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

or

892

so that

That’s what our house would sell for if its price exactly matched inflation. The ratio 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 .

Table 21.6: TABLE 21.5 U.S. Consumer Price Index ()
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