This was originally dreamed up as part of an idea for a sci-fi novel, but because I want to talk about the economics of it rather than its fictional setting, I'm putting it here instead of Creative Projects.
One of the major problems that we'll have to confront in the 21st century, as we've all heard ad nauseum, is income inequality: too few people are hoarding too much money. Generally speaking, many of the proposals for how to fix the problem are redistributionist: tax the rich more and spread the money around in a more equitable manner. Progressive tax brackets have the side effect of making pre-tax money worth less the farther up you go: if your lowest tax bracket is 20% and your highest is 60%, $10k is worth $8k to a poor person and half that to a rich one. (There are other factors at play here, of course, when you start asking how much that money is "worth", not least of which is that rich people and poor people use money in very different ways; you can't compare a thousand dollars of groceries to a thousand dollars of index funds. But the point here is that the real value of equal raises in income can come out as different values depending on your income level. This is really obvious, but attention needs to be brought to it so we can move on.)
There are two quirks with this system, one of which may not be a problem and one of which definitely is. The first, which is only possibly a problem, is that Uncle Sam is doing all the income fiddling after the fact; before that point $10k is $10k, and free to wander through the economy as its owners please. The second is that when your tax code is abnormally complicated (and it is in many countries) rich people who don't want the taxman to tax their money at the usual income bracket find ways to get around him: they can invest it and pay capital gains tax instead, they can buy a Senator and get a special tax break, they can do funny accounting tricks, they can stash it in the Caymans. It is easier to do this in some countries (the United States) than some others (Sweden?), but to my knowledge it's basically always a possibility to some extent. This also has the nasty side effect of punishing people who take lots of money as income (which they're liable to spend and stimulate the economy with) in favor of people who lock their fortunes away where it doesn't really do anybody any good. Thus it's possible that if your only goal is fixing income inequality, it's not necessarily the case that the best way to do that is just to change tax rates.
I was pondering this last night over dinner, and then an idea came to me: this aforementioned effect, where the same amount of money is worth less the richer you get, doesn't necessarily have to be something the IRS does. It could be an inherent property of the currency. In other words, instead of taxing you at 70% so that an extra $100k raise only puts $30k in your bank account, what if the currency operated so that someone who gets a raise from $100k to $200k only has the spending power of $130k under his old salary- not because he got a raise, but because $200k operates like that? This won't really punish people who get raises or inherit extra cash, because more money is always more money. It just isn't as much more the farther up you go, and there will be a practical limit on how rich people can get when the company needs to give them massive, massive raises just to raise their salary by a few million. (Most Americans, at least, would have a major problem with the idea that somebody can only get so rich. There's no reason, though, that the upper limit couldn't be pretty damn high- in the hundreds of millions or billions instead of the low millions- and, having an ascetic and thrifty streak myself, I've never understood why anybody would care beyond the first few million. Past that point all you can use that money for [let's be honest- nobody needs a bigger and bigger yacht] is buying and starting companies, and more than one person can do that.)
The first response people will have to this idea, I think, is that "money doesn't work like that". Well, it could. What is certainly true is that physical money doesn't work like this, at all- twice as many dollar bills must by necessity mean twice as much money. However, we're currently living in a world where the vast amount of transactions do not and never have involved any physical money at all- they're all on your credit card or go one further by just shuffling numbers around on a bank server somewhere. But because we insist that there must be a physical analogue to the economy, the entire system is weighed down by the constraints of physical matter. There's no reason a fully electronic currency could have properties that wouldn't work with a physical one, except that our brains expect things to operate like things. Lots of economics is counter-intuitive, after all.
There is a major, gaping problem with trying this today: if America (or the Eurozone, or Russia, or any country) tried to implement this, there would be massive, massive capital outflows on a scale never before seen as investors try to dump their dollars for currencies that work the way currencies usually work (in other words, where two and two make four instead of three.) This means that such a system is going to be impossible to implement for decades if not a couple centuries to come. It can only work when humanity has only one currency; you can buy lots of gold or other commodities to stash your wealth, but since you'll have to convert it back to currency to do anything useful with it, that defeats the purpose. Buying gold is a hedge against inflation, not progressive income tricks.
(If you're wondering, the plot of the sci-fi novel revolves around this currency scheme; the main villains will be either the equivalent of tax evaders, or reactionary terrorists trying to get inside the crypto-system that protects the currency in order to crash the Solar System's economy. I'm not sure which, yet.)