Every day we hear lamentation of the “wealth gap,” and condemnation of those on the higher side of it. Unequal wealth is a crisis, we are told, that may well lead to the collapse of civilization. But is it really true that unequal wealth is *inherently* harmful? Should this claim be accepted as an axiom? Or does it need to be proved?

Imagine a Tiny World with a surface area of 1000 acres. It is inhabited by 100 residents, each of whom owns 10 of the acres. Each acre is worth $1, and each resident is able to harvest $1 worth of wood from the fast-growing trees that grow there. Thus each Tiny person has $20 of wealth: $10 of income, plus $10 of savings in the form of their land.

It costs $10 per year to feed and clothe a Tiny person at a subsistence level. This consumes all their income, and so their wealth never increases. Each Tiny person has 1% of the World’s $2000, and always has, and always will.

This economic equilibrium is shattered quite suddenly when a Tiny person named Maurice invents the Automatic Wood Chopper. Maurice’s AutoChopper allows Tiny people to harvest twice as much wood from their land, $2 per acre instead of $1.

Maurice begins selling AutoChoppers at a price of $1 each. None of his 99 neighbors has any disposable income, so they pay him in land: Maurice gets one acre from each Tiny person, and in return he gives each of them an AutoChopper.

A year laster, the distribution of wealth has shifted immensely. Previously, each Tiny person had $10 of the $1000 of savings, 1% of the total. Now Maurice has $109, and each of his neighbors has just $9. Maurice has 10.9% of the savings. His income has grown even more: With their new AutoChoppers, the 99 now have incomes of $18, but Maurice’s income is a staggering $317, 15.1% of the total.

The AutoChoppers wear out, so the 99 neighbors must buy new ones from Maurice each year. The gains work out thusly: Each of the 99 gets $18 yearly income, spends $10 on living expenses, spends $1 on AutoChoppers, and adds the remaining $7 to his savings. Maurice gets $317 yearly income, spends $10 on living expenses, and adds the remaining $307 to his savings.

At the end of 10 years, Maurice’s share of the wealth has ballooned from 1% up to 26%. The neighbors’ shares, meanwhile, have declines from 1% down to 0.7%.

It is then that the the neighbors surround Maurice’s house, bearing signs that read “We are the 99%,” and shout for him to come out and face them… so that they can thank him for his service to the community. Naturally they want to thank him, because each of them is far richer than they were 10 years before. Under the old equilibrium, each of them had only $20, with no prospect of ever gaining any more. 10 years after the invention of the AutoChopper, each of them has $98, and their wealth increases every year.

This is because, while the percentage of the wealth controlled by each of the 99 decreased, the total amount increased. The 1% was out of $2000. The 0.7% is out of $13,100, and 0.7% of $13,000 is a lot more than 1% of $2000.

This hypothetical is, of course, naive. Tiny World is simplistic. It ignores a lot of factors and leaves out a lot of details. But that’s alright, because the claim it refutes is equally naive and simplistic.

It is very easy to imagine (and to find in the real world) scenarios where the people at low side of a wealth gap are better off than they would be if the gap did not exist. Figuring up the percentage of wealth a person controls is actually pretty meaningless; what matters is not the percentage, but the actual amount. If the total amount of wealth in a system increases, then it quite possible for a person to have more even as their percentage decreases. A small piece of a big pie may be more than a big piece of a small one.

It cannot be assumed that unequal wealth is bad. It is entirely possible that unequal wealth in a given context is actually good for everyone. Claims to the contrary must be proven, not simply assumed to be true.

It is actually possible to distribute the wealth much more unequally and still have the 99% benefit. If Maurice sells his AutoChoppers for three dollars instead of one, then by year ten he will control 75% of the wealth, but, still, each of the 99 will still be richer than they were in year zero.

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That calculator is great

Interesting read.

Finally in words I can understand. But also yes, the calculator is rad.