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Slides Prepared byJOHN S. LOUCKS

St. Edward’s University

© 2002 South-Western/Thomson Learning

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Chapter 17 Index Numbers

Price Relatives Aggregate Price Indexes Computing an Aggregate Price Index

from Price Relatives Some Important Price Indexes Deflating a Series by Price Indexes Price Indexes: Other Considerations Quantity Indexes

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Price Relatives

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

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Price Relatives

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

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

A base period 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 Products

Price RelativesThe prices Besco paid for newspaper and

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

1992 1997

Newspaper $14,794$29,412

Television 11,469 23,904

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Example: Besco Products

Price RelativesNewspaper Television

Television advertising cost increased at a greater rate.

199)100(794,14

412,291997 I 208)100(

469,11

904,231997 I

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Aggregate Price Indexes

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

An unweighted aggregate price index in period t,denoted by It , is given by

wherePit = unit price for item i in period t

Pi 0 = unit price for item i in the base period

IPPt

it

i

0100( )I

PPt

it

i

0100( )

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

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

where the sums are over all items in the group.

IP QP Qt

it i

i i

0100( )I

P QP Qt

it i

i i

0100( )

Aggregate Price Indexes

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Aggregate Price Indexes

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

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

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Example: City of Newton

Aggregate Price IndexesData on energy consumption and

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

Quantity (BTU) Unit Price ($/BTU)Sector 1985 2000 1985 2000Residential 9,473 8,804$2.12$10.92Commercial 5,416 6,015 1.97 11.32Industrial 21,287 17,832 .79 5.13Transport. 15,293 20,262 2.32 6.16

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Unweighted Aggregate Price Index

I2000 = 10.92 + 11.32 + 5.13 + 6.16 (100) = 466 2.12 + 1.97 + .79 + 2.32

Weighted Aggregate Index (Laspeyres Method)

I2000 = 10.92(9473) + . . . + 6.16(15293) (100) = 443

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

I2000 = 10.92(8804) + . . . + 6.16(20262) (100) = 415

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

Example: City of Newton

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Some Important Price Indexes

Consumer Price Index (CPI)• Primary measure of the cost of living in US.• Based on 400 items including food, housing,

clothing, transportation, and medical items.• Weighted aggregate price index with fixed

weights derived from a usage survey.• Published monthly by the US Bureau of

Labor Statistics.• Its base period is 1982-1984 with an index

of 100.

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

primary markets in the US.• Used as a leading indicator of the future

trend of consumer prices and the cost of living.

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

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

• Weighted average of price relatives using the Laspeyres method.

Some Important Price Indexes

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Dow Jones Averages• Indexes designed to show price trends and

movements on the New York Stock Exchange.

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

• The DJIA is not expressed as a percentage of base-year prices.

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

Some Important Price Indexes

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Deflating a Series by Price Indexes

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

Removing the price-increase effect from a time series is called deflating the series.

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

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Example: McNeer Cleaners

Deflating a Series by Price IndexesMcNeer Cleaners, with 46 branch

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

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Deflating a Series by Price Indexes

Year Total Sales ($1000) CPI

1996 8,446 156.91997 9,062 160.51998 9,830 163.0 1999 10,724 166.62000 11,690 172.6

Example: McNeer Cleaners

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Deflating a Series by Price Indexes

Deflated AnnualYear Sales ($1000) Change(%)

1996 (8,446/156.9)(100) = 5,3831997 (9,062/160.5)(100) = 5,646 +4.91998 (9,830/163.0)(100) = 6,031 +6.8 1999 (10,724/166.6)(100) = 6,437+6.72000 (11,690/172.6)(100) = 6,773 +5.2

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

Example: McNeer Cleaners

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Selection of Items• When the class of items is very large, a

representative group (usually not a random sample) must be used.

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

Selection of a Base Period• As a rule, the base period should not be too

far from the current period.• The base period for most indexes is

adjusted periodically to a more recent period of time.

Price Indexes: Other Considerations

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Price Indexes: Other Considerations

Quality Changes• A basic assumption of price indexes is that

the prices are identified for the same items each period.

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

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

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Quantity Indexes

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

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

A weighted aggregate quantity index is computed in much the same way as a weighted aggregate price index.

A weighted aggregate quantity index for period t 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 17