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The mathematics and pattern of wealth creation

This article is going to discuss what are the causes that drive wealth creation. At first, we will examine the mathematical difference between an employee and an investor. Second, we will look at the behaviors of the investors that lead to even more wealth creation.

If you read this article, there is a very high chance that you live in a capitalist economy. The economy is guided by rules and the motivations of different peoples (players). If you understand the rules, you can master the game. What does “capital” in capitalism mean? Capital means “money available for investing”. Thus, if you have money and you don’t invest it or if you spend money (don’t accumulate money) so you can’t invest it, that means that by definition you are not behaving according to the rules of the “capitalism game”.

Let's look at it from a mathematical perspective. If you have money and you invest it, you expect to get some return on that investment in the future. That means, that in the future you will have your initial investment plus the return on that investment (more money in the future as a result of investment activity). If you have money and you spend it on any object that you can’t resell for a higher price in the future (get a financial return on that object), that means you expect to have less money in the future from that spending activity. This brings us to the next subject of wealthy versus rich.

If a person won the lottery he is now in a possession of a lot of money and you can consider him rich, but he is not wealthy. Why? Because he can spend all that money on one luxury car. Now he needs to keep working to earn money to buy food, and as time passes he could resell his luxury car only for less than the amount that he bought it. That means that in the future he will have less money (he will be less rich). If that person will continue to make spending activities, he will be less and less rich until he will stop to be considered rich.

Another person won the lottery and decides to make an investment activity, for example, invest in real estate. That person also decides not to quit his job, even though he could, so that the job will pay for his spending activity. As a result, that person in the future will have more money (he will be richer). This person will also be considered wealthy since he now in a position of growing his net worth over time.

From that example, we can conclude that it doesn’t matter how much money you have. Play the game by the rules, if you have the money you will have more of it. If you have the money but you don’t play by the rules, you will have less of it.

Let's look at the following example so we can understand better what wealth means. since money is abstract and is harder to grasp from tangible objects, we will observe a tangible example. Person A lives in the wild, finds twelve sheep (six males and six females). He thinks to take advantage of his fortune, so he decides to convert them into meat for food and trade the rest of it for some clothing (spending activity). After some time, he exactly where he started, hungry looking for food. Person B also finds twelve sheep. He thinks to take advantage of his fortune in a different way. He guards the sheep, waiting for them to mate. By the act of mating, new sheep are born, and he is now in possession of twenty-four sheep. He can now trim their wool and make new clothing. By the second year, he will have forty-eight sheep in his possession. He will be able to make more clothes from their wool and sell them to get better food. By the third year, he will have ninety-six sheep in his possession, more than enough to provide all his material needs. Person B is wealthy and will become even wealthier as time passes.

The above examples give a very simplified model for the pattern of wealth creation. Now, we will look at some scientific studies that shed more light on how wealth is created and which behaviors cause it. The studies will be simplified in their presentation, so they will be easy to understand without prior or advanced knowledge on the subject.

Moshe Levy and Haim Levy (2003), bring a mathematical model of income types, that has a very high correlation to the empirical result of the distribution of money between people (Pareto distribution). That means that their model has a very high probability to be accurate and be true. Their model shows the following: people with low equity are in their position because the factors that affect their equity is their salary (income) and their consumption (spending activity). While on the contrary, people with very high equity (wealthy) are in their position because the factors that affect their equity are returns on investments. In simple words, that means that they (wealthy people) make so much money from their investment activities, that their income and consumption are negligible. For example, a high equity person gets $50,000 a month from his real estate investments, while being employed for $5,000 a month and his monthly spendings are $4,000. As you can see, his income and spendings cancel each other, and his equity grows by $50,000 due to the return on his investments.

Their model shows that the Pareto distribution (why people are more wealthy than others) is caused mainly due to luck. But make no mistake, if you do not invest your money, even if you have luck (born to a wealthy family, have a high paid job, won the lottery, found some sheep) you are not going to be wealthy over time, since your income model will be like low equity persons, and eventually you will run out of luck or money, and back to the starting point.

Their study also shows that when a market is less efficient (one sees opportunities), investment skills have a slight positive effect on wealth accumulation. But this slight positive effect can be significant in the accumulated wealth due to the phenomenon of compound interest that exists in investing activity and does not exist in a salary income.

Education effects

According to Jere R. Behrman, Olivia S. Mitchell, Cindy K. Soo and David Bravo(2012), there is a strong positive connection between financial education and wealth and there is no connection between regular education and wealth. People with financial education invest more in pension plans and thus their accumulated equity is much larger than those who do not invest in pension plans. According to John Y. Campbell(2006), poor households with less financial education are more likely to make investment mistakes versus rich households that are more educated financially. Also, some of those investment mistakes give rise to the likelihood that poor households will not participate at all in risky investments (no risk equals no high potential gains). Others will delegate the investment authority to various investment advisers and will pay a lot for commissions.

Entrepreneur personality

According to Marco Cagetti and Mariacristina De Nardi (2006) there is a strong positive relationship between entrepreneurship and wealth. Entrepreneurs are a small percentage of the population yet they hold most of the wealth. Entrepreneurs who have businesses that do not have an active nature in running the business and are very wealthy probably use the business as an investment stream of income. According to the sample conducted in the article, it was found that among the 400 richest people in the US, between 61-80 percent are rich in their own right and they did so by starting a company. The others inherited their family wealth, which was also generated from the business that their parents or grandparents started years ago. That means that originally everyone was "poor”, but participating in investment activities moved them from poor to wealthy.

