Piketty

Rethinking progressive taxation

pnrj core principles, critique of neoclassical economics, ethics, inequality, public policy , , , , , , , , , , , , ,

Apr 17 JDN 2459687

There is an extremely common and quite bizarre result in the standard theory of taxation, which is that the optimal marginal tax rate for the highest incomes should be zero. Ever since that result came out, economists have basically divided into two camps.

The more left-leaning have said, “This is obviously wrong; so why is it wrong? What are we missing?”; the more right-leaning have said, “The model says so, so it must be right! Cut taxes on the rich!”

I probably don’t need to tell you that I’m very much in the first camp. But more recently I’ve come to realize that even the answers left-leaning economists have been giving for why this result is wrong are also missing something vital.

There have been papers explaining that “the zero top rate only applies at extreme incomes” (uh, $50 billion sounds pretty extreme to me!) or “the optimal tax system can be U-shaped” (I don’t want U-shaped—we’re not supposed to be taxing the poor!)


And many economists still seem to find it reasonable to say that marginal tax rates should decline over some significant part of the distribution.

In my view, there are really two reasons why taxes should be progressive, and they are sufficiently general reasons that they should almost always override other considerations.

The first is diminishing marginal utility of wealth. The real value of a dollar is much less to someone who already has $1 million than to someone who has only $100. Thus, if we want to raise the most revenue while causing the least pain, we typically want to tax people who have a lot of money rather than people who have very little.

But the right-wing economists have an answer to this one, based on these fancy models: Yes, taking a given amount from the rich would be better (a lump-sum tax), but you can’t do that; you can only tax their income at a certain rate. (So far, that seems right. Lump-sum taxes are silly and economists talk about them too much.) But the rich are rich because they are more productive! If you tax them more, they will work less, and that will harm society as a whole due to their lost productivity.

This is the fundamental intuition behind the “top rate should be zero” result: The rich are so fantastically productive that it isn’t worth it to tax them. We simply can’t risk them working less.

But are the rich actually so fantastically productive? Are they really that smart? Do they really work that hard?

If Tony Stark were real, okay, don’t tax him. He is a one-man Singularity: He invented the perfect power source on his own, “in a cave, with a box of scraps!”; he created a true AI basically by himself; he single-handedly discovered a new stable island element and used it to make his already perfect power source even better.

But despite what his fanboys may tell you, Elon Musk is not Tony Stark. Tesla and SpaceX have done a lot of very good things, but in order to do they really didn’t need Elon Musk for much. Mainly, they needed his money. Give me $270 billion and I could make companies that build electric cars and launch rockets into space too. (Indeed, I probably would—though I’d also set up some charitable foundations as well, more like what Bill Gates did with his similarly mind-boggling wealth.)

Don’t get me wrong; Elon Musk is a very intelligent man, and he works, if anything, obsessively. (He makes his employees work excessively too—and that’s a problem.) But if he were to suddenly die, as long as a reasonably competent CEO replaced him, Tesla and SpaceX would go on working more or less as they already do. The spectacular productivity of these companies is not due to Musk alone, but thousands of highly-skilled employees. These people would be productive if Musk had not existed, and they will continue to be productive once Musk is gone.

And they aren’t particularly rich. They aren’t poor either, mind you—a typical engineer at Tesla or SpaceX is quite well-paid, and rightly so. (Median salary at SpaceX is over $115,000.) These people are brilliant, tremendously hard-working, and highly productive; and they get quite well-paid. But very few of these people are in the top 1%, and basically none of them will ever be billionaires—let alone the truly staggering wealth of a hectobillionaire like Musk himself.

How, then, does one become a billionaire? Not by being brilliant, hard-working, or productive—at least that is not sufficient, and the existence of, say, Donald Trump suggests that it is not necessary either. No, the really quintessential feature every billionaire has is remarkably simple and consistent across the board: They own a monopoly.

You can pretty much go down the list, finding what monopoly each billionaire owned: Bill Gates owned software patents on (what is still) the most widely-used OS and office suite in the world. J.K. Rowling owns copyrights on the most successful novels in history. Elon Musk owns technology patents on various innovations in energy storage and spaceflight technology—very few of which he himself invented, I might add. Andrew Carnegie owned the steel industry. John D. Rockefeller owned the oil industry. And so on.

