*Note to the reader:
please credit the author when using the following equations, graphs, and tables
since this is original material. *

**A NEW DEFINITION OF CAPITALISM**:
Capitalism is a monetary system which distributes wealth by a **definable distribution** raised to a power
of a base as determined by rank, where the percentage of those with average
wealth and above approximately equals the percentage of those with no wealth
and debt. Given constant average wealth and median wealth, both values become
trivial compared to the wealth of the very richest as the number of entities in
the economy increases. **Capitalism
creates huge levels of wealth inequality by intrinsic exponentiation as determined
by rank.**

If poverty is considered lack of wealth, then poverty must
be intrinsic to capitalism based on empirical evidence from the Survey of
Consumer Finances from 1983 to 2007 as compiled and adjusted by Edward N. Wolff
in *Recent Trends in Household Wealth in
the United States: Rising Debt and the Middle-Class Squeeze---an Update to 2007. *

Above is a graph of a hypothetical wealth distribution of an economy of one million households with an average wealth of $369,385 and median wealth of $76,093 using the First General Wealth Equation. The numbers directly above the gray indicators are the actual averaged numbers from the Wolff data from 1983 to 2007. The gray indicators show the computer calculated percentages.

Since the wealth distribution was apparently so skewed, I worked with the natural log of wealth while trying known distributions to describe the data. There were relatively few data points so it was quite a task to either find or create a distribution to fit the data. Eventually I realized the best fit (among commonly used distributions) would be back to back tails of normal distributions as shown in the Natural log of Wealth graph as pictured below:

*Entire distribution
above is raised as a power to base e to yield the Predicted Wealth
Distribution *

In order to create a general wealth equation, I believed the
equation needed to be scalable in both the wealth and population axes. I found
the trick to doing this is taking the famous "Bell Curve" Normal Distribution
Probability Distribution Function and modifying it where frequency (people) and
probability (wealth) switch axes, where only positive values of wealth are
allowed, and where the mean and standard deviation become zero and one
respectively to create my ** First** **General
Wealth Equation:**

*Wi* is an individual's wealth, *Ri* is the individual's rank either above or below the top 20% in equal decrements in descending order, and *A* and *M* are an offset and multiplier respectively.

To evaluate from the top 20% to the wealthiest, use the equation in this form:

To evaluate from the top 20% to the bottom 17.6375%, use the equation in this form:

Where *Wa* is average wealth,* N* is the total number of households in the
population, and *n* are integers starting at one and counting away
from the top 20%. Households below the bottom 17.6375% have zero wealth.

So using the First General Wealth Equation, one can predict
the wealth distribution knowing only average wealth and population size. So in
the hypothetical economy of one million households, the evaluation begins above
and below the 200,000^{th} richest household in the ranking. Average
wealth happens at the 166328^{th} richest household, and zero wealth
begins at the 176375^{th} poorest household, making those with average
wealth and above at 16.3% approximately equal to those with zero wealth at
17.6% (1.3% difference) considering the entire range of values.

Examining the First General Wealth Equation term,

one can see that as rank decreases (*R * starts at.398942 and always goes lower for
each iteration until the end of the tail is reached), the term increases in
value. Depending on the sign of the multiplier *M*, small linear changes in rank
cause large differences in wealth either increasingly or decreasingly since * e* is being raised to a power which includes
rank.

It is worth noting that the multipliers were evaluated using one million members in the economy. If evaluating with a higher number of members, slight adjustment of the multipliers will be necessary.

Almost
by accident I noticed that if one takes the log of both the wealth and
population axes, and then reverses the axes, a curve much resembling a first
order band pass filter (used in electronics)can be seen over the top 80% of the
distribution. Here is the **Second General
Wealth Equation**:

The symbol * Pw* represents the number of households owning
wealth and * Pi * is an individual household starting with the
wealthiest at 1 and going to 80% of the population. The bottom 20% when using
this equation has no wealth. Taking the log of a predicted Wealth distribution
using this equation gives a very similar S shape curve and very similar
percentages as compared to the curve of the First General Wealth Equation. The
Second General Wealth Equation is also scalable for average wealth and
population:

Second General Wealth Equation Predicted Percentages

(Image by Mark B. Whittington) Permission Details DMCA

*Comparison of First and Second General Wealth
Equations. Similar curves produce similar results from independently derived
equations. *

The Second General Wealth Equation places those with average
wealth and above at 18.2% and those with no wealth at 20.0% (1.8% difference)
again confirming the approximate equality of the two. Here an exponentiation term with a ratio including
rank causes large differences in wealth, although * e* is not being raised to a power as in the First
General Wealth Equation.

If the population is increased above one million, then the exponent (.707) will need to be decreased slightly.

Below are two graphs of Predicted Wealth Distributions using the First General Wealth Equation evaluated with 10,000 entities in the first graph, and then with one million entities in the second graph. Both have approximately equal average and median wealth, but average wealth becomes trivial as the number of entities increases. In a real economy of over one hundred million entities, average wealth is not discernable when graphed with the richest entities.

The First and Second General Wealth Equations will need a slope adjustment if one is concerned with the very top of the distribution. The very top of the distribution is the least predictable in the real world because in either personal wealth or market capitalization the very top tend to break into clusters (shell structure). For some as yet unknown reason the top 26 entities are too high in wealth vs. the empirical data, so adjust the slopes as follows:

Finally, below is a table from Edward N. Wolff's
*Recent Trends in Household Wealth
in the United States: Rising Debt and the Middle-Class Squeeze---an Update to
2007* from which most of the data used in this report was collected.
Looking at part A, one can see that under the *Percentage Share of Wealth or Income Held by:* heading, the
percentages have remained fairly constant concerning net worth since reliable
data began being collected in 1983. The Bottom 40.0% column shows that near
zero wealth has remained constant for decades, implying that something
intrinsic to capitalism itself causes systemic, predictable poverty.

The Size Distribution of Wealth and Income, 1983-2007

(Image by Edward N.Wolff/ Working Paper No. 589) Permission Details DMCA

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