Almost any discussion about poverty and wealth and income inequality at some point includes arguments based on the premise that the wealth of the wealthy is causally related to the poverty of the poor; more specifically, there often seems to be a tacit agreement that the former causes the latter.

This is the basis for many arguments about distributional justice and in particular the notion that inequality is unjust per se or simply socially inefficient. I am however not interested in the discussion of any ethical questions regarding this issue, as this would motivate primarily opinion-based responses. Instead, I would like to know if there exist any (mathematical) models which support the common assumption that the same economic processes which make the wealthy wealthy also make the poor poor.

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    $\begingroup$ How are you measuring wealth? Consider for example two hypothetical societies, one with an equal distribution of 'wealth', the other with an unequal one. Due to the unequal distribution, and the resulting spare time afforded to some but not all of its members, the first society has researched antibiotics and can make them available to every member (rich or poor). The second society does not. How are you defining wealth? $\endgroup$
    – Lumi
    Jan 6, 2015 at 1:11
  • $\begingroup$ I am interested in total wealth and income in monetary terms. About your example, I do not understand (1) why it should be the society with an equal distribution of wealth that affords free time to some but not all of its people; (2) the assumption that innovation results from free time rather than economic activity. $\endgroup$
    – Constantin
    Jan 6, 2015 at 13:41
  • $\begingroup$ You´re right - I got that the wrong way round - it´s the unequal society that ends up researching antibiotics. The reason I gave that example is that there are so many issues with trying to equate wealth with simple quantities of money. In some sense this is the wrong way to look at the question. As far as mathematical models are concerned - this is actually something I´m working on, in terms of what is the evolution over time of interest based credit systems - and afaik the answer is no - even the mathematical question is more complex than it may first appear once banking gets involved. $\endgroup$
    – Lumi
    Jan 6, 2015 at 13:48
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    $\begingroup$ Why shouldn't monetary wealth be a reasonable approximation? And about your example, wouldn't that support the idea that inequality is beneficial to the poor? $\endgroup$
    – Constantin
    Jan 6, 2015 at 14:47
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    $\begingroup$ Essentially because money is a terrible measure for this purpose (most purposes as it happens). Another example, two hypothetical states with the same uneven wealth distribution, but one has public health care available to all, the other does not, and so its poor have very limited access to health care. The example is constructed to provide an argument that inequality might be beneficial to society, but its only a toy example. The larger question is how do you measure wealth? The Weimar republic after all, did not lack for money. $\endgroup$
    – Lumi
    Jan 6, 2015 at 16:54

2 Answers 2


Let me preface this answer with a word of caution: your question is a very good and important one but it is also one that depends tremendously on the definitions of the terms it uses. I'm going to attempt to answer it in the most unassuming and non-technical way. You could pose it in technical terms and get a more precise answer.

The wealth of the rich can be attributed to the poverty of the poor. In North Korea, one of the poorest countries in terms of per-capita GDP, there are few rich people and many poor people. It is well-known that almost all of the rich people work either in the highest levels of government or the military. The poor people who are lucky enough to make any income largely do so at the behest of the rich people, and those who refuse are imprisoned or worse. Since almost all economic activity in North Korea is centrally planned via force, it follows that the rich derive their wealth from the suffering of the poor.

However, in societies with more private ownership of production and capital - and less centralization - force is still useful in general but less of a factor in determining who is wealthy and who is poor.

Regardless of our relative lot in life, if you and I freely trade with each other, we only do so when both of us feel like we are "better off" as as a result. So, if you are a wealthy industrialist and I am a poor banana farmer, and I freely decide to trade 100 of my bananas for 100 of your dollars, you necessarily think a banana is worth at least 1 dollar to you, and I necessarily think a banana is worth at most 1 dollar to me.

Excluding outright fraud (misrepresentation either of your dollars or my bananas) we must conclude that each of us either thinks this is a fair trade or that the other guy is a dope. For instance, you may know something about the value of bananas that I don't. Maybe you've just discovered that bananas have special healing powers or that my bananas are particularly good. On the other hand, maybe I know something you don't. Maybe I know that there are about to be many more banana producers in the area or that I can buy two bananas for 1 dollar somewhere else.

Usually, however, it's just a matter of what each party in the trade is able to do with the traded goods that determines what he/she thinks they are worth.

If you get rich from selling my bananas at a higher price, you are not doing so "at my expense" as long as you are not preventing me from doing the same thing. There may be reasons you have the ability to sell bananas at a higher price that have nothing to do with force - maybe you own a distribution system or retail outlets, and I don't - but my choice isn't between selling retail bananas and selling wholesale bananas, but rather selling bananas at the highest possible price vs not selling bananas at all.

  • $\begingroup$ What about inelastic goods? $\endgroup$
    – user45891
    Jan 10, 2015 at 16:08
  • $\begingroup$ @user45891, What about them? Elasticity of demand is a property of the demanding parties, specifically how sensitive they are to changes in the "price" of the good. What does that have to do with the question? $\endgroup$ Jan 13, 2015 at 6:23
  • $\begingroup$ "We must conclude that each of us either thinks this is a fair trade or that the other guy is a dope.": Or maybe the weaker side does not have any other options. Sometimes people are forced to accept a bad deal for lack of alternatives. $\endgroup$
    – Giorgio
    Jun 28, 2016 at 6:03

I am not sure this question has a clear answer as it is stated. There are two problems that your question imply :

  • The distribution of wealth
  • The total amount of wealth

If the total amount was constant then the answer would be simple : yes. But it is not, and most of the people who would say no to your question will say that rich people save and therefore invest more, take more risks, and so create more wealth than others.

To be sure whether it is true or not, and to what extent, is very complicated. For instance, a lot of macroeconomics are done with representative agents that typically do not enable very well to answer these questions.

Last, this is a very hot topic right now in economics, mainly in the form of a number of papers that try to study links between growth and inequality. Here you can find a recent imf paper on the subject. If you want more papers, I can find some later, just add a comment.


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