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Yard Sale – Part 1

January 18, 2011 by Blue Ridge Leader filed under Columns, Sustainable Planet No Comments

“We make models in science but we also make them in everyday life. Model-dependent realism applies not only to scientific models but also to the conscious and subconscious mental models we all create in order to interpret and understand the everyday world.” Stephen Hawking and Leonard Mlodinow, The Grand Design, 2010 [1].

by Tony Noerpel

In my last article [2], I discussed the difference between thinking dogmatically and thinking critically. In either case we construct models to help us understand reality. Using Paul O’Neill’s terminology, recall that an ideologue’s model is arbitrary and rigidly maintained without regard to facts. A philosopher’s model is based on facts and is continuously adjusted to accommodate new information. One might say that a philosopher (or physicist) is willing to accept the possibility that she might be wrong. The physicists Stephen Hawking and Leonard Mlodinow write in The Grand Design [1] that a good model:

  1. Is elegant
  2. Contains few arbitrary or adjustable elements
  3. Agrees with and explains all existing observations
  4. Makes detailed predictions about future observations that can disprove or falsify the model if they are not borne out.


We can ignore the first two points for now as these are subjective. The third point requires hard work, anathema to ideologues according to O’Neill, and the fourth point requires courage, as the models must be tested with the possibility that they may be incorrect or inadequate. Though economics is a soft science, a good economic model should have these properties also. A good economic model should explain observation and would have anticipated the recent housing bubble, the recession, the run up in gold and oil prices and the credit crises. The economist Gregory Mankiw in his popular text book, Principles of Economics [3] writes:

“In his 1776 book An Inquiry into the Nature and Causes of the Wealth of Nations, economist Adam Smith made the most famous observation in all of economics: Households and firms interacting in markets act as if they are guided by an ‘invisible hand’ that leads them to desirable market outcomes. One of our goals in this book is to understand how this invisible hand works its magic.”

An astute observer might note that James Watts invented the steam engine in the same year, 1776, which allowed the British to exploit the low entropy of their coal and that British coal production peaked in the early 1900’s coincident with the decline of their empire. In other words, a robust economy may have more to do with thermodynamics than magic.

Mankiw’s free market, small government model works reasonably well, though not perfectly, when the resources it ignores are not limited and when pollution does not overwhelm the economic system, but eventually it fails utterly. Given that the U. S. Energy Information Administration (EIA) and the International Energy Agency (IEA) have both acknowledged that peak production of conventional crude oil has already occurred in 2005 and 2006 respectively, our economy is clearly resource constrained. Given the size of ocean dead zones, mountaintop removal mining, soil deterioration and global warming, our economy is further constrained by our pollution. Since our current and on-going economic crisis is thermodynamic in nature, a model which ignores entropy is not likely to do well. Recall that the physicist Arthur Eddington wrote that if your model contradicts the second law of thermodynamics there is no hope for it. We need better economic models. In this series of articles I propose three.

Vilfredo Pareto, an Italian engineer/economist who died in 1923, collected vast amounts of data on wealth and income distribution from many different countries and from several time periods, which included a variety of economic and government types. He found that wealth was always distributed inequitably, following a power law distribution sometimes called the 80-20 rule or the Pareto principle, i.e., 80 percent of the people owned 20 percent of the wealth and 20 percent of the people owned 80 percent of the wealth [4]. One might observe that the invisible hand inevitably makes the rich richer and the poor poorer.

Pareto developed the “yard sale” economic model, which was nicely described in an article in American Scientist by the mathematician Brian Hayes [5]. This is the first of our three simple models. This model holds wealth constant and the initial distribution of wealth is uniform across the population. If the participants engage in transactions which are of exactly fair value (market efficiency holds) then the economy is stable and robust and continues forever with the same equitable distribution of wealth. However, if we assume instead that transactions are of unequal value even if only by a very small amount relative to the total value of the transactions, eventually one person accrues all of the wealth and the economy dies. To justify the latter assumption note that everybody who purchased a home after 2003 paid too much. Cleary the market is not efficient and there is no invisible hand guiding the economy. And this result is independent of skill, hard work, avarice, or intelligence as well as the details of the way the economy operates. An unregulated free market leads to inequality at least until it becomes so unstable that the economy breaks.

Pareto observed that the wealthy accumulated power as well. This destroys democracy and feeds corruption further aggregating both wealth and power in a positive feedback loop.

