Example 15

EXAMPLE 15 The Price of Our House and the Value of a Dollar

Where my family and I live, housing is relatively inexpensive. We bought our house in mid-1992 for $133,000 (close to the median price of U.S. housing then). What would be the equivalent cost in mid-2015 dollars?

We see from Table 21.5 that the CPI for 1992 is 140.3 and the CPI for 2015 is estimated to be 242.3. The table gives the average value for each year, which is very close to the value at mid-year. Month-by-month values are available at the Bureau of Labor Statistics Web site (data.bls.gov/pdq/).

Using the proportion, we have

$\frac{cost in 2015}{cost in 1992} = \frac{CPI for 2015}{CPI for 1992}$

$\frac{cost in 2015}{$ 133, 000} = \frac{241.4}{140.3}$

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so that

$cost in 2015 = $ 133, 000 \times \frac{241.4}{140.3} \approx $ 229, 000$

That’s what our house would sell for if its price exactly matched inflation. The ratio $241.4 / 140.3 \approx 1.721$ is the scaling factor for converting 1992 dollars to 2015 dollars. What we are observing is a proportion, or numerical similarity, between 1992 dollars and 2015 dollars, analogous to the geometric similarity discussed in Chapter 18 (page 738). To convert from 2015 dollars to 1992 dollars, we would multiply by $1 / 1.721 \approx 0.581$ .

Table 21.6: **TABLE 21.5** U.S. Consumer Price Index ( $1982 - 1984 = 100$ )
—	—	1931	15.2	1951	26.0	1971	40.5	1991	136.2
—	—	1932	13.7	1952	26.6	1972	41.8	1992	140.3
1913	9.9	1933	13.0	1953	26.7	1973	44.4	1993	144.5
1914	10	1934	13.4	1954	26.9	1974	49.3	1994	148.2
1915	10.1	1935	13.7	1955	26.8	1975	53.8	1995	152.4
1916	10.9	1936	13.9	1956	27.2	1976	56.9	1996	156.9
1917	12.8	1937	14.4	1957	28.1	1977	60.6	1997	160.5
1918	15.1	1938	14.1	1958	28.9	1978	65.2	1998	163.0
1919	17.3	1939	13.9	1959	29.1	1979	72.6	1999	166.6
1920	20.0	1940	14	1960	29.6	1980	82.4	2000	172.2
1921	17.9	1941	14.7	1961	29.9	1981	90.9	2001	177.1
1922	16.8	1942	16.3	1962	30.2	1982	96.5	2002	179.9
1923	17.1	1943	17.3	1963	30.6	1983	99.6	2003	184.0
1924	17.1	1944	17.6	1964	31.0	1984	103.9	2004	188.9
1925	17.5	1945	18.0	1965	31.5	1985	107.6	2005	195.3
1926	17.7	1946	19.5	1966	32.4	1986	109.6	2006	201.6
1927	17.4	1947	22.3	1967	33.4	1987	113.6	2007	207.3
1928	17.1	1948	24.1	1968	34.8	1988	118.3	2008	215.3
1929	17.1	1949	23.8	1969	36.7	1989	124.0	2009	214.5
1930	16.7	1950	24.1	1970	38.8	1990	130.7	2010	218.1
								2011	224.9
								2012	229.6
								2013	233.0
								2014	236.7
								2015 (est.)	241.4

Table 21.6:

Note: This is the CPI-U index, which covers all urban consumers, about 80% of the U.S. population. Each index is an average for all cities for the year. The basis for the index is the period 1982-1984, for which the index was set equal to 100. For each year, the figure is the average during the year, which is usually close to the value at mid-year.

Source: data.bls.gov/cgi-bin/surveymost?cu