader036.fdocuments.net/reader036/viewer/2022081420/5697bfd31a28abf838cac0cc/html5/thumbnails/1.jpg)
INDEX NUMBERS
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Index Numbers Definition Unweighted and Weighted Index
Numbers ( Simple Index Numbers, Laspeyre’s,
Paasche’s Index, Fisher’s “Ideal” Index) CPI ( Consumer Price Index ) Issues in using Index Numbers
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DefinitionAn index number describes how collected data (statistics) changes over time. They are often used for comparison between price, quantity and value between different time periods.
It provides a summary of information in a simple form and it is widely used by government bodies, for economic policy and business information.
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caseA cup of coffee in a particular café cost $10 in 1995. In 2002, an identical cup of coffee cost $15. How has the price changed between 1995 and 2002?1995 Base period $102002 Given period $15
1501001015
15010010
15
PgPb %50
Index number=
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Unweighted Index Numbers
Simple Index Simple Composite (aggregate) Index Simple Average Index
![Page 7: Definition Unweighted and Weighted Index Numbers ( Simple Index Numbers, Laspeyre’s, Paasche’s Index, Fisher’s “Ideal” Index) CPI ( Consumer Price.](https://reader036.fdocuments.net/reader036/viewer/2022081420/5697bfd31a28abf838cac0cc/html5/thumbnails/7.jpg)
Unweighted Index Numbers
Simple Index Numbers Simple Price Index Simple Quantity Index Composite (aggregate) Index Simple Average Index
![Page 8: Definition Unweighted and Weighted Index Numbers ( Simple Index Numbers, Laspeyre’s, Paasche’s Index, Fisher’s “Ideal” Index) CPI ( Consumer Price.](https://reader036.fdocuments.net/reader036/viewer/2022081420/5697bfd31a28abf838cac0cc/html5/thumbnails/8.jpg)
Unweighted Index Numbers
Simple Index Simple Composite (aggregate) Index Simple Composite (aggregate) Price Index Simple Composite (aggregate) Quantity Index Simple Average Index
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Unweighted Index Numbers
Simple Index Simple Composite (aggregate) Index Simple Average Index Simple Average Price Index Simple Average Quantity Index
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Unweighted Index Numbers
Simple Index Simple Price Index Simple Quantity Index Simple Composite (Aggregate) Index Simple Composite (Aggregate) Price Index Simple Composite (Aggregate) Quantity Index Simple Average Index Simple Average Price Index Simple Average Quantity Index
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1. Simple Index
Simple Price Index
Simple Quantity Index
100Pb
Pg
100Qb
Qg
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2007 (Base year) 2009 (Given year)
Price Quantity Price Quantity
Racquets $120 420 $160 480
Court Hire
$15 2,300 $15 2,500
Shoes $120 390 $100 270
100Pb
Pg
A. What is the simple price index for Racquets?
33.133100120
160
The price of racquets increased by 33.33% from 2007 to 2009.
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2007 (Base year) 2009 (Given year)
Price Quantity Price Quantity
Racquets $120 420 $160 480
Court Hire
$15 2,300 $15 2,500
Shoes $120 390 $100 270
100Qb
Qg
B. What is the simple quantity index for Shoes?
23.69100390
270
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2. Simple Composite (Aggregate) Index
Simple Aggregate Price Index
Simple Aggregate Quantity Index
100Pb
Pg
100Qb
Qg
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2007 (Base year) 2009 (Given year)
Price Quantity Price Quantity
Racquets $120 420 $160 480
Court Hire
$15 2,300 $15 2,500
Shoes $120 390 $100 270A. What is the simple aggregate price
index?
84.10710012015120
10015160
100Pb
Pg
The total price of the selected items increased by 7.84% from 2007 to 2009.
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2007 (Base year) 2009 (Given year)
Price Quantity Price Quantity
Racquets $120 420 $160 480
Court Hire
$15 2,300 $15 2,500
Shoes $120 390 $100 270B. What is the simple aggregate quantity
index?