What about initial capital?

Credit exclusions do not seem to be the factor that prevents entrepreneurs from entering the field of entrepreneurship. Credit exclusions are indeed a deterrent, but it does not prevent anyone who wants to be an entrepreneur from being an entrepreneur. According to Marco Cagetti and Mariacristina De Nardi (2006) due to the exclusion of credit, it is necessary to accumulate assets, and large savings rates are created for entrepreneurs or households who want to enter into entrepreneurship. According to Quadrini, Vincenzo (1999) and Gentry, William M. and R. Glenn Hubbard (2004) higher savings rates can be seen in entrepreneurs than in the rest of the population in general and according to Buera, Francisco (2006) large savings rates were found More so in the years before entering the field of entrepreneurship. Also, according to Marco Cagetti and Mariacristina De Nardi (2006) entrepreneurs who have experienced credit exclusion have used personal collateral as collateral to finance the business and take out loans or have not taken credit at all. According to Carroll, Christopher D. (1997) for the same level of assets and income, people with high entrepreneurial ability tend to have higher savings rates compared to people with low entrepreneurial ability. People with high entrepreneurial ability are persistent so they save significantly more money, compared to those with low entrepreneurial ability, to open their first business in the future. In addition, according to Marco Cagetti and Mariacristina De Nardi (2006) many entrepreneurs face large potential returns that inherent in starting a business but are limited in terms of credit they can borrow. So to expand their business, they continue to save. Thanks to this, they become richer and richer. The most successful lineages share their family wealth with their children, who continue the family business and expand the family fortune further and further. This is in contrast to a social norm which advocates that a young person aged 22-35 should leave his parents’ house, buy an apartment by taking out a mortgage and become an independent person. That is, without using the parents' capital until their death (when he is a parent himself and can’t take the same amount of risk when he is young).

Self-fulfilling prophecy

Fabrizio Ferraro, Jeffrey Pfeffer, and Robert I. Sutton (2005) present how theories can become a self-fulfilling prophecy. Therefore, norms that are based on a particular theory, recommend a particular behavior, and change that behavior until a fit with the theory is obtained. Therefore a certain generation that started from nothing develops a norm and passes it to the next generation. That norm advocates that it too (young generation) should start from nothing and be independent thus creating a norm that leaves a certain population at a low level of wealth. The effect of the language used also greatly influences the behavior, as in this case: a child that is independent versus a dependent child.

More risk more reward

According to Allan G. King (1974) more risky occupations yield greater income. People from richer families tend to choose more risky professions. In addition, the article by Erik Hurst and Annamaria Lusardi (2004) also found a strong positive relationship between affluent families and their level of investment risk. Therefore, people from richer families tend to receive higher incomes on average. As a result, income inequality (which reinforces capital inequality) can also be passed down through the generations, not as a result of the imperfection of the economy, but as a result of professional preferences that is a result of the conditioning of that person’s family income. That is, the rich choose more lucrative professions because they have a certain benchmark of comparison that is related to their family cell. Which in turn produces more wealthy people and strengthens wealth inequality.

To summarize the matter, people become wealthy have the following characteristics:

· They invest and as time passes the returns become their main source of wealth.

· They have financial education, so they can invest wisely.

· They save more money than average, so they can reinvest it.

· They use their family wealth (money from parents) to produce even more wealth.

· They get involved in riskier occupations that have massive potential profits.

If you still have any doubts that the above is true, ask yourself the following questions:

“Why wealthy peoples’ children don’t look for a regular day job?”

“Why don’t any royal family send their children to start from zero and be independent?”


Allan G. King ,Industrial and Labor Relations Review, Vol. 27, No. 4 (Jul., 1974), pp. 586-596.

Buera, Francisco. 2006. “Persistency of Poverty, Financial Frictions, and Entrepreneurship.” Manuscript, Northwestern Univ., Dept. Econ.

Carroll, Christopher D. 1997. “Buffer Stock Saving and the Life Cycle/Permanent Income Hypothesis.” Q.J.E. 112 (February): 1–55

Erik Hurst and Annamaria Lusardi, Journal of Political Economy, Vol. 112, No. 2 (April 2004), pp. 319-347

Fabrizio Ferraro, Jeffrey Pfeffer and Robert I. Sutton, The Academy of Management Review, Vol. 30, No. 1 (Jan., 2005), pp. 8-24.

Gentry, William M., and R. Glenn Hubbard, 2004. “Entrepreneurship and Household Savings.” Advances Econ. Analysis and Policy 4 (1)

Jere R. Behrman, Olivia S. Mitchell, Cindy K. Soo and David Bravo, The American Economic Review, Vol. 102, No. 3, PAPERS AND PROCEEDINGS OF THE One Hundred Twenty Fourth Annual Meeting OF THE AMERICAN ECONOMIC ASSOCIATION ( MAY 2012), pp. 300-304

John Y. Campbell, The Journal of Finance, Vol. 61, No. 4 (Aug., 2006), pp. vi+1553-1604

Marco Cagetti and Mariacristina De Nardi, Journal of Political Economy, Vol. 114, No. 5 (October 2006), pp. 835-870

Moshe Levy and Haim Levy, The Review of Economics and Statistics, Vol. 85, No. 3 (Aug., 2003), pp. 709-725

Quadrini, Vincenzo. 1999. “The Importance of Entrepreneurship for Wealth Concentration and Mobility.” Rev. Income and Wealth 45 (March): 1–19

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