The Washington Post reports that the Democrats have a new plan for middle class tax cuts that will be financed in part by a 0.1 percent tax on financial transactions like stocks, bonds, and derivatives. Since the financial industry and its employees will undoubtedly be pushing tirades telling us that this tax will kill middle class savers, BTP decided to call in Mr. Arithmetic to get his assessment of the issue.

Mr. Arithmetic points out that the amount of the tax born by savers will depend in large part on their response to the tax. Since research indicates that trading volume declines roughly in proportion to the increase in trading costs, this means that ordinary savers will bear almost none of the tax.

To see this point, imagine that our middle class saver has $100,000 in a 401(k). Suppose that 20 percent of it is traded every year and that the trading costs average 0.2 percent. This means that our saver is spending $40 a year on trading costs (0.2 percent of $20,000). 

With the Democrats' proposal, trading costs will rise to 0.3 percent assuming that 100 percent of the tax is passed on in higher trading costs. (This is almost certainly an exaggeration, since the industry will probably not be able to pass the tax on in full.) If trading volume were unchanged, then this middle class saver would now pay $60 a year in trading costs (0.3 percent of $20,000).

However research shows that the folks managing the 401(k) will likely cut back their trading by roughly 50 percent in response to this 50 percent increase in trading costs. This would mean that only 10 percent of the 401(k) or $10,000 would be traded each year. In this case, the 401(k) holder would be paying just $30 a year in trading costs (0.3 percent of $10,000).

Instead of going up, trading costs actually fell. Since 401(k) holders don't on average make money on trading (for every winner there is a loser), they end up better off after the tax. Of course these numbers are approximations and it may well be the case that the decline in trading volume does not fully offset the increase in costs, but the point remains. The vast majority of this tax will fall on the financial industry (think Lloyd Blankfein, Jamie Dimon, and Robert Rubin). The middle class 401(k) holder will be largely unaffected.