100Qb
Qg
50.104100
390300,2420
7022,500804
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3. Simple Average Index
Simple Average Price Index
Simple Average Quantity Indexn
100PbPg
n
100QbQg
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2007 (Base year) 2009 (Given year)
Price Quantity Price Quantity
Racquets $120 420 $160 480
Court Hire
$15 2,300 $15 2,500
Shoes $120 390 $100 270A. What is the simple average price index?
56.1053
100120100
1001515
100120160
n
100PbPg
The price of the selected items,
on average, increased by 7.84% from 2007 to 2009.
![Page 19: Definition Unweighted and Weighted Index Numbers ( Simple Index Numbers, Laspeyre’s, Paasche’s Index, Fisher’s “Ideal” Index) CPI ( Consumer Price.](https://reader036.fdocuments.net/reader036/viewer/2022081420/5697bfd31a28abf838cac0cc/html5/thumbnails/19.jpg)
2007 (Base year) 2009 (Given year)
Price Quantity Price Quantity
Racquets $120 420 $160 480
Court Hire
$15 2,300 $15 2,500
Shoes $120 390 $100 270B. What is the simple average quantity index?
n
100QbQg
40.973
100390270
100300,2
2,500100
420480
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Weighted Index Numbers
Laspeyre’s Index Paasche’s Index Fisher’s “Ideal” Index
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Laspeyere’s Index
100Qb)(Pb
Qb)(Pg
100Qb)(Pb
Qg)(Pb
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2007 (Base year) 2009 (Given year)
Price Quantity Price Quantity
Racquets $120 420 $160 480
Court Hire
$15 2,300 $15 2,500
Shoes $120 390 $100 270
100Qb)(Pb
Qb)(Pg
100)390120()300,215()420120(
)390100()300,215()420160(
83.106
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Paasche’s Index
100Qg)(Pb
Qg)(Pg
100Qb)(Pg
Qg)(Pg
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2007 (Base year) 2009 (Given year)
Price Quantity Price Quantity
Racquets $120 420 $160 480
Court Hire
$15 2,300 $15 2,500
Shoes $120 390 $100 270
100)270120()500,215()480120(
)270100()500,215()480160(
82.110
100Qg)(Pb
Qg)(Pg
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Fisher’s “Ideal” Index
LaspeyrePaasche
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2007 (Base year) 2009 (Given year)
Price Quantity Price Quantity
Racquets $120 420 $160 480
Court Hire
$15 2,300 $15 2,500
Shoes $120 390 $100 270LaspeyrePaasche
81.10882.10183.061
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Laspeyere’s Index
100Qb)(Pb
Qb)(Pg
Paasche’s Index
100Qg)(Pb
Qg)(Pg
Fisher’s Index
LaspeyrePaasche
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Consumer Price Index (CPI)
It examines the changes in the price of groups of goods and services referred to as “the basket”.
100, 1, 2,...,i ig b
i ib b
P QCPI i n
P Q
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Calculation Calculate new CPI after shifting base
year to 2006. Using new CPI convert rental for 2009 to real prices.
Year CPI Salary Revised CPI
2005 160.1 2,000
2006 167.8 2,500 100.00
2007 183.5 3,520 109.36
2008 200.2 4,600 119.31
2009 350.4 5,000 208.82
36.109 100167.8
183.5
100
Current CPINew CPI
Base Year Old CPI
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CalculationYear CPI Salary Revised
CPI
2005 160.1 2,000
2006 167.8 2,500 100.00
2007 183.5 3,520 109.36
2008 200.2 4,600 119.31
2009 350.4 5,000 208.82
Re 100
Actual Valueal Value
CPI
$5,000100 $2,394.41
208.82
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CalculationYear CPI Salary Revised
CPI
2005 160.1 2,000
2006 167.8 2,500 100.00
2007 183.5 3,520 109.36
2008 193.2 4,600 119.31
2009 203.4 5,000 208.82
$2,500 208.82$5,220.5
100
Re
100
al Value CPIActual Value
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Issues in Using Index Numbers
Choice of Formula Choice of “Basket” Choice of Price Choice of Base year