Why do the richer grow richer and the poorer stay poorer?

The November 2019 issue of Scientific American magazine included an article titled, “The Inescapable Casino,” by Bruce M. Boghosian a professor of mathematics at Tufts University, with research interests in applied dynamical systems and applied probability theory.

The article purportedly reveals:

“A novel approach developed by physicists and mathematicians describing the distribution of wealth in modern economics with unprecedented accuracy.”

Economics is based mostly on psychology, which itself is a science only in the loosest application of the term. Thus, unlike most sciences, economics rarely is capable of creating reproducible tests that result in mathematical laws.

But, SA being a science magazine, Professor Boghosian’s article attempts to attach scientific credibility to economics by creating a casino-based mathematical explanation of why the rich get richer and the poor stay poorer.

His own summary of his findings is:

“1. Wealth inequality is escalating in many countries at an alarming rate, with the U.S. arguably having the highest inequality in the developed world.

“2. A remarkably simple model of wealth distribution developed by physicists and mathematicians can reproduce inequality in a range of countries with unprecedented accuracy.

“3. Surprisingly, several mathematical models of free-market economies display features of complex macroscopic physical systems such as ferromagnets, including phase transitions, symmetry breaking and duality.”

Here are a few more snippets from Professor Boghosian’s article:

Suppose you are invited to play a game. You must place some ante—say, $100—on a table, and a fair coin will be flipped. If the coin comes up heads, the casino will pay you 20 percent of what you have on the table, resulting in $120 on the table.

If the coin comes up tails, the house will take 17 percent of what you have on the table, resulting in $83 left on the table. You can keep your money on the table for as many flips of the coin as you would like.

Each time you play, you will win 20 percent of what is on the table if the coin comes up heads, and you will lose 17 percent of it if the coin comes up tails. Should you agree to play this game?

After five wins and five losses in any order, the amount of money remaining on the table will be:

1.2 x 1.2 x 1.2 x 1.2 x 1.2 x 0.83 x 0.83 x 0.83 x 0.83 x 0.83 x $100 = $98.02

so you will have lost about $2 of my original $100 ante.

The rest of the article describes the mathematics of why supposedly even exchanges between richer persons and poorer persons ultimately favor the richer persons. And mathematical examples are given of water boiling, the strength of a ferromagnet and phase transitions.

Aha. But, it’s mathematics, so it must be true — except not only does it have nothing to do with casino play, it has nothing to do with real-world economics.

First, the examples do not describe “wealth.” They seemingly describe net income, a different concept.

But far more important, although the examples are supposed to demonstrate why the richer grow richer and the poorer stay poor (or poorer), they do not.

The problem has long been known in the computer world as “GIGO,” Garbage In, Garbage Out. What is the basis for Boghosian’s 20% and 17% starting figures? There is none.  The professor arbitrarily chose numbers that “worked,” which “amazingly” multiplied to prove his point, whatever that may be.

Had he arbitrarily chosen even slightly different numbers, the results would have been vastly different. Try it yourself with ever-so-slightly different numbers.

Further, the whole concept of paying or receiving a percentage of what’s “on the table” has nothing to do with the way a casino operates, and even less to do with the way your personal finances operate.

You do not make or lose a percentage of what’s on the table. You make or lose a percentage of what you invest.

Finally, Boghosian proves his point by making predictions of the past. It’s a problem all we economists face. Unable to predict the future with any reasonable degree of accuracy, we predict the past.

We take any set of inputs and compare them to all past results, and if we can find some inputs that correspond with results, we claim to have discovered cause and effect.

It’s, for instance, the classic problem of chartists — the people who use graphs of past stock market movements to predict future stock market movements. The graphs provide perfect representations of the past — until they don’t, because the past does not perfectly create the future in psychology.

Not being an economist, Boghosian hasn’t encountered this flaw, so he is excited to have discovered this strange mathematical relationship among boiling water, ferromagnets, phase transitions, and wealth transfers.

(He also has no understanding of Monetary Sovereignty, so he speaks of taxes funding government activities, which is true only of monetarily non-sovereign governments. But that is a mere detail.)

That said, Boghosian is correct about money tending to flow upward from poorer to richer, and he is correct that it involves percentages, but not in the way he claims.

