Johnny (and Susie and Bob and Jane and …) Can’t Add

If you’ve ever faced the “Monty Hall Problem“, you know how tricky math can be.  Seemingly obvious problems can turn out to be more complicated than they seem.

Even though my politics tend to lean left, I am frequently dismayed by the poor reasoning, naivete and, yes, bad math, expressed by my fellow liberals. Recently, there’s been a popular post on Facebook entitled “9 out of 10 Americans are Completely Wrong about this Mind-blowing Fact” (see article here). The general topic of the article is how the average American’s perception of their country’s distribution of wealth is wrong. The video presented in the article charts distributions of wealth and tries to compare “ideal”, respondents notions of “ideal”, respondents notions of “actual” and actual results.

Now, I am not 100% sure of what were the x and y axes in the presented charts, but they appeared to me to be “income” (x) and “wealth” (y).  I presume, too, that by “wealth” the video meant “net worth.”  I could be wrong, but I don’t think so – I looked at the source material from Mother Jones.  If I’m correct, the focus of the video could be restated as “what clusters of income should have what percentage of the wealth”. What percentage of the wealth should be owned by the people who are in the 20th percentile of income? What percentage should be owned by the top 20%?

The video briefly mentions equal ratios (20% income bracket=20% of the wealth) but dismisses this as something that would be derisively considered as “socialism.” The subtle subtext is that the derision is unwarranted and that there’s nothing wrong with this notion. Let me show you why this is even worse than socialism – it’s just plain nuts.

Let’s imagine a simple world with a population of 100 people. 20 of those people make $20,000/year, 60 of them make $40,000/year and 20 make $500,000/year. Now, let’s further state that the poor segment has a 100% propensity to consume. This is an economics term that means these people will spend all of their money on necessities. Likely, it’s worse – they’ll be in debt. Let’s imagine, too, that the middle 60% has a 95% propensity to consume – they save 5% of their income every year. This number is probably not far off from reality for the US middle class. Finally, let’s assume that the wealthy class has a 50% propensity to consume. The rich, having a lot more income, can buy lots of stuff and yet still save a lot.

Now, what happens after 1 year?  The poor have 0% of the wealth, of course! The middle class has collectively saved $120,000 (60*.05*40000). The rich have saved $5,000,000 (20*.5*500000). The collective wealth of our world is $5,040,000. The poor have 0% of the wealth, the middle class has .79% of the wealth and the rich have 99.21%!

The rich have more wealth because they make more money and, thus, can save more – lots more. The poor will never have any money if they can’t save at all. It’s simple math. Just like the Monty Python problem.

Now, you may complain that I’m cooking the numbers by choosing such a variation in incomes between the lower 20% and the upper 20%. The truth is that a factor of 25 (20k vs. 500k) is not that wacky even for socialist countries but let’s pick a smaller ratio and see what happens. Using ratios of 1:5:10 (e.g. $20k, $100k and $200k) but keeping the propensities to consume identical what happens after year?

Of course, the poor still have 0% of the wealth. The middle class have 13% and the rich have 87%. I suspect the video would still “disapprove”.

So what kind of system could possibly result in the poor having an equal proportion of the wealth as the rich? Socialism? Er, no. Tax cuts? Credits? Not if their propensity to consume remains at 100%.

Perhaps there ought to be a video, instead, about the distribution of income in the US, but that’s a whole other topic. If a worker at McDonald’s earns $18,000/year (they do here in WA!) how much should a brain surgeon earn? $180,000/year at least, but that 10x spread, we know, leads to 0:13:87 wealth distribution.

I’m not arguing that the distribution of wealth or income in the US is what it ought to be. In fact, I think it’s quite bad and that the increasing distance between the poor and the wealthy is a very bad thing. I think a lot of our political stability stems from the belief by the poor that they might be rich some day. If this dream turns out to be a delusion, we could see some scary politics over the next decade or two.  I just wish the people trying to raise awareness about the issue weren’t so unknowingly dumb or knowingly manipulative.

Maybe some day I’ll write a similar blog to address conservative complaints about how the rich pay such a large percentage of the taxes. I could pretty much swap all the nouns in this blog and it would serve the same purpose.