According to Mankiw a free market economy will encourage entrepreneurial ambitions and economic growth. This can appear to work if at the same time society is discovering and exploiting new sources of energy. With the discovery of fossil fuels wealth was created faster than the wealthy could co-opt it from the majority. Thus prospects for the majority improved and a large middle class was created in many societies including the United States. This in itself was a positive feedback which encouraged yet more growth. In the end though, the momentum of the unregulated free market is to aggregate wealth in a highly skewed power law distribution. As resources are depleted, wealth aggregation overwhelms wealth creation. The middle class becomes poor and the poor fall out of the economy altogether. This is happening in the United States today. Mankiw’s model does not predict this. In fact Mankiw reprints a gushing article by the articulate and insouciant free-market cheerleader David Brooks from November 27, 2004, just before the economic collapse, titled “Good News about Poverty” [6], describing how remarkably well the world economy was doing.

Pareto’s yard sale model while elegantly simple has obvious deficiencies. It ignores avarice and greed, intelligence and hard work, ambition, and other personality characteristics which might favor some individual’s fate over others. But we can show that these differences exacerbate inherent inequitable wealth accumulation. The yard sale model also starts from an equitable initial condition. In reality some of us are born into poverty and others into wealth. How we start out in life is a substantial disadvantage or advantage. Mankiw writes: “A person’s earnings depend on the supply and demand for that person’s labor, which in turn depend on natural ability, human capital, compensating differentials, discrimination, and so on.” While all that is true, Mankiw ignores initial conditions and pure luck or happenstance in the eventual distribution of income. We can appreciate how these differences might exacerbate inequitable distribution by considering a second model, the Gambler’s Ruin problem from probability theory [7]. We will do this in part two.

Finally, neither Pareto nor Mankiw consider thermodynamic limits. When we discover how to exploit new sources of low entropy, more surplus wealth is created. On the other hand, all wealth is far from thermodynamic equilibrium so that cars rust and bananas rot. Our clothes become threadbare and our infrastructure deteriorates. Wealth is continually destroyed and needs replacing. Pollution and misallocation of resources extract wealth from the economy. The eventual cost of addressing global warming will far exceed, by several orders of magnitude, the relatively meager immediate gains (capital formation) made by the wealthy as a consequence of ignoring the problem. The nuclear arms race had cost the United States over five trillion dollars by 1998 [9]. All of our federal debt can be attributed to misallocating the nation’s capital and low entropy towards military spending and as a consequence our country is being bankrupted by the same forces that bankrupted the Soviet Union. All of these factors, including the incipient housing market collapse were evident by the time Brooks wrote his ill-considered column.

Consider that Mankiw published the fourth edition in 2007, after the housing bubble burst and well into the credit crises and several years after peak oil, yet his book does not contain any information about bubbles, resources, crashes or derivatives. One would think that it would not be so difficult to make predictions after they’ve already happened.

Thermodynamic impacts can be appreciated by considering our third model, Herman Daly’s ecosystem model of the economy. We will address this aspect in part three.

These three models (perhaps not elegant but simple) together can suggest in broad terms what we need to do in the United States in order to preserve our economy and society and ensure its sustainability. They are too crude to supply the detail. However, given the direction in which we are headed, and which most of us inherently understand is not good, comprehending those broad terms would be an enormous benefit.

The conclusion of Pareto’s yard sale model is that happenstance alone naturally exacerbates inequality. As we will see human frailty, such as greed, inevitably makes this condition worse.

[1] Hawking and Mlodinow, The Grand Design, Bantam Books, 2010.

[2] http://brleader.com/?p=2550

[3] Mankiw, Principles of Economics, Fourth Edition, South-Western Cengage Learning, 2007.

[4] http://en.wikipedia.org/wiki/Vilfredo_Pareto

[5] Brian Hayes, Follow the Money, American Scientist, Volume 90, Number 5
Page: 400, DOI: 10.1511/2002.5.400September-October, 2002 http://www.americanscientist.org/issues/pub/follow-the-money/2

[6] David Brooks, Good News about Poverty, The New York Times, November 27, 2004, reprinted page 435 in Mankiw, 2007.

[7] Ghahramani, Fundamentals of Probability, second edition, Prentice-Hall, 2000.

[8] Herman Daly, Beyond Growth, Beacon Press, 1996.

[9] Stephen I. Schwartz, Atomic Audit The Costs and Consequences of U.S. Nuclear Weapons Since 1940, Brookings Institution Press 1998.

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