Copyright © 2009 Pearson Education, Inc. 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.

Slide 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 = x 100 value reference value

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Slide Copyright © 2009 Pearson Education, Inc. 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 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 = × 100 = × 100 = This index number for the current price is 564.4, which means the current gasoline price is 564.4% of the 1975 price. current price 1975 price $3.20 $0.567

Slide Copyright © 2009 Pearson Education, Inc. 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?

Making Comparisons with Index Numbers Slide Copyright © 2009 Pearson Education, Inc. 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 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 = x $7.00 = $28.52

Making Comparisons with Index Numbers Slide Copyright © 2009 Pearson Education, Inc. 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 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 and the index for 1955 was So the cost of gasoline in 1955 compared to the cost in 1995 was Gas that cost $20.00 in 1995 cost x $20.00 = $4.83 in index number for 1955 index number for = =

Slide Copyright © 2009 Pearson Education, Inc. The Consumer Price Index 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.

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Slide Copyright © 2009 Pearson Education, Inc. EXAMPLE 3 CPI Change Suppose you needed $30,000 to maintain a particular standard of living in 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 CPI for 2000 = = That is, typical prices in 2006 were about 1.17 times those in 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.

Slide Copyright © 2009 Pearson Education, Inc. Slide Copyright © 2009 Pearson Education, Inc. 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. Adjusting Prices for Inflation EXAMPLE 4 Baseball Salaries CPI for 2006 CPI for 1987 = = Solution: First, we compare the Consumer Price Indices for 2006 and 1987:

Slide Copyright © 2009 Pearson Education, Inc. Adjusting Prices for Inflation Slide Copyright © 2009 Pearson Education, Inc. Solution: (cont.) Next, we compare the average baseball salaries for those two years: 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. average baseball salary for 2006 average baseball salary for 1987 = = 6.96 $2,867,000 $412,000 EXAMPLE 4 Baseball Salaries

Slide Copyright © 2009 Pearson Education, Inc. 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.

Slide Copyright © 2009 Pearson Education, Inc. The End