A theoretical form of currency designed for social stability. All contemporary currency is linear - take X dollars, add X dollars and you've got 2X dollars. In a non-linear currency, X and X would result in 1.9X effective units of currency. X, X and X would make 2.8X effective units of currency. The more money one had, the more money it would take to make that next effective unit of currency, referred to as eu from here on. Obviously there would have to be an underlying unit turned into effective cash through an algorithm, requiring the use of computers in almost every transaction, but sole use of electronic currency would allow it. Implementation could differ, but the proposed form of non-linear currency would apply to every transfer and valuation of wealth.

What would the advantages of non-linear currency be? Since it would work against enormously large amounts of weath when the point of diminishing returns struck, the disparity between economic classes would stay relatively small. It would provide a strong reason for donations, as ten eus for one person would be one hundreds eus for someone else. Absolute bedrock poverty would be nearly abolished due to this effect. It would encourage affordable prices for most of life's necessities.

Disadvantages? There are certain political issues raised by the authoritarian nature of non-linear currency. The more economic disadvantages include many caused by high inflation. It would discourage the accumulation of wealth and so discourage enterprise both through lessened rewards to successful entrepeneurs and through making it harder to build up capital. The largest disadvantage would be complexity - the numerous rules to cover every situation and attempts to avoid the built-in tax on large amounts of money would be overwhelming. Increased barter would be one consequence, although such could be counted as an advantage. Currency evasion would replace tax evasion as the sport of the rich. Well made but costly products would be refused in preference to cheap products with lower value, raising the cost of life in the long term. Unless material objects were included in the valuation of one's wealth, a troubling idea that would require a realtime estimate of the worth of everything owned and the search against hidden products, it would encourage greatly increased consumer spending (again a possible advantage) as a way to lower one's wealth and therefore increase the purchasing power of new income. Even the choice of algorithm would be extremely complex - what rate of currency decay would be best for society?

Although non-linear currrency would never work in modern society, it's a concept that could inspire something if thrown into the gigantic collective think tank that is Everything.

Interestingly, people seem to treat currency as nonlinear! Conventional wisdom has it that lotteries are a tax on the stupid (although Greg Egan considers them a tax on hope, which is closer to the mark). But here's another way of analysing why people buy lottery tickets (note: I don't).

Money is nonlinear. The utility function for having $X is not linear in X! Rather, for very low values of X it is much shallower. If you see a penny somewhere, often you won't bother to pick it up. But the cost of doing so is far less than 1 penny. The point is you don't expect to be able to get 1/100th the utility of $1 out of 1 cent (of course this does not apply to 100 cents; just to a single cent). So you don't mind losing 1 penny.

Lotteries are the same. I buy a ticket for $5 which with probability 10-6 will get me $2.5M. WHY? Well, evidently I don't think the loss of $5 is so great, compared to a gain of $2499995. With $2.5M, I could buy houses, invest wisely, etc.; with $5, I can't do any of that. They're just not the same sort of commodity!


this nonlinearity is the reverse of that in dragoon's writeup. There, more money is worth less as you get more of it; but in reality, more money is worth more as you get more of it. This has an obvious bearing about the fairness of capitalism.

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