Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved.

Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved. When you have completed this chapter, you will be able to: 1. Describe the term index 2. Understand the difference between a weighted and an unweighted index 3. Construct and interpret a Laspeyres’ price index 4. Construct and interpret a Paasche’s price indexConstruct and interpret a value index 5. Explain how the Consumer Price Index is constructed and interpreted 6.

Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved. T erminology 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 McGraw-Hill Companies, Inc. All rights reserved. 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 Stock 1996 Price 1996 Shares 2001 Price 2001 Shares NWS$130$250 NPC$515$430 GAC$640$620

Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved. continued… Stock 1996 Price 1996 Shares 2001 Price 2001 Shares NWS$130$250 NPC$515$430 GAC$640$620 Compute a simple price index for each stock. Use 1996 as the base year (1996=100) Simple Price Indexes are: NWS ($2/$1)(100) = 200 NPC ($4/$5)(100) = 80 GAC ($6/$6)(100) = 100

Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved. continued… Stock 1996 Price 1996 Shares 2001 Price 2001 Shares NWS$130$250 NPC$515$430 GAC$640$620 Compute a simple index for the number of shares owned for each. Use 1996 as the base year (1996=100) Simple Shares Indexes are: NWS (50/30)(100) = NPC (30/15)(100) = 200 GAC (20/40)(100) = 50

Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved. Reasons for computing indexes: …they facilitate a comparison of unlike series …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 Why Convert Data to Indexes?

Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved. Types of Index Numbers * …this measures the changes in prices from a selected base period to another period. An index can be classified as a: * price index quantity index, value index or special-purpose index

Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved. Types of Index Numbers Consumer Price Index Retail sales of snowmobiles in Canada Has the value of eggs sold for consumption in 2000 increased from earlier years? S&P/TSX composite price index quantity index value index special-purpose index

Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved. Types of Index Numbers 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 McGraw-Hill Companies, Inc. All rights reserved. … measure changes over time in the contractors’ selling prices of new residential houses Types of Index Numbers New Housing Price Indexes Machinery and Equipment Price Indexes Nonresidential Building Construction Price Indexes Farm Input Price Indexes Farm Product Price Indexes Price Indexes of the National Accounts (GDP) …others

Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved. Construction of Index Numbers Simple Price Index, P: Let P O be the base period price, and p t be the price at the selected or given period. Thus, the simple price index is given by: P ptpt popo  (100)

Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved. A weighted index considers both the price and the quantities of items. There are two methods of computing the price index: Laspeyres method and Paasche method Construction of Index Numbers Laspeyres…

Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved. Laspeyres’ Weighted Price Index, P: This method uses the base period quantities as weights. Construction of Index Numbers P pq pq t    0 00 (100) Let p t be the current price, p 0 be the price in the base period, and q 0 be the quantity consumed in the base period

Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved. …here the present year weights are substituted for the original base period weights. Let q t be the current quantity consumed, p 0 be the price in the base period, and p t be the current price. Paasche’s Weighted Price index, P Construction of Index Numbers P pq pq t t t    0 (100)

Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved. …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: Value index Construction of Index Numbers V pq pq tt    00 (100)

Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved. Consumer Price Index 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 McGraw-Hill Companies, Inc. All rights reserved. … 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) Consumer Price Index

Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved. Deflating Sales: Determining the purchasing power of the dollar compared with its value for the base period: Consumer Price Index Deflated Sales = Actual Sales An approximate index (100) Purchasing power of dollar = CPI $1 ()100

Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved. Determine the purchasing power (PP) of the dollar compared with its value for the base period: PP at the end of the period = 112 $54000 ()100 Suppose a person’s income has increased from $ to $ during a 5 year period. Over the same period, the CP has also increased from 100 to 112. What is the real value of the increased income of the person? = $ The real income increase is only $4 214, due to the increase in the cost of living over the 5 years

Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved. When two or more series of index numbers are to be compared, they may not have the same base period. Shifting the base 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 McGraw-Hill Companies, Inc. All rights reserved. Stock 1996 Price 1996 Shares 2001 Price 2001 Shares NWS$130$250 NPC$515$430 GAC$640$620 From the information given, below perform the following operations: Compute a simple aggregate price index for the three stocks.

Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved. Stock 1996 Price 1996 Shares 2001 Price 2001 Shares NWS$130$250 NPC$515$430 GAC$640$620 Compute a simple aggregate price index for the three stocks ) ( 6$5$1$ 6$4$2$ ) (        0 p p P t Using Laspeyres…

Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved. Computing the price index using the Laspeyres method )100( 345$ 360$ == )100( )40(6$)15(5$)30(1$ )40(6$)15(4$)30(2$ = )100( 00 0 S S = qp qp P t Using Paasche…

Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved. Computing the price index using the Paasche method )100( 320$ 340$ == )100( ) 20 (6$)30(5$)50(1$ ) 20 ( 6 $)30(4$)50(2$ = )100( 0 S S = t tt qp qp P Value Index…

Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved. Computing the value index 55.98)100( 345$ 340$   )100( )40(6$)15(5$)30(1$ )20(6$)30(4$)50(2$   )100( 00    qp qp P tt

Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved. Test your learning … Click on… Online Learning Centre for quizzes extra content data sets searchable glossary access to Statistics Canada’s E-Stat data …and much more!

Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved. This completes Chapter 17