Another one of those lovely examples. When physicists decide to come and do economics. The argument here being that look, look, we can prove it! Without redistribution attempts a market economy will inevitably end up in gross oligarchic inequality. Because, you know, our mathematical model says so.
Hmm, well, yes. Except numbers without theory aren’t all that useful. And what’s going wrong here being that our physicists aren’t even interested in the theory. Sigh:
If you simulate this economy, a variant of the yard sale model, you will get a remarkable result: after a large number of transactions, one agent ends up as an “oligarch” holding practically all the wealth of the economy, and the other 999 end up with virtually nothing. It does not matter how much wealth people started with. It does not matter that all the coin flips were absolutely fair. It does not matter that the poorer agent’s expected outcome was positive in each transaction, whereas that of the richer agent was negative. Any single agent in this economy could have become the oligarch—in fact, all had equal odds if they began with equal wealth. In that sense, there was equality of opportunity. But only one of them did become the oligarch, and all the others saw their average wealth decrease toward zero as they conducted more and more transactions. To add insult to injury, the lower someone’s wealth ranking, the faster the decrease.
This outcome is especially surprising because it holds even if all the agents started off with identical wealth and were treated symmetrically.
Thus we need redistribution, obviously:
In 2017 Adrian Devitt-Lee, Merek Johnson, Jie Li, Jeremy Marcq, Hongyan Wang and I, all at Tufts, incorporated the redistribution of wealth. In keeping with the simplicity desirable in applied mathematics models, we did this by having each agent take a step toward the mean wealth in the society after each transaction. The size of the step was some fraction χ (or “chi”) of his or her distance from the mean. This is equivalent to a flat wealth tax for the wealthy (with tax rate χ per unit time) and a complementary subsidy for the poor. In effect, it transfers wealth from those above the mean to those below it. We found that this simple modification stabilized the wealth distribution so that oligarchy no longer resulted. And astonishingly, it enabled our model to match empirical data on U.S. and European wealth distribution between 1989 and 2016 to better than 2 percent. The single parameter χ seems to subsume a host of real-world taxes and subsidies that would be too messy to include separately in a skeletal model such as this one.
So, here we have it, the necessity for a wealth tax is mathematically proven.
Except, of course, it isn’t. Because our physicists have made an assumption. That we are in a technologically stable economy. And economists are entirely willing to agree that in such a technologically stable economy there is that tendency to oligarchy. A stable economy, in this sense, becomes very close to being a zero sum one. In which those who can gain can only do so at the cost to another. And the usual fighting for position and money among humans then means that those who can conquer the system end up with everything.
But we’re not in a technologically stable economy. More, the reason we’re in a market one is because we don’t want to be in a stable one. We like progress, we want to encourage it and markets are what do. And what does technological progress do? It redistributes wealth.
Take just the one example. 18th and 19th century England was dominated, economically, by the great aristocratic fortunes. As the country had been for about a millennia. Those were based on owning all the decent arable land. So, what killed those fortunes? The train and the steamship. For those two technologies opened up first the American prairies then the Ukrainian steppes to being wheat farms for England. Which they became as well. The value of English arable land plummeted and we had a very decent redistribution of wealth. From those aristos to the working man in the form of cheap bread.
So, now review that mathematical model. We lift that assumption of technological stability. And a free market system is, as we know, the finest kind for promoting technological change. Thus we’ve got, within our system, that method of redistribution which prevents that oligarchy. Basically, once someone is noted as getting all the pies then competition arises which redistributes them. This is so basic it’s in Adam Smith from 1776.
Or, as we might put it, by using the necessary economic theory to illuminate our mere maths we’re able to show that we already have the redistribution required, it is not necessary to add it in the form of a wealth tax.
But then physicists would have to learn some economics, wouldn’t they? A task rather more difficult than getting economists to grasp the odd bit of physics.