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1. 1. Index Numbers Chapter 15McGraw-Hill/Irwin Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.
2. 2. Learning ObjectivesLO1 Compute and interpret a simple index.LO2 Describe the difference between a weighted and an unweighted index.LO3 Compute and interpret a Laspeyres price index.LO4 Compute and interpret a Paasche price index.LO5 Construct and interpret a value index.LO6 Explain how the Consumer Price Index is constructed and interpreted. 15-2
3. 3. LO1 Compute and interpret a simple index.Index Numbers INDEX NUMBER A number that 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. 15-3
4. 4. LO1Simple Index – Example The following Excel output shows the number of passengers (in millions) for the five busiest airports in the United States in 2009. What is the index for Atlanta, Chicago, Los Angeles, and Dallas/Ft. Worth compared to Denver? 15-4
5. 5. LO1Simple Index – Example Using the info in the Excel output in the previous slide, the simple indexes for number of passengers (in millions) for the five busiest airports in the United States in 2009. compared to Denver are shown in the table below: 15-5
6. 6. LO1Index Number – Example 1 According to the Bureau of Labor Statistics, in 2000 the average hourly earnings of production workers was \$14.02. In 2009 it was \$18.62. What is the index of hourly earnings of production workers for 2009 based on 2000 data? Average hourly earnings in 2009 \$18.62 P X100 X100 132.81 Average hourly earnings in 2000 \$14.02 15-6
7. 7. LO1Index Number –Example 2 An index can also compare one item with another. Example: The population of the Canadian province of British Columbia in 2010 was 4,494,232 and for Ontario it was 13,069,182. What is the population index of British Columbia compared to Ontario? Population of British Columbia 4,494,232 P X100 X100 34.4 Population of Ontario 13,069,182 15-7
8. 8. LO1Why Convert Data to Indexes? An index is a convenient way to express a change in a diverse group of items.  The Consumer Price Index (CPI), for example, encompasses about 400 items—including golf balls, lawn mowers, hamburgers, funeral services, and dentists’ fees. Prices are expressed in dollars per pound, box, yard, and many other different units. Converting the prices of these many diverse goods and services to one index number allows the federal government and others concerned with inflation keep informed of the overall movement of consumer prices. Converting data to indexes also makes it easier to assess the trend in a series composed of exceptionally large numbers.  The estimate of U.S. retail e-commerce sales for the fourth quarter of 2010, adjusted for seasonal variation, was \$36,200,000 and \$30,700,000 for the fourth quarter of 2009, an increase of \$5,500,000. This increase is 17.9 percent, expressed as an index. 15-8
9. 9. LO1Indexes In many situations we wish to combine several items and develop an index to compare the cost of this aggregation of items in two different time periods.  For example, we might be interested in an index for items that relate to the expense of operating and maintaining an automobile. The items in the index might include tires, oil changes, and gasoline prices.  Or we might be interested in a college student index. This index might include the cost of books, tuition, housing, meals, and entertainment. There are several ways we can combine the items to determine the index. 15-9
10. 10. LO2 Describe the difference between a weighted and an unweighted index number.Different Index Numbers1. Unweighted Indexes  Simple Average of the Price Indexes  Simple Aggregate Index2. Weighted Indexes  Lespeyres Price Index  Paasche Price Index 15-10
11. 11. LO2Unweighted Indexes Where ∑pt is the sum of the prices (rather than the indexes) for the period t and ∑p0 is the sum of the prices for the base period. 15-11
12. 12. LO2Simple Aggregate Index – Example Pt \$14.70 P (100) (100) 134.9 P0 \$10.90 15-12
13. 13. LO2Simple Average - Example Pi 147 .1 ... 109 .3 874 .7 P 145 .78 n 6 6 15-13
