1 1 slide © 2008 thomson south-western. all rights reserved chapter 17 index numbers n price...

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© 2008 Thomson South-Western. All Rights Reserved© 2008 Thomson South-Western. All Rights Reserved

Chapter 17Chapter 17 Index Numbers Index Numbers

Price RelativesPrice Relatives Aggregate Price IndexesAggregate Price Indexes Computing an Aggregate Price Computing an Aggregate Price

IndexIndex

from Price Relativesfrom Price Relatives Some Important Price IndexesSome Important Price Indexes

Deflating a Series by Price Deflating a Series by Price IndexesIndexes Price Indexes: Other Price Indexes: Other ConsiderationsConsiderations Quantity IndexesQuantity Indexes

$9.95$9.95

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Price RelativesPrice Relatives

Price relatives are helpful in understanding Price relatives are helpful in understanding and interpreting changing economic and and interpreting changing economic and business conditions over time.business conditions over time.

Price ofPrice ofGasolineGasoline

ThenThen

NowNow

$0.99$0.99

$3.89$3.89

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Price RelativesPrice Relatives

Price relative in period =Price in period Base period price

( )tt

100Price relative in period =Price in period Base period price

( )tt

100

A A base periodbase period is a given starting point in time.is a given starting point in time.

A price relative expresses the unit price in A price relative expresses the unit price in each period as a percentage of the unit price each period as a percentage of the unit price in the base period.in the base period.

A A price relativeprice relative shows how the current price shows how the current price per unit for a given item compares to a base per unit for a given item compares to a base period price per unit for the same item.period price per unit for the same item.

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An An aggregate price indexaggregate price index is developed for the is developed for the specific purpose of measuring the combined specific purpose of measuring the combined change of a group of items.change of a group of items.

Aggregate Price IndexesAggregate Price Indexes

IPPt

it

i

0100( )I

PPt

it

i

0100( )I

PPt

it

i

0100( )I

PPt

it

i

0100( )

wherewhere

PPitit = unit price for item = unit price for item i i in period in period tt

PPii 00 = unit price for item = unit price for item ii in the base period in the base period

An unweighted aggregate price index in period An unweighted aggregate price index in period tt,,

denoted by denoted by IItt , is given by, is given by

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Letting Letting QQii = quantity for item = quantity for item ii, the weighted , the weighted aggregate price index in period aggregate price index in period t t is given by is given by

IP QP Qt

it i

i i

0100( )I

P QP Qt

it i

i i

0100( )


where the sums are over all items in the groupwhere the sums are over all items in the group

With a With a weighted aggregate indexweighted aggregate index each item in each item in the group is weighted according to its the group is weighted according to its importance, which typically is the quantity of importance, which typically is the quantity of usage.usage.

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When the weights are based on period When the weights are based on period tt usage, the index is a usage, the index is a Paasche indexPaasche index..

When the fixed quantity weights are When the fixed quantity weights are determined from the base-year usage, the determined from the base-year usage, the index is called a index is called a Laspeyres indexLaspeyres index. .

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• Its base period is 1982-1984 with an index of Its base period is 1982-1984 with an index of 100.100.

• Published monthly by the U.S. Bureau of Published monthly by the U.S. Bureau of Labor Statistics.Labor Statistics.

• Weighted aggregate price index with fixed Weighted aggregate price index with fixed weights derived from a usage survey.weights derived from a usage survey.

• Based on 400 items including food, housing, Based on 400 items including food, housing, clothing, transportation, and medical items.clothing, transportation, and medical items.

• Primary measure of the cost of living in U.S.Primary measure of the cost of living in U.S.

Some Important Price IndexesSome Important Price Indexes

Consumer Price Index (CPI)Consumer Price Index (CPI)

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• Weighted average of price relatives using the Weighted average of price relatives using the Laspeyres method.Laspeyres method.