I honestly can’t find any real exceptions: Basically every billionaire either owned a monopoly or inherited from ancestors who did. The closest things to exceptions are billionaire who did something even worse, like defrauding thousands of people, enslaving an indigenous population or running a nation with an iron fist. (And even then, Leopold II and Vladimir Putin both exerted a lot of monopoly power as part of their murderous tyranny.)

In other words, billionaire wealth is almost entirely rent. You don’t earn a billion dollars. You don’t get it by working. You get it by owning—and by using that ownership to exert monopoly power.

This means that taxing billionaire wealth wouldn’t incentivize them to work less; they already don’t work for their money. It would just incentivize them to fight less hard at extracting wealth from everyone else using their monopoly power—which hardly seems like a downside.

Since virtually all of the wealth at the top is simply rent, we have no reason not to tax it away. It isn’t genuine productivity at all; it’s just extracting wealth that other people produced.

Thus, my second, and ultimately most decisive reason for wanting strongly progressive taxes: rent-seeking. The very rich don’t actually deserve the vast majority of what they have, and we should take it back so that we can give it to people who really need and deserve it.

Now, there is a somewhat more charitable version of the view that high taxes even on the top 0.01% would hurt productivity, and it is worth addressing. That is based on the idea that entrepreneurship is valuable, and part of the incentive for becoming and entrepreneur is the chance at one day striking it fabulously rich, so taxing the fabulously rich might result in a world of fewer entrepreneurs.

This isn’t nearly as ridiculous as the idea that Elon Musk somehow works a million times as hard as the rest of us, but it’s still pretty easy to find flaws in it.

Suppose you were considering starting a business. Indeed, perhaps you already have considered it. What are your main deciding factors in whether or not you will?

Surely they do not include the difference between a 0.0001% chance of making $200 billion and a 0.0001% chance of making $50 billion. Indeed, that probably doesn’t factor in at all; you know you’ll almost certainly never get there, and even if you did, there’s basically no real difference in your way of life between $50 billion and $200 billion.

No, more likely they include things like this: (1) How likely are you to turn a profit at all? Even a profit of $50,000 per year would probably be enough to be worth it, but how sure are you that you can manage that? (2) How much funding can you get to start it in the first place? Depending on what sort of business you’re hoping to found, it could be as little as thousands or as much as millions of dollars to get it set up, well before it starts taking in any revenue. And even a few thousand is a lot for most middle-class people to come up with in one chunk and be willing to risk losing.

This means that there is a very simple policy we could implement which would dramatically increase entrepreneurship while taxing only billionaires more, and it goes like this: Add an extra 1% marginal tax to capital gains for billionaires, and plow it into a fund that gives grants of $10,000 to $100,000 to promising new startups.

That 1% tax could raise several billion dollars a year—yes, really; US billionaires gained some $2 trillion in capital gains last year, so we’d raise $20 billion—and thereby fund many, many startups. Say the average grant is $20,000 and the total revenue is $20 billion; that’s one million new startups funded every single year. Every single year! Currently, about 4 million new businesses are founded each year in the US (leading the world by a wide margin); this could raise that to 5 million.

So don’t tell me this is about incentivizing entrepreneurship. We could do that far better than we currently do, with some very simple policy changes.

Meanwhile, the economics literature on optimal taxation seems to be completely missing the point. Most of it is still mired in the assumption that the rich are rich because they are productive, and thus terribly concerned about the “trade-off” between efficiency and equity involved in higher taxes. But when you realize that the vast, vast majority—easily 99.9%—of billionaire wealth is unearned rents, then it becomes obvious that this trade-off is an illusion. We can improve efficiency and equity simultaneously, by taking some of this ludicrous hoard of unearned wealth and putting it back into productive activities, or giving it to the people who need it most. The only people who will be harmed by this are billionaires themselves, and by diminishing marginal utility of wealth, they won’t be harmed very much.

