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CHAPTER 15 – Index Numbers. Slides Created by Masuma Jaffer, Seneca College. Chapter Fifteen. Index Number. LEARNING OBJECTIVES When you have completed this chapter, you will be able to:. ONE Describe the term index . TWO Explain the difference between a weighted and
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CHAPTER 15 – Index Numbers Slides Created by Masuma Jaffer, Seneca College
Chapter Fifteen Index Number LEARNING OBJECTIVES When you have completed this chapter, you will be able to: ONEDescribe the term index. TWOExplain the difference between a weighted and an unweighted index. THREEConstruct and interpret a Laspeyers price index.
Chapter Fifteen continued Index Number LEARNING OBJECTIVES When you have completed this chapter, you will be able to: FOURConstruct and interpret a Paasche price index. FIVEConstruct and interpret a value index. SIXExplain how the consumer Price Index is constructed and interpreted.
Simple Index Numbers • AnIndex Number expresses the relative change in price, quantity, or value compared to a base period. If the index number is used to measure change in just one variable, such as hourly wages in manufacturing, we refer to this as a simple index.
EXAMPLE 1 • According to Statistics Canada, in 1995 the average salary of wage earners 15 years and older in Newfoundland and Labrador was $20 828 per year. In 2001, it was $24 165 per year. What is the index of yearly earnings of workers over age of 15 in Newfoundland and Labrador for 2001 based on 1995. • Thus, the yearly salaries in 2001 compared to 1995 was 116 percent. This means that there was a 16 percent increase in yearly salaries during the six years from 1995 to 2002 • ( 116.0 -100 = 16.0)
Construction of Index Numbers • Simple price Index ‘P’ can be expressed as:
EXAMPLE 2 • The price of a standard lot at the shady Rest Cemetery in 1998 was $450. The price rose to $795 in 2004. what is the price index for 2004 using 1998 as the base value? • The price of a cemetery lot increased 76.7 percentage from 1998 to2004.
Unweighted Indexes Table Showing computation of Index for Food Price 2005, 1995 = 100 • Simple Average of the price index
Unweighted Indexes • Average of the price index cont. • SIMPLE AVERAGE OF THE PRICE RELATIVES • This indicates that the mean of the group of indexes increased 50 percent from 1995 to 2005
Unweighted Indexes • The index for the above food items is found by summing the prices in 1995 and 2005.The sum of the prices for the base period is $10.94 and for the given period it is $13.24. • The simple aggregate index is 121.0, an increase of 21 percent in the ten-year period. • Simple Aggregate Index
Weighted Indexes • Laspeyres’ Price Index • Where:
EXAMPLE 3 • The prices and quantities consumed by a typical family for the six food items from Table 1 are shown below for the years 1995 and 2005
EXAMPLE 3 cont. • The weighted price index for 2005 is 165.4 and is computed as follows: • Laspeyres’ Price index = 165.4 • And we conclude that the price of this group of items has increased 65.4 percent in the ten years period. • .
Weighted Indexes • Paasche’s Price Index • Where:
EXAMPLE 3 • The prices for the six food items from Table 1 are shown below that also includes the number of units of each consumed by a typical family in 1995 and 2005
EXAMPLE 3 cont. • The index for 2005 is 168.4 and is computed as follows: • Paasche’s Price index = 168.4 • And we conclude that the price of this group of items has increased 68.4 percent in the ten years period. • .
Weighted Indexes • Laspeyres’ • Advantages: • Requires quantity from the base period. • The changes in the index can be attributed to changes in price. • Disadvantages: • Does not reflect changes in buying pattern over time. • It may overweight goods whose prices increase. • (Laspeyres’ index tends to overweight goods whose prices have increased.)
Weighted Indexes • Paasche’s • Advantages: • Because it uses quantities from the current period, it reflects current buying habits. • Disadvantages: • Difficult to obtain quantity data for each year. • It is impossible to attribute changes in the index to changes in price alone. Price have to be recomputed each year. • (Paasche’s index tends to overweight goods whose prices have gone down.)
Weighted Indexes • Fisher’s Ideal index • It is a geometric mean of Laspeyres and Paasche indexes. Theoretically, this index is ideal as it combines the best features of both Laspeyres and Paasche. • Fisher’s ideal index = (Laspeyres’ index)( Paasche’s index) • For the data in Table 3 • Fisher’s ideal index = (165.4)(168.4) = 166.9
Weighted Indexes • Value index • A value index measures changes in both the price and quantities involved and is computed as follows:
EXAMPLE 4 • The prices and quantities sold at the Waleska Department Store for various items of apparel for May 2005 are: • What is the index of value for May 2005 using May 2000 as the base period? • .
EXAMPLE 4 cont. • .
Special – Purpose Indexes • The Consumer price Index:It describes the changes in prices from one period to another from a “market basket” of goods and services. (reported monthly by Statistics Canada) • S&P/TSX Composite Index: It represents the average performance of 300 of Canada's largest public companies traded on theToronto Stock Exchange. • Dow Jones Industrial Average (DJIA): It is supposed to be the mean price of 30 specific industrial stocks on the New York Stock Exchange.
