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Chapter 17

Index. Numbers. Chapter 17. 1. Describe the term index. Understand the difference between a weighted and an unweighted index. 2. 3. 4. Construct and interpret a Laspeyres’ price index. Construct and interpret a Paasche’s price index. 5. Construct and interpret a value index.

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Chapter 17

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  1. Index Numbers Chapter 17

  2. 1. Describe the term index Understand the difference between a weighted and an unweighted index 2. 3. 4. Construct and interpret a Laspeyres’ price index Construct and interpret a Paasche’s price index 5. Construct and interpret a value index Explain how the Consumer PriceIndexis constructed and interpreted 6. Chapter Goals When you have completed this chapter, you will be able to:

  3. Terminology 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 Example

  4. Example 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

  5. Compute a simple price index for each stock. Use 1996 as the base year (1996=100) Example continued… NWS ($2/$1)(100)= 200 Simple Price Indexes are: NPC ($4/$5)(100)= 80 GAC ($6/$6)(100)= 100

  6. Compute a simpleindex for the number of shares owned for each.Use 1996 as the base year (1996=100) Example continued… NWS (50/30)(100)= 166.67 Simple Shares Indexes are: NPC (30/15)(100)= 200 GAC (20/40)(100)= 50

  7. Reasons for computing indexes: …they facilitate a comparison of unlike series …they are aconvenient 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?

  8. Types of Index Numbers An index can be classified as a: * price index quantity index, value index or special-purpose index *…this measures the changes in prices from a selected base period to another period. Examples

  9. Types of Index Numbers Examples price index 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/cgi-win/CNSMCGI.EXE special-purpose index S&P/TSX composite www.tse.com More Examples...

  10. 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 More Examples...

  11. Types of Index Numbers New Housing Price Indexes … measure changes over time in the contractors’ selling prices of new residential houses …others 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)

  12. pt = P (100) po Construction of Index Numbers Simple Price Index, P: Let PO be the base period price, and ptbe the price at the selected or given period. Thus, the simple price index is given by:

  13. Construction of Index Numbers A weighted index considers both the price and the quantities of items. There are two methods of computing the price index: Laspeyresmethod and Paaschemethod Laspeyres…

  14. S p q = 0 t P (100) S p q 0 0 Construction of Index Numbers 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 q0be the quantity consumed in the base period

  15. p q S t t P = (100) p q S 0 t Construction of Index Numbers Paasche’s Weighted Price index, P …here the present year weights are substituted for the original base period weights. Let qtbe the current quantity consumed, p0 be the price in the base period, and pt be the current price.

  16. S p q = t t (100) V S p q 0 0 Construction of Index Numbers Value index …here both the price and quantity changefrom the base period to the given period. A value index reflects changes in both price and quantity:

  17. 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 Uses...

  18. Consumer Price Index … 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) CPI Uses... Examples...

  19. Actual Sales (100) Deflated Sales = An approximate index $1 Purchasing power of dollar = ( 100 ) CPI Consumer Price Index Deflating Sales: Determining the purchasing power of the dollar compared with its value for the base period: Question

  20. A $54000 ( 100 ) 112 Suppose a person’s income has increased from $44 000 to $54 000 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? Determine the purchasing power (PP) of the dollar compared with its value for the base period: PP at the end of the period = = $48 214 The real income increase is only $4 214, due to the increase in the cost of living over the 5 years

  21. 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 numbersas the denominators and convert each series to the new base period.

  22. From the information given, below perform the following operations: Compute a simple aggregate price index for the three stocks.

  23. S + + p $ 2 $ 4 $ 6 t = = = P ( 100 ) ( 100 ) 100 . 0 S + + p $ 1 $ 5 $ 6 0 Compute a simple aggregate price index for the three stocks. Using Laspeyres…

  24. S p q t 0 = P ( 100 ) S p q 0 0 + + $ 2 ( 30 ) $ 4 ( 15 ) $ 6 ( 40 ) = ( 100 ) + + $ 1 ( 30 ) $ 5 ( 15 ) $ 6 ( 40 ) $ 360 = = ( 100 ) 104 . 35 $ 345 Computing the price index using the Laspeyres method Using Paasche…

  25. S p q t t = P ( 100 ) S p q 0 t + + ) $ 2 ( 50 ) $ 4 ( 30 ) $ ( 6 20 = ( 100 ) + + ) $ 1 ( 50 ) $ 5 ( 30 ) $ 6 ( 20 $ 340 = = ( 100 ) 106 . 25 $ 320 Computing the price index using the Paasche method Value Index…

  26. S p q t t = P ( 100 ) p q S 0 0 + + $ 2 ( 50 ) $ 4 ( 30 ) $ 6 ( 20 ) = ( 100 ) + + $ 1 ( 30 ) $ 5 ( 15 ) $ 6 ( 40 ) $ 340 = = ( 100 ) 98 . 55 $ 345 Computing the value index

  27. www.mcgrawhill.ca/college/lind for quizzes extra content data sets searchable glossary access to Statistics Canada’s E-Stat data …and much more! Test your learning… Click on… Online Learning Centre

  28. This completes Chapter 17

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