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Slides Prepared bySlides Prepared byJOHN S. LOUCKSJOHN S. LOUCKS

St. Edward’s UniversitySt. Edward’s University

© 2002 South-Western/Thomson Learning© 2002 South-Western/Thomson Learning

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Chapter 17Chapter 17 Index Numbers Index Numbers

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

from Price Relativesfrom Price Relatives Some Important Price IndexesSome Important Price Indexes Deflating a Series by Price IndexesDeflating a Series by Price Indexes Price Indexes: Other ConsiderationsPrice Indexes: Other Considerations Quantity IndexesQuantity Indexes

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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.

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Price RelativesPrice Relatives

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.

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

Price relative in period =Price in period Base period price

( )tt

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

( )tt

100

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Example: Besco ProductsExample: Besco Products

Price RelativesPrice Relatives

The prices Besco paid for newspaper and The prices Besco paid for newspaper and television ads in 1992 and 1997 are shown television ads in 1992 and 1997 are shown below. Using 1992 as the base year, compute below. Using 1992 as the base year, compute a 1997 price index for newspaper and a 1997 price index for newspaper and television ad prices.television ad prices.

19921992 19971997

NewspaperNewspaper $14,794$14,794$29,412$29,412

TelevisionTelevision 11,46911,469 23,90423,904

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Example: Besco ProductsExample: Besco Products

Price RelativesPrice Relatives

NewspaperNewspaper Television Television

Television advertising cost increased at a Television advertising cost increased at a greater rate.greater rate.

199)100(794,14

412,291997 I 199)100(

794,14

412,291997 I

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Aggregate Price IndexesAggregate Price Indexes

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.

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

wherewhere

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

PPi i 00 = unit price for item = unit price for item ii in the base in the base periodperiod

IPPt

it

i

0100( )I

PPt

it

i

0100( )I

PPt

it

i

0100( )I

PPt

it

i

0100( )

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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.

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

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

IP QP Qt

it i

i i

0100( )I

P QP Qt

it i

i i

0100( )

Aggregate Price IndexesAggregate Price Indexes

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Aggregate Price IndexesAggregate Price Indexes

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. .

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

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Example: City of NewtonExample: City of Newton

Aggregate Price IndexesAggregate Price Indexes

Data on energy consumption and Data on energy consumption and expenditures by sector for the city of Newton are expenditures by sector for the city of Newton are given below. Construct an aggregate price index given below. Construct an aggregate price index for energy expenditures in 2000 using 1985 as the for energy expenditures in 2000 using 1985 as the base year.base year.

Quantity (BTU) Unit Price Quantity (BTU) Unit Price ($/BTU)($/BTU)

SectorSector 19851985 20002000 19851985 20002000

Residential Residential 9,473 9,473 8,804 8,804 $2.12$2.12 $10.92$10.92

CommercialCommercial 5,416 5,416 6,015 6,015 1.97 1.97 11.32 11.32

IndustrialIndustrial 21,28721,287 17,83217,832 .79 .79 5.13 5.13

Transport.Transport. 15,29315,293 20,26220,262 2.32 2.32 6.16 6.16

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Unweighted Aggregate Price IndexUnweighted Aggregate Price Index

II2000 2000 = 10.92 + 11.32 + 5.13 + 6.16 = 10.92 + 11.32 + 5.13 + 6.16 (100) (100) = 466= 466

2.12 + 1.97 + .79 + 2.322.12 + 1.97 + .79 + 2.32 Weighted Aggregate Index (Laspeyres Method)Weighted Aggregate Index (Laspeyres Method)

II20002000 = 10.92(9473) + . . . + 6.16(15293) = 10.92(9473) + . . . + 6.16(15293) (100) (100) = 443= 443

2.12(9473) + . . . + 2.32(15293)2.12(9473) + . . . + 2.32(15293) Weighted Aggregate Index (Paasche Method)Weighted Aggregate Index (Paasche Method)

II20002000 = 10.92(8804) + . . . + 6.16(20262) = 10.92(8804) + . . . + 6.16(20262) (100) (100) = 415= 415

2.12(8804) + . . . + 2.32(20262)2.12(8804) + . . . + 2.32(20262)The Paasche value being less than the Laspeyres The Paasche value being less than the Laspeyres indicates usage has increased faster in the lower-indicates usage has increased faster in the lower-priced sectors.priced sectors.