14. 14. LO3 Compute and interpret a Lespeyres price index.Weighted Index: Laspeyres Advantages Requires quantity data from only the base period. This allows a more meaningful comparison over time. The changes in the index can be attributed to changes in the price. Disadvantages Does not reflect changes in buying patterns over time. Also, it may overweight goods whose prices increase. 15-14
15. 15. LO3Lespeyres Index - Example 15-15
16. 16. LO3Laspeyres Index - Example pt q0 \$695.72 P (100) (100) 137.0 p0 q0 \$507.64 15-16
17. 17. LO4 Compute and interpret a Paasche price index.Weighted Index: Paasche Index Where p is the price index pt is the current price p0 is the price of the base period qt is the quantity used in the current period q0 is the quantity used in the base period Advantages Because it uses quantities from the current period, it reflects current buying habits. Disadvantages It requires quantity data for the current year. Because different quantities are used each year, it is impossible to attribute changes in the index to changes in price alone. It tends to overweight the goods whose prices have declined. It requires the prices to be recomputed each year. 15-17
18. 18. LO4Paasche Index - Example pt qt \$811.60 P (100) (100) 135.64 p0 qt \$598.36 15-18
19. 19. LO4Fisher’s Ideal Index  Laspeyres’ index tends to overweight goods whose prices have increased. Paasche’s index, on the other hand, tends to overweight goods whose prices have gone down.  Fisher’s ideal index was developed in an attempt to offset these shortcomings.  It is the geometric mean of the Laspeyres and Paasche indexes. 15-19
20. 20. LO4Fisher’s Ideal Index - Example Fisher s ideal index (Laspeyres Index)(Paa sches Index) (135 .64 )(137 .0) 136 .24 15-20
21. 21. LO5 Compute and interpret a value index.Value Index A value index measures changes in both the price and quantities involved. A value index, such as the index of department store sales, needs the original base-year prices, the original base-year quantities, the present-year prices, and the present year quantities for its construction. Its formula is: 15-21
22. 22. LO5Value Index - Example The prices and quantities sold at the Waleska Clothing Emporium for various items of apparel for May 2000 and May 2009 are:What is the index of value for May 2009 using May 2000 as the base period? 15-22
23. 23. LO5Value Index - Example pt qt \$10,6000,000 V (100) (100) 117.8 p0 q0 \$9,000,000 15-23
24. 24. LO6 Explain how the Consumer Price Index is constructed and interpreted.Consumer Price Index The U.S. Bureau of Labor Statistics reports this index monthly. It describes the changes in prices from one period to another for a ―market basket‖ of goods and services. 15-24
25. 25. LO6Producers Price Index Formerly called the Wholesale Price Index, it dates back to 1890 and is also published by the U.S. Bureau of Labor Statistics. It reflects the prices of over 3,400 commodities. Price data are collected from the sellers of the commodities, and it usually refers to the first large-volume transaction for each commodity. It is a Laspeyres-type index. 15-25
26. 26. LO6Dow Jones Industrial Average (DJIA)  DJIA is an index of stock prices, but perhaps it would be better to say it is an ―indicator‖ rather than an index.  It is supposed to be the mean price of 30 specific industrial stocks.  However, summing the 30 stock prices and dividing by 30 does not calculate its value. This is because of stock splits, mergers, and stocks being added or dropped.  When changes occur, adjustments are made in the denominator used with the average. 15-26
27. 27. LO6CPI Uses 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 is an economic indicator of the rate of inflation in the United States. It computes real income:  real income = money income/CPI X (100) 15-27
28. 28. LO6CPI Uses - Formulas 15-28
29. 29. LO6CPI and Real Income CPI is used to determine real disposable personal income, to deflate sales or other variables, to find the purchasing power of the dollar, and to establish cost-of- living increases. 15-29
30. 30. LO6CPI as a Deflator  A price index can also be used to ―deflate‖ sales or similar money series. Deflated sales are determined by: . 15-30
31. 31. LO6CPI and Real IncomeThe Consumer Price Index is also used to determinethe purchasing power of the dollar. Suppose the Consumer Price Index this month is 200.0 (1982–84 100). What is the purchasing power of the dollar? 15-31