After studying this chapter you will be able to understand: Describe the term index, understand the difference between a weighted and an unweighted index, construct and interpret a Laspeyres’ price index, construct and interpret a Paasche’s price index, construct and interpret a value index, explain how the consumer price index is constructed and interpreted.
17 1 Copyright © 2004 by The McGrawHill Companies, Inc. All rights reserved. 17 2 When you have completed this chapter, you will be able to: Describe the term index Understand the difference between a weighted and an unweighted index Construct and interpret a Laspeyres’ price index Construct and interpret a Paasche’s price index Construct and interpret a value index Explain how the Consumer Price Index is constructed and interpreted Copyright © 2004 by The McGrawHill Companies, Inc. All rights reserved. Terminology 17 3 Index Number … measures the relative change in price, quantity, value, or some other item of interest from one time period to another Simple Index Number …measures the relative change in just one variable Copyright © 2004 by The McGrawHill Companies, Inc. All rights reserved. 17 4 Mr. Wagner owns stock in three companies. Shown below is the price per share at the end of 1996 and 2001 for the three stocks and the quantities he owned in 1996 and 2001 1996 1996 2001 2001 Stock Price Shares Price Shares NWS $1 30 $2 50 NPC $5 15 $4 30 GAC $6 40 $6 20 Copyright © 2004 by The McGrawHill Companies, Inc. All rights reserved. continued… 17 5 Compute a simple price index for each stock Use 1996 as the base year (1996=100) Stock 1996 Price 1996 Shares NWS NPC GAC $1 $5 $6 30 15 40 2001 2001 Price Shares $2 $4 $6 50 30 20 NWS ($2/$1)(100) = 200 Simple Price Indexes are: NPC ($4/$5)(100) = 80 GAC ($6/$6)(100) = 100 Copyright © 2004 by The McGrawHill Companies, Inc. All rights reserved. continued… 17 6 Compute a simple index for the number of shares owned for each Use 1996 as the base year 1996 (1996=100) 1996 2001 2001 Stock Price Shares Price Shares NWS NPC GAC $1 $5 $6 30 15 40 $2 $4 $6 50 30 20 NWS (50/30)(100) = 166.67 Simple Shares Indexes are: NPC (30/15)(100) = 200 GAC (20/40)(100) = 50 Copyright © 2004 by The McGrawHill Companies, Inc. All rights reserved. Reasons for computing indexes: Reasons for computing indexes: 17 7 …they facilitate a comparison of unlike series Why Why Convert Convert Data to Data to Indexes? Indexes? …they are a convenient way to express the change in the total of a heterogeneous group of items …they allow for a percent change to be easier to comprehend than actual numbers, especially when the numbers are extremely large Copyright © 2004 by The McGrawHill Companies, Inc. All rights reserved. Types of Index Numbers Types of Index Numbers 17 8 An index can be classified as a: * price index quantity index, value index or specialpurpose index *…this measures the changes in prices from a selected base period to another period Copyright © 2004 by The McGrawHill Companies, Inc. All rights reserved. Types of Index Numbers Types of Index Numbers price index 17 9 Consumer Price Index quantity index Retail sales of snowmobiles in Canada http://www.snowmobile.org/stats_2001_units_canada.asp value index Has the value of eggs sold for consumption in 2000 increased from earlier years? http://estat.statcan.ca/cgiwin/CNSMCGI.EXE specialpurpose index S&P/TSX composite www.tse.com Copyright © 2004 by The McGrawHill Companies, Inc. All rights reserved. Types of Index Numbers Types of Index Numbers 17 10 Industrial Product Price Indexes …measure the changes in prices received by Canadian manufacturers for goods as they leave the factory gate. Indirect taxes, transportation, and wholesale and retail costs are not included in the price Raw Materials Price Indexes …measure price changes for the purchase of raw materials by Canadian industry. The term “raw material” refers either to a commodity that is sold for the first time after being extracted from nature, or a substitutable recycled product Copyright © 2004 by The McGrawHill Companies, Inc. All rights reserved. Construction of Index Numbers 17 14 Laspeyres’ Weighted Price Index, P: This method uses the base period quantities as weights Let pt be the current price, p0 be the price in the base period, and q0 be the quantity consumed in the base period p q P Copyright © 2004 by The McGrawHill Companies, Inc. All rights reserved. t p0 q (100) Construction of Index Numbers 17 15 Paasche’s Weighted Price index, P …here the present year weights are substituted for the original base period weights. Let qt be the current quantity consumed, p0 be the price in the base period, and pt be the current price P Copyright © 2004 by The McGrawHill Companies, Inc. All rights reserved. pt qt p0 qt (100) Construction of Index Numbers 17 16 Value index …here both the price and quantity change from the base period to the given period. A value index reflects changes in both price and quantity: V Copyright © 2004 by The McGrawHill Companies, Inc. All rights reserved. pt q t (100) p0 q Consumer Price Index 17 17 In 1978 two consumer price indexes were published: one designed for urban wage earners and clerical workers …another designed for all urban households Copyright © 2004 by The McGrawHill Companies, Inc. All rights reserved. Consumer Price Index 17 18 … 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 is an economic indicator of the rate of inflation in Canadian … it computes real income: real income = money income/CPI(100) Copyright © 2004 by The McGrawHill Companies, Inc. All rights reserved. Consumer Price Index 17 19 Deflating Sales: Deflated Sales = Actual Sales (100) An approximate index Determining the purchasing power of the dollar compared with its value for the base period: $1 Purchasing power of dollar = (100) CPI Copyright © 2004 by The McGrawHill Companies, Inc. All rights reserved. 17 20 Suppose a person’s income has increased from Suppose a person’s income has increased from $44 000 to $54 000 during a 5 year period. Over the $44 000 to $54 000 during a 5 year period. Over the same period, the CP has also increased from 100 to 112. same period, the CP has also increased from 100 to 112 What is the real What is the rea value of the increased income of the person? value of the increased income of the person? Determine the purchasing power (PP) of the dollar compared with its value for the base period: PP at the end of the period = $54000 (100) ==$48 $48214 214 112 The real income increase is only $4 214, due to the The real income increase is only $4 214, due to the increase in the cost of living over the 5 years increase in the cost of living over the 5 years Copyright © 2004 by The McGrawHill Companies, Inc. All rights reserved. Shifting the base Shifting the base 17 21 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 Copyright © 2004 by The McGrawHill Companies, Inc. All rights reserved. 17 22 From the information given, below perform the following operations: Compute a simple aggregate price index Compute a simple aggregate price index for the three stocks. for the three stocks. Stock 1996 Price 1996 Shares NWS NPC $1 $5 30 15 $2 $4 50 30 GAC $6 40 $6 20 Copyright © 2004 by The McGrawHill Companies, Inc. All rights reserved. 2001 2001 Price Shares 17 23 Compute a simple aggregate price index for the Compute a simple aggregate price index for the three stocks. three stocks. P Stock 1996 Price NWS NPC $1 $5 30 15 $2 $4 50 30 GAC $6 40 $6 20 p t (100 ) p0 1996 2001 2001 Shares Price Shares $2 $4 $6 (100 ) $1 $5 $6 Copyright © 2004 by The McGrawHill Companies, Inc. All rights reserved. 100 Using Laspeyres… Using Laspeyres… 17 24 Computing the price index using the SLaspeyres method pt q P = ( 100 ) Sp q $ ( 30 ) + $ ( 15 ) + $ ( 40 ) = ( 100 ) $ 1( 30 ) + $ ( 15 ) + $ ( 40 ) $ 360 = ( 100 ) = 104 35 $ 345 Using Paasche… Using Paasche… Copyright © 2004 by The McGrawHill Companies, Inc. All rights reserved. 17 25 Computing the price index using the S pPaasche method t qt P = Sp q t (100) + $ (30 ) + $ (20 ) $ ( 50 ) = (100) $ 1(50) + $ ( 30) + $ ( 20) $ 340 = ( 100 ) = 106 25 $ 320 Value Index… Value Index… Copyright © 2004 by The McGrawHill Companies, Inc. All rights reserved. 17 26 Computing the value index P pt qt (100 ) p0 q0 $ ( 50 ) $ 1( 30 ) $ ( 30 ) $ ( 20 ) (100 ) $ (15 ) $ ( 40 ) $ 340 (100 ) $ 345 Copyright © 2004 by The McGrawHill Companies, Inc. All rights reserved. 98 55 Test your learning… … Test your learning … … n o n o k ilcick CCl www.mcgrawhill.ca/college/lind Online Learning Centre for quizzes extra content data sets searchable glossary access to Statistics Canada’s EStat data …and much more! Copyright © 2004 by The McGrawHill Companies, Inc. All rights reserved. 17 27 17 28 This completes Chapter 17 Copyright © 2004 by The McGrawHill Companies, Inc. All rights reserved. ... …others Machinery and Equipment Price Indexes Machinery and Equipment Price Indexes Nonresidential Building Construction Price Indexes Nonresidential Building Construction Price Indexes Farm Input Price Indexes... Copyright © 2004 by The McGrawHill Companies, Inc. All rights reserved. Types of Index Numbers Types of Index Numbers price index 17 9 Consumer Price Index quantity index Retail sales of snowmobiles in Canada http://www.snowmobile.org/stats_2001_units_canada.asp... this chapter, you will be able to: Describe the term index Understand the difference between a weighted and an unweighted index Construct and interpret a Laspeyres’ price index Construct and interpret a Paasche’s price index