Are Rich People Good or Bad?

Including externalities in optimal tax calculations

The standard view of taxing labor incomes is that the optimal tax rate can be given by knowing the curvature of the utility function with respect to wealth, and the elasticity of income with respect to tax rates. We tax top earners, who gain less utility for every dollar, and give it to people at the bottom, until we reach the point that increasing taxes on high earners decreases the total revenue that we are able to obtain. Solving for the optimal tax rate is simply a question of finding what rate maximizes utility. The tax brackets are taken as given, and we solve by essentially taking the derivative. (See Saez (2001) for details).

This approach gives us very high optimal tax rates, often in excess of 70%. The story becomes considerably more complicated once we add in externalities, however. These can be either positive or negative. On the positive side, people with high incomes are disproportionately likely to be inventors or creators of businesses. They work in ideas, the benefits of which they cannot fully capture. Raising taxes creates deadweight loss not only through discouraging labor and reducing income, but from ideas which are never found or implemented. The top optimal tax rate totally flips around and can even become negative under some specifications, although the ill-effects of taxing income are rarely comparable to the positive effects of subsidizing particularly innovative professions, or of subsidizing innovation directly.

On the other hand, the rich might have negative externalities. It could be the result of rent-seeking from the government, of executives diverting funds from the rightful recipients, or simply executives driving a harder bargain. Since bargaining is zero-sum, spending more on it is necessarily wasteful. In this world, the optimal tax rate should be higher than the one you obtain if you assume the only way in which the rich affect others is through reducing their labor effort.

The two views of the externalities are best covered, respectively, in Chad Jones’ “Taxing Top Incomes in a World of Ideas” (2021) and Piketty, Saez, and Stantcheva’s “Optimal Taxation of Top Labor Incomes: A Tale of Three Elasticities” (2014). Jones is focused on the role of ideas, and so synthesizes evidence from numerous sources on who generates ideas, and how this changes when taxes increase. These are estimated imprecisely, although we can say with certainty that the income distribution of inventors is extremely skewed and correlated with the social value of their inventions, and that the wealthy are far more likely to own a business (businesses which are also larger, on average). Not totally implausible parameter values deliver negative top tax rates. Jones really emphasizes the distinction between welfare maximizing, and revenue maximizing, tax rates. A toy example is that when the elasticity of labor supply is .1 in the model (and very close to perfectly inelastic), the revenue maximizing tax rate is 95%, while the welfare maximizing tax rate is 50%.

Piketty, Saez, and Stantcheva focus on the negative externalities of harder bargaining. The “three elasticities” of the title are the elasticity of labor supply, the elasticity of tax avoidance, and the elasticity of bargaining or rent extraction. Tax avoidance is not all that large in the United States, and in any event, is best solved by broadening the tax base rather than changing tax rates. (The tax avoidance channel does tend to obfuscate the effects of prior changes in tax rates. We observe a big surge in growth, which is actually just previously hidden fortunes surfacing).

The three authors decompose the total elasticity of income into the three channels of labor supply, avoidance, and rent extraction, and argue that over half of the observed elasticity is due to the last. Their evidence for this largely rests on CEO pay after controlling for firm performance. If CEOs are paid more for the same performance in countries with lower tax rates, then that indicates that they are really being paid for something socially deleterious, especially if the correlation is stronger in poorly governed firms.

Henrik Kleven (2025) contains a method of backing out the optimal tax rate which is totally agnostic to which externalities prevail, or through what channel those externalities come from, largely built upon Jakobsen, Kleven, Kolsrud, Landais, and Munoz (2024), which used extremely detailed records from Sweden to see how immigration and reduced labor supply affect the economy. Kleven basically just has the same formula from Saez (2001), but with an additional term characterizing externalities.

The interesting part is that it matters who the externalities from high earners affect. If they (in the extreme case) affect only other top earners, then the problem greatly simplifies to simply maximizing revenue. We only care about spillovers in this case when the spillovers are from the top onto the bottom. Kleven finds that the net externalities of top earners are positive, although the top tax rate is still a bit higher than the current tax rate.

I will insert my own gloss here. Everyone believes that everything is more elastic in the long run. For example, suppose people are choosing between a high paid job with less pleasant work, or a lower paying job with more pleasant work. In the short run, people are stuck in the professions for which they trained; in the long run, people choose to go work in different fields. If you are someone who, like me, cares about the future, then we must be cautious with taxes.

The counterargument, however, is that measures of the elasticity of labor supply are often coming from migration, rather than necessarily stopping effort. If we care about global wellbeing, then we should have a lower elasticity. Of course, we also just know that there are lots of things which we can’t quite measure. Reading all this has made me considerably less certain about what the optimal tax rate is, and whether we can ever really know it. I can say with some confidence, though, that we would prefer directly subsidizing innovation and human capital accumulation, rather than bankshot methods through income taxes. For more, you can read my prior work on Marta Prato.

Either way, we should be extremely skeptical of those who think that the wealthy are not good for society, and that they should be abolished. It is common to see claims that “billionaires shouldn’t exist” or the like. I do not think those holding those sentiments have really grappled with whether the net externalities of the rich are positive or negative.