Fortunately, the tide is turning, and more economists are starting to see the light. One of the best examples comes from Piketty, Saez, and Stantcheva in their paper on how CEO “pay for luck” (e.g. stock options) respond to top tax rates. There are a few other papers that touch on similar issues, such as Lockwood, Nathanson, and Weyl and Rothschild and Scheuer. But there’s clearly a lot of space left for new work to be done. The old results that told us not to raise taxes were wrong on a deep, fundamental level, and we need to replace them with something better.

What if you couldn’t own land?

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JDN 2457145 EDT 20:49.

Today’s post we’re on the socialism scale somewhere near the The Guess Who, but not quite all the way to John Lennon. I’d like to questions one of the fundamental tenets of modern capitalism, but not the basic concept of private ownership itself:

What if you couldn’t own land?

Many things that you can own were more-or-less straightforwardly created by someone. A car, a computer, a television, a pair of shoes; for today let’s even take for granted intellectual property like books, movies, and songs; at least those things (“things”) were actually made by someone.

But land? We’re talking about chunks of the Earth here. They were here billions of years before us, and in all probability will be here billions of years after we’re gone. There’s no need to incentivize its creation; the vast majority of land was already here and did not need to be created. (I do have to say “the vast majority”, because in places like Japan, Hong Kong, and the Netherlands real estate has become so scarce that people do literally build land out into the sea. But this is something like 0.0001% of the world’s land.)

What we want to incentivize is land development; we want it to be profitable to build buildings and irrigate deserts, and yes, even cut down forests sometimes (though then there should be a carbon tax with credits for forested land to ensure that there isn’t too much incentive). Yet our current property tax system doesn’t do this very well; if you build bigger buildings, you end up paying more property taxes. Yes, you may also make some profit on the buildings—but it’s risky, and you may not get enough benefit to justify the added property taxes.

Moreover, we want to allocate land—we want some way of deciding who is allowed to use what land where and when (and perhaps why). Allowing land to be bought and sold is one way to do that, but it is not the only way.

Indeed, land ownership suffers from a couple of truly glaring flaws as an allocation system:

      1. It creates self-perpetuating inequality. Because land grows in value over time (due to population growth and urbanization, among other things), those who currently own land end up getting an ever-growing quantity of wealth while those who do not own land do not, and very likely end up having to pay ever-growing rents to the landlords. (I like calling them “landlords”; it really drives home the fact that our landholding system is still basically the same as it was under feudalism.) In fact, the recent rise in the share of income that goes to owners of capital rather than workers is almost entirely attributable to the rise in the price of real estate. As that post rightly recognizes, this does nothing to undermine Piketty’s central message of rising inequality due to capital income (pace The Washington Post); it merely tells us to focus on real estate instead of other forms of capital.
      2. It has no non-arbitrary allocation. If we want to decide who owns a car, we can ask questions like, “Who built it? Did someone buy it from them? Did they pay a fair price?”; if we want to decide who owns a book, we can ask questions like, “Who wrote it? Did they sell it to a publisher? What was the royalty rate?” That is, there is a clear original owner, and there is a sense of whether the transfer of ownership can be considered fair. But if we want to decide who owns a chunk of land, basically all we can ask is, “What does the deed say?” The owner is the owner because they are the owner; there’s no sense in which that ownership is fair. We certainly can’t go back to the original creation of the land, because that was due to natural forces gigayears ago. If we keep tracing the ownership backward, we will eventually end up with some guy (almost certainly a man, a White man in fact) with a gun who pointed that gun at other people and said, “This is mine.” This is true of basically all the land in the world (aside from those little bits of Japan and such); it was already there, and the only reason someone got to own it was because they said so and had a bigger gun. And a flag, perhaps: “Do you have a flag?” I suppose, in theory at least, there are a few ways of allocating land which seem less arbitrary: One would be to give everyone an equal amount. But this is practically very difficult: What do you do when the population changes? If you have 2% annual population growth, do you carve off 2% of everybody’s lot each year? Another would be to let people squat land, and automatically own the land that they live on—but again practical difficulties quickly become enormous. In any case, these two methods bear about as much resemblance to our actual allocation of land as a squirrel does to a Tyrannosaurus.