Here, in simple terms, are the three reasons why the richer grow richer and the poorer stay poorer.

1. Richer people have higher incomes.
2. Richer people spend a lower percentage of their higher incomes.
3. Richer people save and invest a higher percentage of their higher incomes.

Put those three bits of mathematics together and you can see the rather obvious solution to the title question.

Consider three classic nuclear families of two parents and two children.

In nuclear family “A” the parents together earn $30,000 a year. To pay for food, housing, clothing, taxes, entertainment, school, etc. the nuclear family just scrapes by, spending $30,000 a year, and saving/investing $0. After 10 years, they have saved $0, and their children will receive nothing when the parents die.

In nuclear family “B” the parents together earn $50,000 a year. To pay for food, housing, clothing, taxes, entertainment, school, etc. the nuclear family spends $45,000 a year, and saves/invests $5,000, about 10% of their income. After 10 years, they have saved about $50,000, more or less, depending on how well they invested, and their children may, or may not, receive a minimal amount when the parents die.

In nuclear family “C” the parents together earn $1,000,000 a year. To pay for food, housing, clothing, taxes, entertainment, school, etc. this nuclear family spends $500,000 a year, and saves/invests $500,000, about 50% of their income. After ten years they have saved about $5 million, depending on how well they invested, and their children will receive millions when the parents die.

And there it is, in simplistic terms, the reason why the richer grow richer and the poorer stay poorer, and the Gap between them widens.

Choose any set of numbers you wish, and you will find that the richer are able to save and invest not just more of their incomes, but a higher percentage of their incomes, and they are able to pass down to their children substantially more.

The pseudo-mathematical formula is:

More x More = Increasingly more.

So mathematically, the Gap between the richer and the poorer not only must grow, but it must grow at an increasing rate.

But there’s even more.

The Gap is what make the rich rich and the poor poor. Without the Gap no one would be rich or poor. We all would be the same. So to feed their desire to become richer, the rich must widen the Gap, which can be accomplished by increasing their own wealth or by decreasing the wealth of the poorer.

This desire to widen the Gap is known as “Gap Psychology.”

The rich run the politics of America. To become richer, they pay politicians to provide favorable tax laws for the rich, and to resist giving benefits to the poor. They also pay the media and university economists to disseminate false statements about Social Security, Medicare, and other social benefits becoming “unsustainable” and  “insolvent.”

In summary, the Gap between the rich and the rest naturally widens, not because of a mathematical formula involving inter-class transactions, but rather because the rich are able to retain, invest, and pass to their children a higher percentage of their higher incomes.

And that is why a nation’s overall prosperity depends on such efforts as are described in the Ten Steps to Prosperity (below).

Rodger Malcolm Mitchell
Monetary Sovereignty
Twitter: @rodgermitchell
Search #monetarysovereignty Facebook: Rodger Malcolm Mitchell

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The most important problems in economics involve:

1. Monetary Sovereignty describes money creation and destruction.
2. Gap Psychology describes the common desire to distance oneself from those “below” in any socio-economic ranking, and to come nearer those “above.” The socio-economic distance is referred to as “The Gap.”

Wide Gaps negatively affect poverty, health and longevity, education, housing, law and crime, war, leadership, ownership, bigotry, supply and demand, taxation, GDP, international relations, scientific advancement, the environment, human motivation and well-being, and virtually every other issue in economics.

Implementation of Monetary Sovereignty and The Ten Steps To Prosperity can grow the economy and narrow the Gaps:

Ten Steps To Prosperity:

1. Eliminate FICA

2. Federally funded Medicare — parts A, B & D, plus long-term care — for everyone

3. Provide a monthly economic bonus to every man, woman and child in America (similar to social security for all)

4. Free education (including post-grad) for everyone

5. Salary for attending school

6. Eliminate federal taxes on business

7. Increase the standard income tax deduction, annually. 

8. Tax the very rich (the “.1%”) more, with higher progressive tax rates on all forms of income.

9. Federal ownership of all banks

10. Increase federal spending on the myriad initiatives that benefit America’s 99.9% 

The Ten Steps will grow the economy and narrow the income/wealth/power Gap between the rich and the rest.

MONETARY SOVEREIGNTY