1. 1 1 Slide © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. Slides by John Loucks St. Edward’s University

2. 2 2 Slide © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. Chapter 17 Index Numbers n Price Relatives n Aggregate Price Indexes n Computing an Aggregate Price Index from Price Relatives from Price Relatives n Some Important Price Indexes n Deflating a Series by Price Indexes n Price Indexes: Other Considerations n Quantity Indexes

3. 3 3 Slide © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. Price Relatives n A base period is a given starting point in time. n A price relative expresses the unit price in each period as a percentage of the unit price in the base period. n A price relative shows how the current price per unit for a given item compares to a base period price per unit for the same item. n Price relatives are helpful in understanding and interpreting changing economic and business conditions over time.

4. 4 4 Slide © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. Price Relatives Television 11,469 23,904 Newspaper $14,794 $29,412 1998 2008 The prices Besco paid for newspaper and television ads in 1998 and 2008 are shown below. television ads in 1998 and 2008 are shown below. Using 1998 as the base year, compute a 2008 price Using 1998 as the base year, compute a 2008 price index for newspaper and television ad prices. index for newspaper and television ad prices. n Example: Besco Products

5. 5 5 Slide © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. Price Relatives Television advertising cost increased at a greater rate. NewspaperTelevision

6. 6 6 Slide © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. n An aggregate price index is developed for the specific purpose of measuring the combined change of a group of items. Aggregate Price Indexes where P it = unit price for item i in period t P i 0 = unit price for item i in the base period n An unweighted aggregate price index in period t, denoted by I t, is given by

7. 7 7 Slide © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. n Letting Q i = quantity for item i, the weighted aggregate price index in period t is given by Aggregate Price Indexes where the sums are over all items in the group n With a weighted aggregate index each item in the group is weighted according to its importance, which typically is the quantity of usage.

8. 8 8 Slide © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. Aggregate Price Indexes n When the weights are based on period t usage, the index is a Paasche index. n When the fixed quantity weights are determined from the base-year usage, the index is called a Laspeyres index.

9. 9 9 Slide © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. Aggregate Price Indexes Data on energy consumption and expenditures by sector for the city of Rockdale are given on the by sector for the city of Rockdale are given on the next slide. Construct an aggregate price index for next slide. Construct an aggregate price index for energy expenditures in 2008 using 1990 as the base energy expenditures in 2008 using 1990 as the base year. year. n Example: City of Rockdale

10. 10 Slide © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. Aggregate Price Indexes Transport.15,29320,262 2.32 6.16 Industrial21,28717,832.79 5.13 Commercial 5,416 6,015 1.97 11.32 Residential 9,473 8,804$2.12 $10.92 Sector 1990 2008 1990 2008 Quantity (BTU) Unit Price ($/BTU) Quantity (BTU) Unit Price ($/BTU) n Example: City of Rockdale

11. 11 Slide © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. Unweighted Aggregate Price Index Aggregate Price Indexes n Example: City of Rockdale

12. 12 Slide © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. Weighted Aggregate Index (Laspeyres Method) Aggregate Price Indexes The Paasche value being less than the Laspeyres indicates usage has increased faster in the lower-priced sectors. Weighted Aggregate Index (Paasche Method) n Example: City of Rockdale

13. 13 Slide © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. Dina wants an index that measures the change in Dina wants an index that measures the change in the overall cost of her lawn care. Price and quantity data for her annual lawn expenses are listed on the next slide. Example: Annual Cost of Lawn Care Dina Evers is pleased with her lovely lawn, but she Dina Evers is pleased with her lovely lawn, but she is concern about the increasing cost of maintaining it. The cost includes mowing, fertilizing, watering, and more. Aggregate Price Indexes

14. 14 Slide © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. Item Quantity(Units) Mowing Leaf Removal Watering (1000s gal.) Fertilizing Sprinkler Repair 32 340 2 1 Unit Price ($) 20042008 57.00 57.00 56.00 56.00 1.83 1.83 56.00 56.00109.00 79.00 79.00 71.00 71.00 2.78 2.78 67.00 67.00128.00 Example: Annual Cost of Lawn Care Aggregate Price Indexes

15. 15 Slide © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. Unweighted where: P it = unit price for item i in period t P it = unit price for item i in period t P i 0 = unit price for item i in the base period P i 0 = unit price for item i in the base period Unweighted aggregate price index in period t is: A 24% increase in annual lawn care expenses A 24% increase in annual lawn care expenses Aggregate Price Indexes

