INDEX NUMBERS

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Chapter 17 Index Numbers

• Price Relatives

• Aggregate Price Index Numbers

• Computing an Aggregate Price Index
• from Price Relatives

• Some Important Price Index Numbers

• Deflating a Series using a Price Index

• Price Indices Other Considerations

• Quantity Index Numbers

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Price Relatives

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

1.43
Now
Price of Petrol
Then
0.32
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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.

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Price Relatives

• Example Besco Products

The prices Besco paid for newspaper and
television ads in 1996 and 2006 are shown below.
Using 1996 as the base year, compute 2006 price
relatives for newspaper and television ad prices.
1996 2006
Newspaper 14,794 29,412
Television 11,469 23,904
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Price Relatives
Newspaper
Television
Television advertising cost increased at a
greater rate.
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Aggregate Price Indices

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

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

where Pit unit price for item i in period
t Pi0 unit price for item i in the base period
and the sums are over all items in the group
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Aggregate Price Indices

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

• 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
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Aggregate Price Indices

• When the fixed quantity weights are determined in
  the base period, the index is called a Laspeyres
  index.

• When the weights are determined in the current
  period, the index is a Paasche index.

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Aggregate Price Indices

• Example City of Rockdahl

• Data on energy consumption
• and prices by sector for the
• city of Rockdahl are given on the
• next slide. Construct an aggregate
• price index for energy in 2006,
• using 1985 as the base year.

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Aggregate Price Indices

• Energy Consumption and Prices

Quantity (kJ)
Unit Price (/kJ)
Sector 1985 2006
1985 2006
Residential 9,473 8,804 2.12
10.92
Commercial 5,416 6,015 1.97 11.32
Industrial 21,287 17,832 0 .79 5.13
Transport 15,293 20,262 2.32 6.16
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Aggregate Price Indices

• Unweighted Aggregate Price Index

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Aggregate Price Indices

• Weighted Aggregate Index (Laspeyres Method)

• Weighted Aggregate Index (Paasche Method)

The Paasche value is less than the Laspeyres
value, indicating that consumption has increased
faster in the lower-priced sectors.
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Some Important Price Index Numbers

• Consumer Price Index (CPI)

• Most countries maintain a CPI, to monitor the
  cost of living.

• The U.K. CPI has replaced the Retail Prices Index
  (RPI) as the main measure for general price
  inflation.

• Weighted aggregate price index with fixed weights
  derived from an expenditure survey.

• The U.K. CPI is published monthly by the Office
  for National Statistics.

• The CPI base period is 2005 with an index value
  of 100.

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Some Important Price Index Numbers

• Share price indices

• Index numbers designed to show price trends and
  movements in share prices.

• The share index most commonly reported for the
  U.K. economy is the FTSE 100, an index based on
  the share prices of the largest 100 companies
  quoted on the London stock exchange.

• The Dow Jones Industrial Average (DJIA) is an
  important U.S. index based on the share prices of
  30 industrial firms quoted on the New York stock
  exchange.

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Deflating a Series Using a Price Index

• In order to correctly interpret business activity
  over time when it is expressed in monetary
  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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Deflating a Series Using a Price Index

• Example McNeer Cleaners

• McNeer Cleaners, with 46 branch
• locations, has had total sales
• revenues for the last five years as
• shown on the next slide. Deflate
• the sales revenue figures, using
• the CPI figures (which have a
• base year of 1990). Is the increase in
• sales revenue due entirely to the
• price-increase effect?

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Deflating a Series Using a Price Index

• Example McNeer Cleaners

Year Total Sales (1000) CPI
2002 8,446 163.0
2003 9,062 166.6
2004 9,830 172.2
2005 10,724 177.1
2006 11,690 179.9
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Deflating a Series Using a Price Index

• Adjusting Revenue For the Price-Increase Effect

Deflated Sales (000s)
Annual Change ()
Year
2002 (8,446/163.0)(100) 5182
2003 (9,062/166.6)(100) 5439 5.0
2004 (9,830/172.6)(100) 5695 4.7
2005 (10,724/177.1)(100) 6055 6.3
2006 (11,690/179.9)(100) 6498 7.3
After deflating, revenue is still increasing at
an average rate of 5.8 per year.
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Price Indices Other Considerations

• 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.

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Price Indices Other Considerations

• Selection of a Base Period

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

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

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

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Price Indices Other Considerations

• Quality Changes

• A basic assumption of price index numbers 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 Index Numbers

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

• Probably the best known type of 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

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End of Chapter 17