2 4 Index Numbers LEARNING GOAL Understand the

2. 4 Index Numbers LEARNING GOAL Understand the concept of an index number; in particular, understand how the Consumer Price Index (CPI) is used to measure inflation. Copyright © 2009 Pearson Education, Inc.

Index Numbers An index number provides a simple way to compare measurements made at different times or in different places. The value at one particular time (or place) must be chosen as the reference value (or base value). The index number for any other time (or place) is index number = value x 100 reference value Copyright © 2009 Pearson Education, Inc. Slide 2. 4 - 2

Copyright © 2009 Pearson Education, Inc. Slide 2. 4 - 3

EXAMPLE 1 Finding an Index Number Suppose the cost of gasoline today is $3. 20 per gallon. Using the 1975 price as the reference value, find the price index number for gasoline today. Solution: Table 2. 1 shows that the price of gas was 56. 7¢, or $0. 567, per gallon in 1975. If we use the 1975 price as the reference value and the price today is $3. 20, the index number for gasoline today is index number = $3. 20 current price × 100 = 564. 4 $0. 567 1975 price This index number for the current price is 564. 4, which means the current gasoline price is 564. 4% of the 1975 price. Copyright © 2009 Pearson Education, Inc. Slide 2. 4 - 4

TIME OUT TO THINK Find the actual price of gasoline today at a nearby gas station. What is the gasoline price index for today’s price, with the 1975 price as the reference value? Copyright © 2009 Pearson Education, Inc. Slide 2. 4 - 5

Making Comparisons with Index Numbers EXAMPLE 2 Using the Gas Price Index Use Table 2. 1 to answer the following questions. a. Suppose that it cost $7. 00 to fill your gas tank in 1975. How much did it cost to buy the same amount of gas in 2005? Solution: a. Table 2. 1 shows that the price index (1975 = 100) for 2005 was 407. 4, which means that the price of gasoline in 2005 was 407. 4% of the 1975 price. So the 1995 price of gas that cost $7. 00 in 1975 was 407. 4% x $7. 00 = 4. 074 x $7. 00 = $28. 52 Copyright © 2009 Pearson Education, Inc. Slide 2. 4 - 6

Making Comparisons with Index Numbers EXAMPLE 2 Using the Gas Price Index Use Table 2. 1 to answer the following questions. b. Suppose that it cost $20. 00 to fill your gas tank in 1995. How much did it cost to buy the same amount of gas in 1955? Solution: b. Table 2. 1 shows that the price index (1975 = 100) for 1995 was 212. 5 and the index for 1955 was 51. 3. So the cost of gasoline in 1955 compared to the cost in 1995 was index number for 1955 5. 13 = = 0. 2414 index number for 1995 212. 5 Gas that cost $20. 00 in 1995 cost 0. 2414 x $20. 00 = $4. 83 in 1955. Slide 2. 4 - 7 Copyright © 2009 Pearson Education, Inc.

The Consumer Price Index (CPI), which is computed and reported monthly, is based on prices in a sample of more than 60, 000 goods, services, and housing costs. Copyright © 2009 Pearson Education, Inc. Slide 2. 4 - 8

Copyright © 2009 Pearson Education, Inc. Slide 2. 4 - 9

EXAMPLE 3 CPI Change Suppose you needed $30, 000 to maintain a particular standard of living in 2000. How much would you have needed in 2006 to maintain the same living standard? Solution: We compare the Consumer Price Indices for 2006 and 2000: CPI for 2006 = 201. 6 = 1. 17 172. 2 CPI for 2000 That is, typical prices in 2006 were about 1. 17 times those in 2000. So if you needed $30, 000 in 2000, you would have needed 1. 17 x $30, 000 = $35, 100 to have the same standard of living in 2006. Copyright © 2009 Pearson Education, Inc. Slide 2. 4 - 10

Adjusting Prices for Inflation EXAMPLE 4 Baseball Salaries In 1987, the mean salary for major league baseball players was $412, 000. In 2006, it was $2, 867, 000. Compare the increase in mean baseball salaries to the overall rate of inflation as measured by the Consumer Price Index. Solution: First, we compare the Consumer Price Indices for 2006 and 1987: CPI for 2006 CPI for 1987 = 201. 6 113. 6 Copyright © 2009 Pearson Education, Inc. = 1. 77 Slide 2. 4 - 11

Adjusting Prices for Inflation EXAMPLE 4 Baseball Salaries Solution: (cont. ) Next, we compare the average baseball salaries for those two years: average baseball salary for 2006 $2, 867, 000 = = 6. 96 average baseball salary for 1987 $412, 000 During the same period of time that average prices (as measured by the CPI) rose about 77%, the mean baseball salary rose by almost 600%. In other words, the salaries of major league baseball players rose about 600/77 ≈ 8 times as much as the overall rate of inflation. Copyright © 2009 Pearson Education, Inc. Slide 2. 4 - 12

Other Index Numbers The Consumer Price Index is only one of many index numbers that you’ll see in news reports. Some are also price indices, such as the Producer Price Index (PPI), which measures the prices that producers (manufacturers) pay for the goods they purchase (rather than the prices that consumers pay). Other indices attempt to measure more qualitative variables. For example, the Consumer Confidence Index is based on a survey designed to measure consumer attitudes so that businesses can gauge whether people are likely to be spending or saving. New indices are created frequently by groups attempting to provide simple comparisons. Copyright © 2009 Pearson Education, Inc. Slide 2. 4 - 13