The tax would be tiny for investors who buy and hold, but could prove to be significant for traders who place millions of orders a day.

Under the proposal, a trade of shares worth 10,000 euros would face a tax of one-tenth of 1 percent, or 10 euros. A trade of a derivative would face a tax of one-hundredth of 1 percent. But that tax would be applied to the notional value, which can be very large relative to the cost of the derivative. So a credit-default swap on 1 million euros of debt would have a tax of 100 euros, or about 0.4 percent of the annual premium on such a swap.

I’ll get to how Europe thinks it can prevent widespread evasion in a minute. But for now, assume the Europeans could accomplish that. And assume, as European officials say they hope will happen, that the tax spreads to other major markets, something Europe is trying to encourage by offering to share the tax revenue with other countries that impose a similar tax.

What would happen?

It would not destroy markets that have good reason to exist — that is, markets that serve actual investors. The tax would be far smaller than the fixed commissions that American investors once took for granted, and even less than the costs implicit in the fact that until decimalization arrived in 2001, that most stocks could move only in increments of one-eighth of a dollar, or 12.5 cents. Markets, and the American economy, managed to prosper.

But there would nevertheless be significant changes — changes that might be for the better in some ways. High-frequency trading, which was encouraged by allowing prices to move in increments of a penny or less, and by technological advances, would be discouraged. So too would be some of the strategies used by hedge funds that involve trades expected to yield very narrow — but presumably very safe — profits. To make such trades worth doing, funds borrow a lot of money and make the trades using very little equity. That is a strategy that is guaranteed to work — or to blow up disastrously if markets do not act as expected. Discouraging it might be a good thing.