Inequality, Power Laws, and Sustainability: Part I

This is the first of a series of posts that will address the issue of economic inequality, a pressing issue in the upcoming national elections in November of this year.

If you navigate to the Wikipedia link on economic inequality, you'll find a list of hypothetical causes, including declining wages, education, technology, globalization, tax structures, racism, and gender, among others. I will argue that none of these factors are determinant, nor are they, in toto, sufficient to explain the divergence of wealth and income in the world.

The Wiki entry goes on to offer some mitigating factors that reduce inequality. These include public education, progressive taxation, minimum wages, nationalization and subsidization. Each of these attempts to use political power to redistribute wealth and income. I will argue while these various proposals can indeed mitigate inequality on the surface, none are sufficient or necessary, either alone or in toto, to compensate for the dynamic forces in the market economy driving the inequality wedge. Furthermore, each of these policy proposals impose costs and trade-offs to consider.

There has been much loose talk about the 1% vs. the 99% in political discourse. This narrative gets at the nature of inequality that assumes the qualities of a power law. As defined in WikiP:

A power law is a mathematical relationship between two quantities. When the frequency of an event varies as a power of some attribute of that event (e.g. its size), the frequency is said to follow a power law. For instance, the number of cities having a certain population size is found to vary as a power of the size of the population and hence follows a power law. There is evidence that the distributions of a wide variety of physical, biological, and man-made phenomena follow a power law, including the sizes of earthquakes, craters on the moon and of solar flares,[1] the foraging pattern of various species,[2] the sizes of activity patterns of neuronal populations,[3] the frequencies of words in most languages, frequencies of family names, the species richness in clades of organisms,[4] the sizes of power outages and wars,[5] and many other quantities.

The mathematical relationship follows an inverse proportional relationship between two variables, something like y = 1/x. Graphically, they represent a distribution and look like this: (the y-axis would be the level of wealth or income accumulation and the x-axis is the increasing share of the population)

Power Law

Because power laws have been found to describe many different phenomena, they are often referred to by different names, such as the Pareto principle, the 80-20 rule, Zipf 's Law, or even Winner-take-all. (You can peruse these in Wikipedia).

The Pareto principle, or 80-20 rule, is probably the easiest to grasp in concrete terms. Italian economist Vilfredo Pareto observed in 1906 that 80% of the land in Italy was owned by 20% of the population; he developed the principle by observing that 20% of the pea pods in his garden contained 80% of the peas. The 80-20 rule has also been confirmed to describe the fact that 80% of the wealth in the world is owned by 20% of the population. Of course, this distribution varies widely across countries, but it is politically salient that the ratio has grown even worse in developed countries over the past generation.

Here is some data on the US cited from a study conducted by Prof. William Domhoff: (I am not endorsing this study or its analysis - only citing the data.)

Table 1: Distribution of net worth and financial wealth in the United States, 1983-2007

Total Net Worth

Top 1 percent Next 19 percent Bottom 80 percent
1983 33.8% 47.5% 18.7%
1989 37.4% 46.2% 16.5%
1992 37.2% 46.6% 16.2%
1995 38.5% 45.4% 16.1%
1998 38.1% 45.3% 16.6%
2001 33.4% 51.0% 15.6%
2004 34.3% 50.3% 15.3%
2007 34.6% 50.5% 15.0%

Financial Wealth

Top 1 percent Next 19 percent Bottom 80 percent
1983 42.9% 48.4% 8.7%
1989 46.9% 46.5% 6.6%
1992 45.6% 46.7% 7.7%
1995 47.2% 45.9% 7.0%
1998 47.3% 43.6% 9.1%
2001 39.7% 51.5% 8.7%
2004 42.2% 50.3% 7.5%
2007 42.7% 50.3% 7.0%

We can easily observe from this data that over the 25-year period, 20% of the population controlled between 80-85% of the net worth in the US and over 90% of net financial wealth. The question is: How do we explain this and what does it mean? (Domhoff attributes this to power, but the political power of exploitation, rather than the power of numbers in nature.)

In the next few posts I will try to demonstrate that power laws are rooted in natural dynamic processes and counteracting those processes requires that we understand the process, rather than just the results. In the case of economic inequality, I will also argue that such power laws are unsustainable and have been so throughout the history of market exchange and wealth accumulation.

In Part II I will address the dynamics of power laws and wealth distributions with some simple observations, intuitive logic, and tests.