In simple economic models taxing capital has one of the biggest long-run negative effects on the economy of any tax. It looks OK in the short run, but with lower investment, the capital stock gradually declines. In this spirit you would be better off taxing land a la Henry George, since the amount of land won’t decline even if you tax it…. One way to tax capital some in a way that won’t hurt capital formation is to shift from labor taxation (such as Social Security taxes) to consumption taxation, since in the long run the shift to consumption taxation increases taxes on people who have the wealth to consume more than they earn…. [T]he short-run temptation is much like the short-run temptation to have rent control…. If the government taxes capital now and promises never to tax it again, the story gets more interesting. In theory, forcing all companies to issue non-voting stock to the government worth 90% of a firm’s value would have no distorting effects, and so would be the perfect tax as long as people believed the government would never do it again…. Getting government institutions set up to block the recurrence of this ultimately self-contradictory logic behind taxing capital a lot now and promising never to do it again is actually one of the trickiest problems….
Abstract: It is well known that, in standard growth models, the optimal tax on capital income goes to zero asymptotically. Even some serious economists (cough Glenn Hubbard cough) seem to have decided this means that capital income taxes should be eliminated right now….
One can tell more if one looks at the simplest cases of standard growth models: an aK model with optimizing consumers who have logarithmic utility, or a Cass-Koopmans model with Cobb-Douglas production and logarithmic utility…. Consider such an economy in which the distribution of wealth is unequal at time 0. A utilitarian state would want to redistribute income. The first-best way to do this is with a lump sum transfer. Let's rule that out by setting an upper limit on the tax on wealth (or an upper limit on the tax on capital income). What is the best policy? The best policy would be to tax capital income at the maximum allowed by the assumption and use the revenues to reduce inequality until perfect equality is achieved. After perfect equality is achieved, there is no more reason to tax and taxes are zero. Thus, as noted above, the optimal tax goes to zero in the long run. The reason is that it is optimal to tax as much as is allowed by assumption so long as there is any reason at all to tax. Then stop….
The assumption of logarithmic utility is not at all innocent…. A more general assumption… is constant elasticity of substitution utility. In this case… if the state can't precommit, the implications are just like those for logarithmic utility described above: tax as much as possible so long as there is any reason to tax at all, then stop when everyone is perfectly equal. With precommitment, if the intertemporal elasticity of substitution is less than one (as are all empirical estimates of said elasticity) the result is to tax even more, that is to tax as much as possible until the initially rich are as poor as the initially poor, then tax them some more.
These conclusions follow from analysis using standard techniques of the simplest case of the standard model.
I think that they are not noted in the literature.
I conclude, as always, that to the economics profession mathematical analysis of stylized models is taken seriously exactly so long as the conclusions fit the prejudices of economists. Thus when an economist says "Mathematical analysis which you wouldn't understand of my model shows that X is a bad policy" you should hear "I don't like X."