# Tax the Rich

Dylan Matthews has a typically excellent explainer about taxing the rich. Just click the link.
I have one thought. Matthews is soft on capital income.

Matthews wrote

Saez and Diamond also argued that capital income — income from things like capital gains, corporate profits, dividends, etc. — should be taxed, which broke with previous models of optimal tax theory. (Our current capital gains top rate is 23.8 percent.) Those models had suggested the proper tax rate on capital income was zero, on the grounds that it discouraged savings: If you spend money on an investment, your profits are taxed, but if you spend money on food or a house or what have you, you don’t get hit with a capital tax — so a capital tax’s presence pushes you to spend more and save less.

This is a roughly correct description of the previous models, but it isn’t exact. In fact, the mathematical result is that as time goes to infinity the tax rate on capital income should go to zero. There is no justification for arguing that this means the rate should be zero in 2019 or 3019. The infinite jump from t goes to infinity to now is simply a dishonest rhetorical trick.

Another problem is that the academic literature on capital income taxation is not sound. The classic paper by Judd is simply mathematically incorrect. Yet it is still regularly cited. The key assumption which Judd made which makes his conclusion a mistake (a mistake like 2+2=5 not a mistake like taking a crazy assumption seriously) is that the state runs a balanced budget. Given Judd’s assumptions, the correct math shows a positive tax rate on capital income for all time.

It is interesting that a math boo boo could be so influential. One might almost guess that ideology and self interest are involved.

If the state is allowed to run deficits or surpluses, then the optimal policy involves building up a huge sovereign wealth fund so high that all desired spending is financed by the socialist profits on state owned means of production (this is just what the math says). At that point, the optimal tax on capital income is zero, because there is no reason not to tax. In particular if one wishes to tax capital income because one cares about inequality, the math suggests no compromise at all. In the simplest model it is optimal to tax capitalists until the richest capitalist has the national average income. With more reasonable assumptions, an egalitarian who also cares about efficiency would end up taxing the rich until they become poorer than average.

An egalitarian would accept that the tax on capital income eventually go to zero when the recipients of capital income are as poor as the average person or poorer. A class warrior who wanted the rich to starve but didn’t want to deprive workers of capital to work will would tax the rich till they starved.

A critique of the standard anti capital income taxation program should conclude “it is not until capital income ceases to go to the rich and goes to the relatively poor can we inscribe on our banner from each capitalist zero taxes and to each capitalist the full market income”

In contrast, if some have high labor income, it is best to let them end up with above average income. As is often argued, the equality efficiency tradeoff is different for capital income taxation, but it is different because less is optimally conceeded to the rich in the name of efficiency. Nothing or less than nothing should be conceded.

This is a simple mathematical result based on standard assumptions.

Also the standard model assumes dynamic effiency. Matthews is very smart, but he accepts the assumption that we should encourage saving. This is an implication of the Ramsey Cass Koopmans model, which might or might not have anything to do with reality. It is possible to decide if a higher steady state ratio of capital to effective labor implies higher or lower welfare.

It has been argued that the standard case for more capital is valid if r>g where r is the expected return on capital (including the expected value of risky returns) and g is the trend rate of gdp growth. In fact, it is valid only if rf > g where rf is the safe rate of interest which has almost always been less than g. This isn’t a fringe claim. It is Public Debt and Low Interest Rates Olivier Blanchard — another Frenchman, January 2019.