• Includes the output of manufacturing, Includes the output of manufacturing, agriculture, forestry, fishing, mining, gas and agriculture, forestry, fishing, mining, gas and electricity, and public utilities.electricity, and public utilities.

• Covers raw, manufactured, and processed Covers raw, manufactured, and processed goods at each level of processing.goods at each level of processing.

• Used as a Used as a leading indicatorleading indicator of the future of the future trend of consumer prices and the cost of trend of consumer prices and the cost of living.living.

• Measures the monthly changes in prices in Measures the monthly changes in prices in primary markets in the U.S.primary markets in the U.S.

Producer Price Index (PPI)Producer Price Index (PPI)


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• Another average is computed for 20 Another average is computed for 20 transportation stocks, and another for 15 transportation stocks, and another for 15 utility stocks.utility stocks.

• The DJIA is The DJIA is notnot expressed as a percentage of expressed as a percentage of base-year prices.base-year prices.

• The The Dow Jones Industrial AverageDow Jones Industrial Average (DJIA)(DJIA) is is based on common stock prices of 30 based on common stock prices of 30 industrial firms.industrial firms.

• Indexes designed to show price trends and Indexes designed to show price trends and movements on the New York Stock Exchange.movements on the New York Stock Exchange.

Dow Jones AveragesDow Jones Averages


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Deflating a Series by Price IndexesDeflating a Series by Price Indexes

Deflating actual hourly wages results in Deflating actual hourly wages results in real real wageswages or the or the purchasing powerpurchasing power of wages.of wages.

In order to correctly interpret business activity In order to correctly interpret business activity over time when it is expressed in dollar over time when it is expressed in dollar amounts, we should adjust the data for the amounts, we should adjust the data for the price-increase effect.price-increase effect. Removing the price-increase effect from a time Removing the price-increase effect from a time series is called series is called deflating the seriesdeflating the series..

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• When the class of items is very large, a When the class of items is very large, a representative group (usually not a random representative group (usually not a random sample) must be used.sample) must be used.

• The group of items in the aggregate index The group of items in the aggregate index must be periodically reviewed and revised if must be periodically reviewed and revised if it is not representative of the class of items in it is not representative of the class of items in mind.mind.

Selection of ItemsSelection of Items

Price Indexes: Other ConsiderationsPrice Indexes: Other Considerations

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• For example, a CPI with a 1945 base period For example, a CPI with a 1945 base period would be difficult for most individuals to would be difficult for most individuals to understand due to unfamiliarity with understand due to unfamiliarity with conditions in 1945.conditions in 1945.

Selection of a Base PeriodSelection of a Base Period


• The base period for most indexes is The base period for most indexes is adjusted periodically to a more recent adjusted periodically to a more recent period of time.period of time.

• As a rule, the base period should not be too As a rule, the base period should not be too far from the current period.far from the current period.

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• A substantial quality improvement also may A substantial quality improvement also may cause an increase in the price of a product.cause an increase in the price of a product.

• Is a product that has undergone a major Is a product that has undergone a major quality change the same product it was?quality change the same product it was?

• A basic assumption of price indexes is that A basic assumption of price indexes is that the prices are identified for the the prices are identified for the samesame items items each period.each period.


Quality ChangesQuality Changes

== ??

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Quantity IndexesQuantity Indexes

A weighted aggregate quantity index for A weighted aggregate quantity index for period period tt is given by is given by

IQ wQ wt

it i

i i

0100( )I

Q wQ wt

it i

i i

0100( )

An index used to measure changes in quantity An index used to measure changes in quantity levels over time is called a levels over time is called a quantity indexquantity index..

Probably the best known quantity index is the Probably the best known quantity index is the Index of Industrial Production and Capacity Index of Industrial Production and Capacity UtilizationUtilization.. A A weighted aggregate quantity indexweighted aggregate quantity index is is computed in much the same way as a computed in much the same way as a weighted aggregate price index.weighted aggregate price index.

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