Index Numbers Chapter 17 17-1 Copyright ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Learning Objectives LO17-1 LO17-2 LO17-3 LO17-4 LO17-5 17-2 Compute and interpret a simple, unweighted index Compute and interpret an unweighted aggregate index Compute and interpret a weighted aggregate index List and describe special-purpose indexes Apply the Consumer Price Index Copyright ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Index Numbers INDEX NUMBER A number that expresses the relative change in price, quantity, or value compared to a base period. The major characteristics of an index are It is a percentage, but the percent sign is usually omitted It has a base period The reasons for computing an index are To facilitate the comparison of unlike series If the numbers are very large, often it is easier to comprehend the change of the index rather than the change inCopyright numbers ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without 17-3 the prior written consent of McGraw-Hill Education. Hourly Wages Index Example According to the Bureau of Labor Statistics, in 2000, the average hourly earnings of production workers was $14.02. In January 2019, it was $27.56. What is the index of hourly earnings of production workers for January 2019 based on 2000 data? P = (100) = (100) = 196.58 Thus, the hourly earnings in 2019 compared to 2000 were 196.58%. This means there was a 96.58% increase in hourly earnings during the period, found by 196.58 – 100.0 = 96.58 17-4 Copyright ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Population Index Example An index can also compare one item to another. The population of the Canadian province of British Columbia in 2019 was 4,862,610, and for Ontario it was 14,374,084. What is the population index of British Columbia compared to Ontario? The index of population for British Columbia is 33.9 found by: P = (100) = (100) = 33.8 The population of British Colombia is 33.8% (about one-third) of the population of Ontario, or another way to say that is the population of British Columbia is 66.2% less than the population of Ontario (100 – 33.8 = 66.2) 17-5 Copyright ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Airport Index Example The following chart shows the number of passengers (in millions) for the 10 busiest airports in the United States in 2014. Use the McCarran International Airport in Las Vegas as the base. What is the index for the other airports compared to Las Vegas? To find the 10 indexes, divide the passengers for Las Vegas into the passengers for the other 9 airports. So the index for Atlanta is 224.2 found by (96.2 ÷ 42.9) × (100) = 224.2 17-6 Copyright ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. E-Commerce Sales Index Example Converting data to indexes makes it easier to see the trend in a series of very large numbers For example US retail e-commerce sales in 2018 were $504,582,000 In 2010, e-commerce sales were $168,895,000 An increase of $335,687,000 Index = 2018 e−commerce sales $504,582,000 (100) = (100) = 298.8 2010 e−commerce sales $168,895,000 This means 2018 sales increased 198.8% in the eight-year period. 17-7 Copyright ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Construction of Index Numbers To calculate a simple price index P, using 100 as the base value for any given year, use the formula below Suppose the price of a fall weekend package at Tryon Mountain Lodge in western North Carolina in 2000 was $450. The price rose to $795 in 2019. What is the price index for 2019 using 2000 as the base period and 100 as the base value? P $795 P = P t (100) = (100) = 176.7 $450 0 The fall weekend package increased 76.7% from 2000 to 2019. 17-8 Copyright ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Converting to Indexes using Different Base Periods Below is a table for prices of a Benson Automatic Stapler, Model 3, converted to indexes using three different base periods. First, a single year (2015) is used and each year’s price is divided by 20. Next, two years (2015-2016) are used as the base; the base price of the stapler would be $21, found by averaging the price of the stapler in the two years (20 + 22) ÷ 2 = $21and then dividing each year’s price by 21. Finally, the prices $20, $22, $23 are averaged if we use three years (2015-2017) as the base and then each year’s price is divided by 21.67 to obtain the price index. 17-9 Copyright ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Unweighted Indexes In an unweighted index, we do not consider the quantities We may wish to combine several related items and compare this group of items in two different time periods An index for items related to owning and operating an automobile (tires, oil changes, and gasoline) An index for items related to expenses of a college student (books, tuition, housing, meals, entertainment) In the simple average of price indexes, we add the simple indexes for each item and divide by the number of items 17-10 Copyright ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Simple Average of Price Indexes Example This table reports the prices for several food items in 2009 and 2019. We would like to develop an index for this food group for 2019 using 2009 prices as the base. This is written 2009=100 First, we use formula 17-1 to compute the simple index for each food item. P 1.274 For instance, the index for bread, P = P t (100) = 1.381 (100) = 92.3 0 Now use formula 17-2 to compute the percentage change in the group. ΣP 92.3+ …. +147.9 591.0 P= i= = = 98.5 n 6 6 The mean price of food decreased 1.5% 2009 to 2019. 17-11 Copyright ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Simple Aggregate Price Index In a simple aggregate price index, the prices of the items in the group are totaled for both periods and compared The simple aggregate index for food items on the previous slide is found by dividing the sum of prices in 2019 by the sum of the prices in 2009. P = (100) = (100) = 103.7 This means that the aggregate group of prices had increased 3.7% from 2009 to 2019. 17-12 Copyright ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Weighted Indexes: Laspeyres Method In a weighted index, the quantities are considered In the Laspeyres method, base period quantities are used in both the base period and the given period Advantage of the Laspeyres method Only quantity data from the base period is used which allows for more meaningful comparison over time Disadvantage Does not reflect changes in buying patterns over time It may overweight goods whose prices increase 17-13 Copyright ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Laspeyres Price Index Example First we determine the total amount spent for the six items in the base period, 2009. To find this value, multiply the base period (2009) price for bread, $1.381, by the base period quantity of 50. The result is $69.2. Continue that for all items and total the result. The base period total is $648.23. The current year total is computed in a similar fashion. For bread, we multiply the quantity in 2009 by the price of bread in 2019; 50 times $1.274 is $70.07. We make the same calculation for the other items and total to get $667.783. P = (100) = (100) = 103.0 We conclude the price of this group of items has increased 3.0% from 2009 to 2019. 