16. 16 Slide © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. Weighted aggregate price index in period t is: Weighted (Fixed Quantity) where: Q i = quantity for item i Note that Q i does not have a second subscript for a time period. A 36% increase in annual lawn care expenses A 36% increase in annual lawn care expenses Aggregate Price Indexes

17. 17 Slide © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. Weighted (Base-Period Quantity) A variable- quantity index Special case of the fixed quantity index LaspeyresIndex PaascheIndex More widely used than the Paasche index Pro: Reflects current usage; Con: Weights require contin- ual updating Weighted (Period t Quantity) Aggregate Price Indexes

18. 18 Slide © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. The 5-year increases in unit price ranged from a low of 17.4% for sprinkler repair to a high of 51.9% for water. Aggregate Price Indexes Item i Mowing Leaf Removal Water (1000s gal.) Fertilizing Sprinkler Repair Unit Price ($) 20042008 57.00 57.00 56.00 56.00 1.83 1.83 56.00 56.00109.00 79.00 79.00 71.00 71.00 2.78 2.78 67.00 67.00128.00 Pi 0Pi 0Pi 0Pi 0 Pi tPi tPi tPi t PriceRelative ( P i t / P i 0 )100 138.6126.8151.9119.6117.4

19. 19 Slide © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. Item PriceRelative ( P it / P i 0 ) 100 MowingLeavesWaterFertilizeSprinkler Base Price ($) 57.00 57.00 56.00 56.00 1.83 1.83 56.00 56.00109.00 QiQiQiQi 138.6126.8151.9119.6117.4 Pi 0Pi 0Pi 0Pi 0 Quantity 32 340 2 1 Weight wi = Pi 0Qiwi = Pi 0Qiwi = Pi 0Qiwi = Pi 0Qi Weighted Price Relative ( P it / P i 0 )( 100 ) w i 1,824.0 168.0 168.0 73.2 73.2 112.0 112.0 109.0 109.0252,806.40 21,302.40 21,302.40 11,119.08 11,119.08 13,395.20 13,395.20 12,796.60 12,796.60 Total2,286.2311,419.68 Aggregate Price Indexes This value is the same as the one identified by the weighted aggregate index computation. This value is the same as the one identified by the weighted aggregate index computation.

20. 20 Slide © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. Its base period is 1982-1984 with an index of 100. Its base period is 1982-1984 with an index of 100. Published monthly by the U.S. Bureau of Labor Statistics. Published monthly by the U.S. Bureau of Labor Statistics. Weighted aggregate price index with fixed weights derived from a usage survey. Weighted aggregate price index with fixed weights derived from a usage survey. Based on 400 items including food, housing, clothing, transportation, and medical items. Based on 400 items including food, housing, clothing, transportation, and medical items. Primary measure of the cost of living in U.S. Primary measure of the cost of living in U.S. Some Important Price Indexes n Consumer Price Index (CPI)

21. 21 Slide © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. Consumer Price Index (CPI) Base 1982-1984 = 100.0 Base 1982-1984 = 100.0 Note: For 1982 – 1984 that (96.5 + 99.6 + 103.9)/3 = 100.0 Some Important Price Indexes

22. 22 Slide © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. Is a weighted average of price relatives using the Laspeyres method. Is a weighted average of price relatives using the Laspeyres method. Includes the output of manufacturing, agriculture, forestry, fishing, mining, gas and electricity, and public utilities. Includes the output of manufacturing, agriculture, forestry, fishing, mining, gas and electricity, and public utilities. Covers raw, manufactured, and processed goods at each level of processing. Covers raw, manufactured, and processed goods at each level of processing. Used as a leading indicator of the future trend of consumer prices and the cost of living. Used as a leading indicator of the future trend of consumer prices and the cost of living. Measures the monthly changes in prices in primary markets in the U.S. Measures the monthly changes in prices in primary markets in the U.S. n Producer Price Index (PPI) Some Important Price Indexes

23. 23 Slide © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. Another average is computed for 20 transportation stocks, and another for 15 utility stocks. Another average is computed for 20 transportation stocks, and another for 15 utility stocks. The DJIA is not expressed as a percentage of base- year prices. The DJIA is not expressed as a percentage of base- year prices. The Dow Jones Industrial Average (DJIA) is based on common stock prices of 30 industrial firms. The Dow Jones Industrial Average (DJIA) is based on common stock prices of 30 industrial firms. Indexes designed to show price trends and movements on the New York Stock Exchange. Indexes designed to show price trends and movements on the New York Stock Exchange. n Dow Jones Averages Some Important Price Indexes

24. 24 Slide © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. Dow Jones Industrial Average (DJIA) 30 Companies 30 Companies As of 04/2009 Some Important Price Indexes

25. 25 Slide © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. Deflating a Series by Price Indexes n Deflating actual hourly wages results in real wages or the purchasing power of wages. n In order to correctly interpret business activity over time when it is expressed in dollar amounts, we should adjust the data for the price-increase effect. n Removing the price-increase effect from a time series is called deflating the series.

