18- 1 Chapter Eighteen McGraw-Hill/Irwin © 2005 The McGraw-Hill Companies, Inc., All Rights Reserved. 18- 2 Chapter Eighteen Index Numbers 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 18- 3 Chapter Eighteen continued Index Numbers 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 18- 4 36-Month CPI 2000-2002 4 3 CPI An Index Number expresses the relative change in price, quantity, or value compared to a base period. 2 1 0 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 Month beginning 1/1/2002 A Simple Index Number measures the relative change in just one variable. Index Numbers 35 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. 18- 5 Stock 1997 1997 2002 2002 Price Shares Price Shares NWS $1 30 $2 50 NPC $5 15 $4 30 GAC $6 40 $6 20 Simple indexes using 1997 as base year (1997=100) Price Share ($2/$1)(100)=200 (50/30)(100)=167 (30/15)(100)=200 ($4/$5)(100)=80 (20/40)(100)=50 ($6/$6)(100)=100 Example 1 Easier to Indexes comprehend than actual numbers $345,651,289,560 (percent or 10%? change) Facilitate comparison of unlike series Bread Car Dress Surgery 18- 6 Why compute indexes? Provide convenient ways to express the change in the total of a heterogeneous CPI group of items $0.89 $18,000 $200 $400,000 Why Convert Data to Indexes? Indexes: Four classifications Price Measures the changes in prices from a selected base period to another period. 18- 7 Quantity Measures the changes in quantity consumed from the base period to another period. Special purpose Combines and weights a Value heterogeneous group of series Measures the change in the to arrive at an overall index value of one or more items showing the change in from the base period to the business activity from the given period (PxQ). base period to the present. Types of Index Numbers 18- 8 Price Index 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). CFMMI CFMMI Auto Quantity Chicago Midwest Manufacturing Index Base year 1997=100 180 160 140 Federal Reserve Quantity Output Index 120 100 80 60 40 20 0 YEAR 1996 1997 1998 1999 2000 2001 2002 Price and Quantity Indexes 18- 9 Jewellery, watchs and clocks and valuable gifts Department stores Furniture and fixtures electrical goods and photographic Motor vehicles and parts 100 90 80 70 60 50 40 30 20 10 0 Consumer durable goods Value Index Value Index of Feb '03 Retail Sales Base February (Monthly Average of Oct 1999-Sept 2000)=100 Special purpose Value and Special Purpose Indexes 18- 10 Simple Price Index, P pt P (100) p0 where po the base period price pt the price at the selected or given period. From Example 1 a simple aggregate price index for the three stocks p t P (100) p 0 $2 $5 $6 (100) $1 $5 $6 100.0 Construction of Index Numbers 18- 11 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 Laspeyres method Paasche method Uses the base period quantities as weights pt q0 P (100) p0q0 where pt is the current price p0 is the price in the base period q0 is the quantity consumed in the base period Paasche Weighted Price Index, P Present year weights substituted for the original base period weights 18- 12 Tends to overweight goods whose prices have gone down pt qt P (100) p0qt where qt is the current quantity consumed p0 is the price in the base period pt is the current price. Construction of Index Numbers 18- 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 18- 14 Value Index Reflects changes in both price and quantity Both the price and quantity change from the base period to the given period pt qt V (100) p0q0 Value Index 18- 15 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. Millions of employees in automobile, steel, and other industries have their wages adjusted upward when the CPI increases. Consumer Price Index 18- 16 Usefulness of CPI It allows consumers to determine the effect of price increases on their purchasing power. It is a yardstick for revising wages, pensions, alimony payments, etc. It computes real income: real income = money income/CPI (100) It is an economic indicator of the rate of inflation in the United States. Consumer Price Index 18- 17 Deflating Sales Actual sales Deflated sales (100) An approximate index Determining the purchasing power of the dollar compared with its value for the base period $1 Purcha sin g power of dollar (100) CPI Consumer Price Index 17-18 18- 18 Shifting the base 101 115 When two or more series of index numbers are to be compared,they may not 101 115 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 18- 19 Stock 1997 1997 2002 2002 Price Shares Price Shares Mr. Wagner owns stock in NWS $1 30 $2 50 three companies. $5 15 $4 30 Shown below is NPC the price per GAC $6 40 $6 20 share at the end of 1997 and Laspeyres Weighted Price Index, P 2002 for the p t q 0 P (100 ) three stocks and p 0 q 0 the quantities he $2(30 ) $4(15) $6(40 ) (100 ) owned in 1997 $1(30 ) $5(15 ) $6(40 ) and 2002. $360 (100 ) 104 .35 $345 18- 20 Paasche Weighted Price Index, P p t q t P (100 ) p 0 q t $2(50 ) $4(30 ) $6(20 ) (100 ) Value Index $1(50 ) $5(30 ) $6(20 ) $340 p t q t (100 ) 106 .25 P (100 ) $320 p 0 q 0 Fisher’s Ideal Index F = (104.35)(106.25) $2(50 ) $4(30 ) $6(20 ) (100 ) $1(30 ) $5(15 ) $6(40 ) $340 (100 ) 98 .55 $345 =105.3 Example 1 continued