17-14 Copyright ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Weighted Indexes: Paasche Method In the Paasche method, current period quantities are used Advantage of Paasche method Current buying habits are reflected Disadvantage It requires quantity data for the current year and it tends to overweight goods whose prices have declined It requires the product of prices and quantities to be recomputed each year 17-15 Copyright ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Paasche Price Index Example The following table shows the calculations to determine the Paasche index. Σp q $667.78 P = t t (100) = (100) = 88.7 Σp0qt $753.00 This result indicates that there has been an decrease of 11.3% in the price of this “market basket” of goods between 2009 and 2019. 17-16 Copyright ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Fisher’s Ideal Index Fisher’s ideal index is the geometric mean of the Laspeyres and Paasche indexes Determine Fisher’s ideal index for the data in Table 17-3 using our results from the earlier examples. Fisher’s ideal index = ) = So, Fisher’s ideal index is 95.6 17-17 Copyright ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Value Index A value index uses both base period and current period prices and quantities The prices and quantities sold at the Waleska Clothing Emporium for ties, suits, and shoes for May 2015 and May 2019 are given in the table on the left. What is the index of value for May 2019 using May 2015 as the base period? Total sales in May 2019 were $10,600 and in 2015 is $9,000. Σp q $10,600 V = Σp tqt (100) = (100) = 117.8 $9,000 0 0 The value of apparel sales increased 17.8% from May 2015 to May 2019. 17-18 Copyright ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Special-Purpose Indexes Here is an example of using an index as a measure of general business activity for northwest US The Seattle Chamber of Commerce wants to develop a measure of general business activity. It will be called the General Business Activity Index of the Northwest and will include department store sales (40%), regional employment (30%), freight car loadings (10%), and exports from Seattle harbor (20%). Business activity has increased 57.0% from 2005 to 2010 and 57.1% from 2005 to 2018. 17-19 Copyright ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Consumer Price Index The BLS reports this index monthly. It describes the changes in prices from one period to another for a “market basket” of goods and services. 17-20 Copyright ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Producer Price Index The PPI reflects the prices of over 3,400 commodities and price data is collected from the sellers. The PPI is a Laspeyres type index. 17-21 Copyright ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Dow Jones Industrial Average (DJIA) This is an index of stock prices. It represents the prices of 30 specific stocks of large publicly owned U.S. based companies. 17-22 Copyright ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Consumer Price Index (CPI) Prices are collected on about 80,000 items monthly from retail stores, service establishments, rental units, and doctors offices The CPI is often used to show the rate of inflation in the United States It is reported monthly by the U.S. Bureau of Labor Statistics The current base period is 1982-84 The CPI is used to compute “real” income and purchasing power and to adjust pensions and tax brackets 17-23 Copyright ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Real Income Suppose Ms. Watts earned $20,000 per year in the base period of 1982, 1983, and 1984. She has a current income of $40,000. Note that although her money income has doubled since the base period of 1982-84, the prices she pays for food, gasoline, clothing, and other items has also doubled. Compute her real income. Ms. Watts purchasing power (real income) has remained the same at $20,000. 17-24 Copyright ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Deflating Sales The sales of Hill Enterprises, a small injection molding company in upstate New York, increased from 1982 to 2018. The owner, Harry Hill, realizes that the price of raw materials used in the production process has also increased, so Mr. Hill wants to deflate sales to account for the increase in raw materials. What are the deflated sales for 1990, 2000, 2005, 2010, 2015, and 2018 expressed in constant 1982 dollars? 17-25 Copyright ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 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? Purchasing power of dollar = (100) = (100) = $0.50 The CPI of 200 indicates that prices have doubled from the years 1982-84 to this month. Thus, the purchasing power of the dollar has been cut in half. That is, a 1982-84 dollar is only worth 50 cents this month. 17-26 Copyright ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Chapter 17 Practice Problems 17-27 Copyright ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Question 1 LO17-1 PNC Bank Inc., which has its headquarters in Pittsburgh, reported the following commercial loan totals for years 2010 through 2018. Using 2010 as the base, develop a simple index of commercial loans for the following years 17-28 Copyright ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Question 5 LO17-1,2,3 Following are the prices of toothpaste (9 oz.), shampoo (7 oz.), cough tablets (package of 100), and antiperspirant (2 oz.) for August 2010 and August 2018. Also included are the quantity purchased. Use August 2010 as the base. a. b. c. d. e. Determine the simple price indexes. Determine the simple aggregate price index for the two years. Determine the Laspeyres price index. Determine the Paasche price index. Determine Fisher’s ideal index. 17-29 Copyright ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Question 11 LO17-4 You want to construct a leading indicator for Erie County in upstate New York. The index is to be based on 2000 data. Because of the time and work involved, you decide to use only four time series. As an experiment, you select these four series: unemployment in the county, a composite index of county stock prices, the County Price Index, and retail sales. Here are the figures for 2000 and 2018 The weights you assign are unemployment rate 20%, stock prices 40%, County Price Index 25%, and retail sales 15%. a. Using 2000 as the base period, construct a leading economic indicator for 2018. b. Interpret your leading index. 17-30 Copyright ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Question 15 LO17-5 In 2000, the mean salary of classroom teachers in Tinora School District was $28,650. By 2010, the mean salary increased to $33,972, and further increased in 2018 to $37,382. The American Federation of Classroom Teachers maintains information on the trends throughout the United States in classroom teacher salaries. Its index, which has a base period of 2000, was 122.5 for 2010 and 136.9 for 2018. Compare the Tinora teachers to the national trends. 17-31 Copyright ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.