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Chapter Eighteen McGraw-Hill/Irwin

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1 Chapter Eighteen McGraw-Hill/Irwin
© 2005 The McGraw-Hill Companies, Inc., All Rights Reserved.

2 Index Numbers Chapter Eighteen GOALS
When you have completed this chapter, you will be able to: ONE Describe the term index. TWO Understand the difference between a weighted price index and an unweighted price index. THREE Construct and interpret a Laspeyres Price index. FOUR Construct and interpret a Paasche Price index. Goals

3 Index Numbers Chapter Eighteen continued GOALS
When you have completed this chapter, you will be able to: FIVE Construct and interpret a Value Index. SIX Explain how the Consumer Price index is constructed and interpreted. Goals

4 An Index Number expresses the relative change in price, quantity, or value compared to a base period. A Simple Index Number measures the relative change in just one variable. Index Numbers

5 Simple indexes using 1997 as base year (1997=100)
Mr. Wagner owns stock in three companies. Given is the price per share at the end of 1997 and 2002 for the three stocks and the quantities he owned in 1997 and 2002. Simple indexes using 1997 as base year (1997=100) Price ($2/$1)(100)=200 ($4/$5)(100)=80 ($6/$6)(100)=100 Share (50/30)(100)=167 (30/15)(100)=200 (20/40)(100)=50 Example 1

6 Why Convert Data to Indexes?
Easier to comprehend than actual numbers (percent change) Why compute indexes? Provide convenient ways to express the change in the total of a heterogeneous group of items Facilitate comparison of unlike series Bread $0.89 Car $18,000 Dress $200 Surgery $400,000 Why Convert Data to Indexes?

7 Indexes: Four classifications
Quantity Measures the changes in quantity consumed from the base period to another period. Price Measures the changes in prices from a selected base period to another period. Special purpose Combines and weights a heterogeneous group of series to arrive at an overall index showing the change in business activity from the base period to the present. Value Measures the change in the value of one or more items from the base period to the given period (PxQ). Types of Index Numbers

8 Price and Quantity Indexes
Producer Price Index - measures the average change in prices received in the primary markets of the US by producers of commodities in all stages of processing (1982=100). Price Index Quantity Federal Reserve Quantity Output Price and Quantity Indexes

9 Value and Special Purpose Indexes

10 Construction of Index Numbers
Simple Price Index, P From Example 1 a simple aggregate price index for the three stocks where po the base period price pt the price at the selected or given period. Construction of Index Numbers

11 Considers both the price and the quantities of items
Weighted index Considers both the price and the quantities of items Tends to overweight goods whose prices have increased Laspeyres Weighted Price Index, P Two methods of computing the price index Uses the base period quantities as weights Laspeyres method Paasche method where pt is the current price p0 is the price in the base period q0 is the quantity consumed in the base period

12 Construction of Index Numbers
Paasche Weighted Price Index, P Present year weights substituted for the original base period weights Tends to overweight goods whose prices have gone down where qt is the current quantity consumed p0 is the price in the base period pt is the current price. Construction of Index Numbers

13 Fisher’s Ideal Index Fisher’s ideal index = (Laspeyres’ index)(Paasche’s index) The geometric mean of Laspeyres and Paasche indexes Balances the negative effects of the Laspeyres’ and Paasche’s indices. Requires that a new set of quantities be determined each year. Fisher’s Ideal Index

14 Reflects changes in both price and quantity
Value Index Reflects changes in both price and quantity Both the price and quantity change from the base period to the given period Value Index

15 Millions of employees in automobile, steel, and other industries have their wages adjusted upward when the CPI increases. In 1978 two consumer price indexes were published. One was designed for urban wage earners and clerical workers. It covers about one third of the population. Another was designed for all urban households. It covers about 80% of the population. Consumer Price Index

16 It computes real income: real income = money income/CPI (100)
Usefulness of CPI It allows consumers to determine the effect of price increases on their purchasing power. It is an economic indicator of the rate of inflation in the United States. It computes real income: real income = money income/CPI (100) It is a yardstick for revising wages, pensions, alimony payments, etc. Consumer Price Index

17 Determining the purchasing power of the dollar
Deflating Sales Determining the purchasing power of the dollar compared with its value for the base period Consumer Price Index

18 First select a common base period for all series.
17-18 Shifting the base When two or more series of index numbers are to be compared,they may not have the same base period. First select a common base period for all series. Then use the respective base numbers as the denominators and convert each series to the new base period. Consumer Price Index

19 Laspeyres Weighted Price Index, P
Mr. Wagner owns stock in three companies. Shown below is the price per share at the end of 1997 and 2002 for the three stocks and the quantities he owned in 1997 and 2002. Laspeyres Weighted Price Index, P

20 Paasche Weighted Price Index, P
Value Index Fisher’s Ideal Index F = (104.35)(106.25) =105.3 Example 1 continued


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