So, what else might we use? The system that makes the most sense to me is that we would own all land as a society. In practical terms this would mean that all land is Federal land, and if you want to use it for something, you need to pay rent to the government. There are many different ways the government could set the rent, but the most sensible might be to charge a flat rate per hectare regardless of where the land is or what it’s being used for, because that would maximize the incentive to develop the land. It would also make the rent fall entirely on the landowner, because the rent would be perfectly inelastic—meaning that you can’t change the quantity you make based on the price, because you aren’t making it; it’s just already sitting there.

Of course, this idea is obviously politically impossible in our current environment—or indeed any foreseeable political environment. I’m just fantasizing here, right?

Well, not quite. There is one thing we could do that would be economically quite similar to government-only land ownership; it’s called a land tax. The idea is incredibly simple: you just collect a flat tax per hectare of land. Economists have known that a land tax is efficient at providing revenue and reducing inequality since at least Adam Smith. So maybe ownership of land isn’t actually foundational to capitalism, after all; maybe we’ve just never fully gotten over feudalism. (I basically agree with Adam Smith, and for doing so I am often called a socialist.) The beautiful thing about a land tax is that it has a tax incidence in which the owners of the land end up bearing the full brunt of the tax.

Tax incidence is something it’s very important to understand; it would be on my list of the top ten economic principles that people should learn. We often have fierce political debates over who will actually write the check: Should employers pay the health insurance premium, or should employees? Will buyers pay sales tax, or sellers? Should we tax corporate profits or personal capital gains?

Please understand that I am not exaggerating when I say that these sorts of questions are totally irrelevant. It simply does not matter who actually writes the check; what matters is who bears the cost. Making the employer pay the health insurance premium doesn’t make the slightest difference if all they’re going to do is cut wages by the exact same amount. You can see the irrelevance of the fact that sellers pay sales tax every time you walk into a store—you always end up paying the price plus the tax, don’t you? (I found that the base price of most items was the same between Long Beach and Ann Arbor, but my total expenditure was always 3% more because of the 9% sales tax versus the 6%.) How do we determine who actually pays the tax? It depends on the elasticity—how easily can you change your behavior in order to avoid the tax? Can you find a different job because the health insurance premiums are too high? No? Then you’re probably paying that premium, even if your employer writes the check. If you can find a new job whenever you want, your employer might have to pay it for you even if you write the check.

The incidence of corporate taxes and taxes on capital gains are even more complicated, because it could affect the behavior of corporations in many different ways; indeed, many economists argue that the corporate tax simply results in higher unemployment or lower wages for workers. I don’t think that’s actually true, but I honestly can’t rule it out completely, precisely because corporate taxes are so complicated. You need to know all sorts of things about the structure of stock markets, and the freedom of trade, and the mobility of immigration… it’s a complete and total mess.

It’s because of tax incidence that a land tax makes so much sense; there’s no way for the landowner to escape it, other than giving up the land entirely. In particular, they can’t charge more for rent without being out-competed (unless landowners are really good at colluding—which might be true for large developers, but not individual landlords). Their elasticity is so low that they’re forced to bear the full cost of the tax.

If the land tax were high enough, it could eliminate the automatic growth in wealth that comes from holding land, and thereby reducing long-run inequality dramatically. The revenue could be used for my other favorite fiscal policy, the basic income—and real estate is a big enough part of our nation’s wealth that it’s actually entirely realistic to fund an $8,000 per person per year basic income entirely on land tax revenue. The total value of US land is about $14 trillion, and an $8,000 basic income for 320 million people would cost about $2.6 trillion; that’s only 19%. You’d actually want to make it a flat tax per hectare, so how much would that be? Well, 60% of US land is privately owned at present (no sense taxing the land the government already owns), and total US land area is about 9 million square kilometers, so to raise $2.5 trillion you’d need a tax of $289,000 per square kilometer, or $2,890 per hectare. If you own a hectare—which is bigger than most single-family lots—you’d only pay $2,890 per year in land tax, well within what most middle-class families could handle. But if you own 290,000 acres like Jeff Bezos, (that’s 117,000 hectares) you’re paying $338 million per year. Since Jeff Bezos has about $38 billion in net wealth, he can actually afford to pay that ($338 million per year is about one-tenth of what Jeff Bezos makes automatically on dividends), though he might consider selling off some of the land to avoid the taxes, which is exactly the sort of incentive we wanted to create.

