New Math Lessons Learned Floyd A. Wyczalek FW Lilly, Inc.

While the prices of homes and automobiles, two vital expenditures required to live normal lifestyles, appear to have increased dramatically over the past 50 years, their price has not really changed.

This unofficial proposition has been my personal impression, based on the observation that, regardless of sales and/or sticker prices, the ratio of the current dollar value of my midrange home divided by my midrange new car purchase price, appeared to remain almost constant, at about ten to one over the past 50-years.

Consequently, for many years, I have applied this “shelter / transportation ratio” to calibrate my progress during my career, and to deflate my ego in the face of, what appeared to be, exceptionally gratifying improvements in personal income.

To place this observation on a more factual basis, I undertook an evaluation of the Purchasing Power of the Dollar Index (pp$), and Consumer Price Indexes (cpi) published in the “116th Edition of the StatisticalAbstract of the United States - 1996”The results are summarized in the following figures and paragraphs.

cpi-u expressed as dollars and normalized to pp$=$l.O in the base years 1982-84. Therefore, we can simplify our comparisons by referring to the cpi, exclusively.

cpi indexes over the interval 1953, the earliest cpi data available, through 1995, normalized to cpi=l.O for a base year=1953. We conclude that these two correlate surprisingly well up to the year 1981. Thereafter, the shelter cpi becomes suspiciously linear and exhibits a constant slope, suggestive of shelter cpi tinkering, and, the transportation cpi exhibits two distinct linear constant slope intervals, suggestive of tinkering and two downgrading adjustments of transportation’s role in the cost of living.

Figure 2 shows a plot of the ratio of the shelter cpi divided by the transportation cpi, with the shelter cpi arbitrarily normalized to equal 10 in the 1953 base year, while the transportation cpi is held equal to 1.0 in the 1953 base year. This plot clearly emphasizes three distinct step functions: the first showing a ratio of about 10 to 1; the second a ratio of about 12 to 1; and the third showing a ratio a little over 14 to 1.

productivity improvements also need to be examined when making cpi comparisons, over this 50-year time interval. Therefore, Figure 3 shows a comparison of cpi vs. ppi (producer price index) for finished consumer goods, excluding food. The base year begins in 1960 where ppi was normalized to equal 1.0, since this is the earliest ppi data available.

consumers goods track one another closely until about 1982, suggesting small improvements in productivity prior to 1982. However, after 1982 the ppi finished consumers goods decreases to lower ppi values, clearly indicating more significant gains in

One conclusion was that the pp$ is the reciprocal of the overall

For example, Figure 1 compares the shelter and transportation

To place the previous comparison into proper perspective,

In this case, it is evident that the cpi and ppi finished

Author’s Current Address: FW Lilly, Inc., 155 S . Williamsbury Road, Bloomfield Hills, MI 48301.

Manuscript received January 10, 1997.

0885-8985/97/ $10.00 Q 1997 IEEE

Fig.

” 1960 1980 2000

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2. Ratio Shelter/Transport I .4 z

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Fig. 3. Overall CPI & Producer PPI Fig. 4. Ratio CPI /PPI

CPI

productivity after 1982 and continuing improvements to 1995, the latest ppi data available. Finally, Figure 4 shows a plot of the ratio of cpi divided by ppi, which confirms the productivity gains in the early 1960-1973 period, suggests a decline in productivity in the 1974-1980 interval, and a return to productivity improvements thereafter until 1995, the latest ppi data available.

Comparisons of consumer price indexes and producer price indexes resulted in the following conclusions:

1) The shelter cpi and transportation cpi ratio remains relatively constant for significant intervals of time, and this ratio is currently about 14 to 1. The ratio has increased from a historic value of 10 to 1 as a result of downward adjustments in the transportation cpi, which has been judged to be a relatively less significant factor in estimating the cost of living.

2) The fact that the shelter and transportation of indexes show linear behavior after 1980, in comparison to a historic cubic curve trend, suggests a belief that the pre-1980 formulation of cpi was not representative of the cpi behavior of these sectors of the US economy, and consequently, we are in a period of managed adjustments in the formulation of the cpi model.

indicates that productivity improvements have, and are, continuing to be realized.

4) In order to place the inflated dollar into perspective on a long term basis, and calibrate our inflated ego perceptions, it is useful to utilize the ratio of shelter cpi to transportation cpi, to adjust our understanding.

3) The comparison of overall cpi and ppi producer price indexes

IEEE AES Systems Magazine, April 1997 41