The gross domestic product (GDP) is the total national output of goods and services valued at market prices. As such, the GDP is a commonly used barometer of the U.S. economy. One component of the GDP is personal consumption expenditures, which is itself the sum of expenditures for durable goods, nondurable goods, and services. The GDP for these components (in billions of dollars) is shown in the next table, in 5-year increments from 1970 to 2015.

a. Using these three component values, construct a simple composite index for the personal consumption component of GDP. Use 1970 as the base year.

b. Suppose we want to update the index by using 1980 as the base year. Update the index using only the index values you calculated in part a, without referring to the original data.

c. Graph the personal consumption expenditure index for the years 1960-2015, first using 1970 as the base year and then using 1980 as the base year. What effect does changing the base year have on the graph of this index?

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Year Durables Nondurables Services 1970 1975 1980 1985 90 134 226 353 497 636 916 1,106 1,089 1,329 229 416 573 919 330 475 956 1,395 2,344 3,172 4,371 5,745 6,923 8,293 1990 1995 2000 2005 2010 2015 994 1,180 1,543 1,968 2,336 2,654