Example: City of NewtonExample: City of Newton

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Some Important Price IndexesSome Important Price Indexes

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

• Primary measure of the cost of living in US.Primary measure of the cost of living in US.

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

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

• Published monthly by the US Bureau of Published monthly by the US Bureau of Labor Statistics.Labor Statistics.

• Its base period is 1982-1984 with an index Its base period is 1982-1984 with an index of 100.of 100.

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Producer Price Index (PPI)Producer Price Index (PPI)• Measures the monthly changes in prices in Measures the monthly changes in prices in

primary markets in the US.primary markets in the US.• 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.

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

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

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

Some Important Price IndexesSome Important Price Indexes

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Dow Jones AveragesDow Jones Averages

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

• 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.

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

• 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.

Some Important Price IndexesSome Important Price Indexes

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Deflating a Series by Price IndexesDeflating a Series by Price Indexes

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..

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.

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Example: McNeer CleanersExample: McNeer Cleaners

Deflating a Series by Price IndexesDeflating a Series by Price Indexes

McNeer Cleaners, with 46 branch McNeer Cleaners, with 46 branch locations, has had the total sales revenues locations, has had the total sales revenues shown on the next slide for the last five years. shown on the next slide for the last five years. Deflate the sales revenue figures on the basis Deflate the sales revenue figures on the basis of 1982-1984 constant dollars. Is the increase of 1982-1984 constant dollars. Is the increase in sales due entirely to the price-increase in sales due entirely to the price-increase effect?effect?

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Deflating a Series by Price IndexesDeflating a Series by Price Indexes

YearYear Total Sales ($1000)Total Sales ($1000) CPICPI

1996 1996 8,446 8,446 156.9156.9

19971997 9,062 9,062 160.5160.5

19981998 9,830 9,830 163.0163.0

1999 1999 10,72410,724 166.6166.6

20002000 11,69011,690 172.6172.6

Example: McNeer CleanersExample: McNeer Cleaners

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Deflating a Series by Price IndexesDeflating a Series by Price Indexes

DeflatedDeflated AnnualAnnualYearYear Sales ($1000)Sales ($1000) Change(%)Change(%)

19961996 (8,446/156.9)(100) = 5,383 (8,446/156.9)(100) = 5,38319971997 (9,062/160.5)(100) = 5,646 (9,062/160.5)(100) = 5,646+4.9+4.919981998 (9,830/163.0)(100) = 6,031 (9,830/163.0)(100) = 6,031+6.8+6.8

1999 1999 (10,724/166.6)(100) = 6,437(10,724/166.6)(100) = 6,437+6.7+6.720002000(11,690/172.6)(100) = 6,773(11,690/172.6)(100) = 6,773+5.2+5.2

After adjusting revenue for the price-After adjusting revenue for the price-increase effect, revenue is still increasing at an increase effect, revenue is still increasing at an average rate of 5.9% per year.average rate of 5.9% per year.

Example: McNeer CleanersExample: McNeer Cleaners

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Selection of ItemsSelection of Items

• 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 a Base PeriodSelection of a Base Period

• 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.

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

Price Indexes: Other ConsiderationsPrice Indexes: Other Considerations

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Price Indexes: Other ConsiderationsPrice Indexes: Other Considerations

Quality ChangesQuality Changes

• 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.

• 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 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.

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Quantity IndexesQuantity Indexes

An index that measures changes in quantity An index that measures changes in quantity levels over time is called a levels over time is called a quantity index.quantity index.

Probably the best known quantity index is the Probably the best known quantity index is the Index of Industrial ProductionIndex of Industrial Production..

A weighted aggregate quantity index is A weighted aggregate quantity index 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.

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( )

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End of Chapter 17End of Chapter 17