The way I understood it (by way of the paper's gold panning illustration) is that with a progressive tax system based on total aggregate income (i.e. you don't distinguish rent income from non-rent income), high marginal tax rates result in a multitude of rent-seekers each collecting a fraction of the total available rents. This is so because as their income for the year accumulates and their marginal tax rate increases, the tax rate overcomes the collection effort required. Once they've maximized their income they rest for the remainder of the year. If they're not collecting rents that means someone else can. The market in rent-seeking supports a larger number of rent-seekers, which diminishes the base of people doing productive work.

By contrast, imagine if all the rents went to a single rent-seeker. In that situation only one individual is doing unproductive work instead of many. Assuming that the rents were going to be collected regardless, then we're better off if there's only one individual pursing that unproductive activity than many.

How do you ensure there's only one rent-seeker? By creating conditions that favor someone monopolizing the rent-seeking market. You can do so by taxing high income earners less than you might otherwise, preserving the incentive for a single rent-seeker to collect all the rents. The lone rent-seeker is taxed less, but that's okay because he's keeping everybody else out of the rent-seeking market. Taxes on other high-income earners is less but that's okay, too, because they're doing productive activity--generating wealth and thus more taxable surplus--and now there's more of them.

Like the Laffer Curve the devil is in the details.[1] But it's an interesting point.

[1] I don't mean to impugn the paper by comparing it with the Laffer Curve and the toxic political economics surrounding it. I just mean to say that the quantitative values matter.

Isn't there a fairly toxic political question buried in this paper as well? Who is going to decide which behaviors are rent-seeking and which are productive?

Yes, if pundits and lobbyists abuse this paper by relying on it to expound policies that it can't actually support. (Maybe they already have?) But that's a more general problem with how our political culture permits politicians and pundits to abuse science in their rhetoric.

There's also a problem in academia where intense pressures to publish and to be cited incentivize researchers to make radical claims, exaggerate the practical utility of their findings, gloss over weak points, etc, ripe for political fodder. I won't claim to understand all the technical details in the paper but I didn't sense any of that in the paper. The authors seemed to establish a fair analytical context, and they plainly articulated a limited policy conclusion--"it does not necessarily imply that taxes should be more steeply progressive". (Emphasis added.) Those don't feel like weasel words; just true and straight-forward without inviting misinterpretation.

It's a cool paper that credibly does what it sets out to: explore what can happen (in a formal and fair but, clearly, limited model) when you give rent-seeking a first-class treatment and carefully analyze how it interplays with the rest of the system.

By contrast, Arthur Laffer very actively advertised his research as justifying policies that it simply could not. And he continues to do it--he actively promoted the 2017 tax cut using the same intentionally misleading arguments he always has.

The part of that paragraph where it falls apart for me is the assumption that a well capitalized rent seeker is going to decided to become productive instead of finding other opportunities to do rent seeking.

That doesn't seem to fit real life very well.

If that happens, the only effect is that you create a class of ultra-wealthy under-taxed rent seekers who still produce nothing.