18- Chapter Eighteen McGraw- © 2005 The McGraw-Hill Companies, Inc., All 18- 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- 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 An Index Number expresses the relative change in price, quantity, or value compared to a base period 18- A Simple Index Number measures the relative change in just one variable Index Numbers 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- 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 Easier to Indexes comprehend than actual numbers $ ,6 ,2 ,5 (percent or 10% ? change) Facilitate comparison of unlike series Bread Car Dress Surgery $0.89 Why compute indexes? 18- Provide convenient ways to express the change in the total of a heterogeneous CPI group of items $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- 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- 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) Quantity Federal Reserve Quantity Output Price and Quantity Indexes 18- Value 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 a simple aggregate price index for the three stocks p t P (100) p $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 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 p t q P (100) p q $2(30) $4(15) $6(40) (100) $1(30) $5(15) $6(40) $360 (100) 104.35 $345 18- 20 Paasche Weighted Price Index, P p t q t P (100) p 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 q Fisher’s Ideal Index F = (104.35)(106.25) =105.3 $2(50) $4(30) $6(20) (100) $1(30) $5(15) $6(40) $340 (100) 98.55 $345 Example continued ... 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... to: FIVE Construct and interpret a Value Index SIX Explain how the Consumer Price index is constructed and interpreted Goals An Index Number expresses the relative change in price, quantity, or... 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- Price Index Producer Price Index - measures