The following thought occurred from teaching a college based quantitative reasoning class. An example of exponential growth rates provided in the textbook was a bacterium colony which doubles in size every minute for an hour. What happens when the jar gets nearly full? With 5 minutes left the jar is still only 1/32 full. One smart bacterium calculated that in 5 minutes the jar would be full and tried to alert his fellow bacteria but they would not listen since the entire jar was still almost empty. The graph of said growth rate is almost a straight horizontal line until the last 5-8 minutes of growth. The bacteria did not listen of course and went on doubling until it was too late. The bottle filled up and the gig was up. This is analogous to the state of people’s understanding of the economic conditions today; the debt will grow without bound and the gig will be up!
Analogous to the Current Economic Conditions:
So what is the point? What if the US debt curve looked much like the bacterial growth curve. Plotting the US debt every year since 1835, the year Andrew Jackson paid off the debt, an interesting pattern occurs. Please see the plot in figure 1. It looks like the bacterium growth rate curve. A model of doubling of the debt curve did not work and was far too aggressive. However, after 1971 a quite interesting pattern appears. Why only after 1971? This was the year that the US went off the gold standard internationally ands there was no more controls on US debt growth. The US went off the gold standard nationally in 1933 when Americans were asked to turn in all their gold coins.
Using the compounding growth rate formula:
y2010 = y1972*(1 + r)x
where y2010 is the US debt in 2010
y1972 is the US debt in 1972
x is the number of years from 1972 – 2010 namely 38
r is the growth rate.
Solving for “r” yields 0.095 or 9.5% as the compound growth rate. Thus, the debt is growing at a compound 9.5% rate per annum over these 38 years. How surprising is this? Everyone knows the debt is growing. So what is the point?
Yet rumors are surfacing that even more stimulus is needed to pull the economy out of recession and set it off on a recovery. In fact the CBPP in June 2010 projected the US budget deficit through 20191. Including these figures in the above analysis indicates that the budget deficit growth from 1972 to 2019 estimate is 8.83% compounded annually. This assessment used 9%. Please see figure 2.
Summary: So the US debt looks like the bacterium colony only growing at a 9% annual rate per year. It is easy to see that debt growth faster than GDP growth is unsustainable! But does the Congress in Washington want to address this problem? The picture in the graph is the take home message, unless something is done, the people of the US will be adversely affected and sooner rather than later.
1) Ruffing, Kathy A. and Horney, James R. “Critics Still Wrong on What’s Driving deficits in Coming Years” Center on Budget and Policy Priorities – Special Series: Economic Recovery Watch. Updated June 28th, 2010
About the Author: William J. Michie, Jr. has a BS and MS degree in Chemical Engineering from Drexel University and an MBA degree from Rutgers University. He has had a 32.5 year career in Polyethylene Product Development with Union Carbide and Dow Chemical Corp. and is the holder of a number of patents. H. Marsman and D. Madio also contributed to this article.