26. 26 Slide © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. McNeer Cleaners, with 46 branch locations, has had the total sales revenues shown on the next had the total sales revenues shown on the next slide for the last five years. Deflate the sales revenue figures on the basis of 1982-1984 constant dollars. Is figures on the basis of 1982-1984 constant dollars. Is the increase in sales due entirely to the price-increase the increase in sales due entirely to the price-increase effect? effect? n Example: McNeer Cleaners Deflating a Series by Price Indexes

27. 27 Slide © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. n Example: McNeer Cleaners Deflating a Series by Price Indexes 2008 11,690 215.3 2007 10,724 207.3 2006 9,830 201.6 2005 9,062 195.3 2004 8,446 188.9 Year Total Sales ($1000) CPI

28. 28 Slide © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. n Adjusting Revenue For the Price-Increase Effect After adjusting, revenue is still increasing at an average rate of 5.0% per year. 2008 (11,690/215.3)(100) = 5,430 +5.0 2007 (10,724/207.3)(100) = 5,173 +6.1 2006 (9,830/201.6)(100) = 4,876 +5.1 2005 (9,062/195.3)(100) = 4,640 +3.8 2004 (8,446/188.9)(100) = 4,471 Year Deflated Sales ($1000) Annual Change (%) Deflating a Series by Price Indexes

29. 29 Slide © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. Real Sales Revenue ($1000s) 2004 2005 2006 2007 2008 A real sales increase of 21.45% from 2004 to 2008 4500 4750 5000 5250 5500 4250 Year 4471 4640 5173 5430 4876 Deflating a Series by Price Indexes

30. 30 Slide © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. When the class of items is very large, a representative group (usually not a random sample) must be used. The group of items in the aggregate index must be periodically reviewed and revised if it is not representative of the class of items in mind. Selection of Items Price Indexes: Other Considerations

31. 31 Slide © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. For example, a CPI with a 1945 base period would be difficult for most individuals to understand, due to unfamiliarity with conditions in 1945. Selection of a Base Period The base period for most indexes is adjusted periodically to a more recent period of time. As a rule, the base period should not be too far from the current period. The CPI’s base period base period was changed to 1982-84 in 1988. Price Indexes: Other Considerations

32. 32 Slide © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. An increase in an item’s quality may or may not result in a price increase... and a decrease in quality may or may not result in a price decrease. Is a product that has undergone a major quality change the same product it was ? A basic assumption of a price index is that prices over time are identified for the same item. Quality Changes Price Indexes: Other Considerations

33. 33 Slide © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. An index used to measure changes in quantity levels over time is called a quantity index. A weighted aggregate quantity index is computed in much the same way as a weighted aggregate price index. A quantity relative shows how the current quantity level for a single item compares to a base period quantity level for the same item. Quantity Indexes

34. 34 Slide © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. Example: Appliance Mart Appliance Mart reports the 1999 and 2008 sales for Appliance Mart reports the 1999 and 2008 sales for three major kitchen appliances as shown below. Compute quantity relatives and use them to develop Compute quantity relatives and use them to develop a weighted aggregate quantity index for 2008. Kitchen Appliance Sales Price (1999) Dishwasher Range Refrigerator Sales (Units) 19992008 720 540 980 950 610 1110 $325 $450 $710 Quantity Indexes

35. 35 Slide © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. KitchenAppliance DishwasherRangeRefrigerator Sales (Units) 19992008 720540980 950 950 610 610 1110 1110 Quantity Relative (950/720)100 = 131.9 (950/720)100 = 131.9 (610/540)100 = 113.0 (610/540)100 = 113.0 (1110/980)100 = 113.3 Quantity Indexes

36. 36 Slide © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. Unweighted where: Q it = quantity for item i in period t Q i 0 = quantity for item i in the base period Q i 0 = quantity for item i in the base period Unweighted aggregate quantity index in period t is: Quantity Indexes

37. 37 Slide © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. Weighted (Base-Period Price) where: P i 0 = price for item i in the base period Weighted aggregate quantity index in period t is: Quantity Indexes

38. 38 Slide © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. Weighted (Fixed Price) Weighted (Period t Price) Note that P i does not have a second subscript for a time period. Quantity Indexes

39. 39 Slide © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. End of Chapter 17