Indeed, when I contemplate this policy I’m struck by the fact that it has basically no downside—usually in public policy you’re forced to make hard compromises and tradeoffs, but a land tax plus basic income is a system that carries almost no downsides at all. It won’t disincentivize investment, it won’t disincentivize working, it will dramatically reduce inequality, it will save the government a great deal of money on social welfare spending, and best of all it will eliminate poverty immediately and forever. The only people it would hurt at all are extremely rich, and they wouldn’t even be hurt very much, while it would benefit millions of people including some of the most needy.

Why aren’t we doing this already!?

No, capital taxes should not be zero

pnrj critique of neoclassical economics, public policy , , , , , , , , , , , , , , , , , , ,

JDN 2456998 PST 11:38.

It’s an astonishingly common notion among neoclassical economists that we should never tax capital gains, and all taxes should fall upon labor income. Here Scott Sumner writing for The Economist has the audacity to declare this a ‘basic principle of economics’. Many of the arguments are based on rather esoteric theorems like the Atkinson-Stiglitz Theorem (I thought you were better than that, Stiglitz!) and the Chamley-Judd Theorem.

All of these theorems rest upon two very important assumptions, which many economists take for granted—yet which are utterly and totally untrue. For once it’s not assumed that we are infinite identical psychopaths; actually psychopaths might not give wealth to their children in inheritance, which would undermine the argument in a different way, by making each individual have a finite time horizon. No, the assumptions are that saving is the source of investment, and investment is the source of capital income.

Investment is the source of capital, that’s definitely true—the total amount of wealth in society is determined by investment. You do have to account for the fact that real investment isn’t just factories and machines, it’s also education, healthcare, infrastructure. With that in mind, yes, absolutely, the total amount of wealth is a function of the investment rate.

But that doesn’t mean that investment is the source of capital income—because in our present system the distribution of capital income is in no way determined by real investment or the actual production of goods. Virtually all capital income comes from financial markets, which are rife with corruption—they are indeed the main source of corruption that remains in First World nations—and driven primarily by arbitrage and speculation, not real investment. Contrary to popular belief and economic theory, the stock market does not fund corporations; corporations fund the stock market. It’s this bizarre game our society plays, in which a certain portion of the real output of our productive industries is siphoned off so that people who are already rich can gamble over it. Any theory of capital income which fails to take these facts into account is going to be fundamentally distorted.

The other assumption is that investment is savings, that the way capital increases is by labor income that isn’t spent on consumption. This isn’t even close to true, and I never understood why so many economists think it is. The notion seems to be that there is a certain amount of money in the world, and what you don’t spend on consumption goods you can instead spend on investment. But this is just flatly not true; the money supply is dynamically flexible, and the primary means by which money is created is through banks creating loans for the purpose of investment. It’s that I term I talked about in my post on the deficit; it seems to come out of nowhere, because that’s literally what happens.

On the reasoning that savings is just labor income that you don’t spend on consumption, then if you compute the figure W – C , wages and salaries minus consumption, that figure should be savings, and it should be equal to investment. Well, that figure is negative—for reasons I gave in that post. Total employee compensation in the US in 2014 is $9.2 trillion, while total personal consumption expenditure is $11.4 trillion. The reason we are able to save at all is because of government transfers, which account for $2.5 trillion. To fill up our GDP to its total of $16.8 trillion, you need to add capital income: proprietor income ($1.4 trillion) and receipts on assets ($2.1 trillion); then you need to add in the part of government spending that isn’t transfers ($1.4 trillion).

If you start with the fanciful assumption that the way capital increases is by people being “thrifty” and choosing to save a larger proportion of their income, then it makes some sense not to tax capital income. (Scott Sumner makes exactly that argument, having us compare two brothers with equal income, one of whom chooses to save more.) But this is so fundamentally removed from how capital—and for that matter capitalism—actually operates that I have difficulty understanding why anyone could think that it is true.

The best I can come up with is something like this: They model the world by imagining that there is only one good, peanuts, and everyone starts with the same number of peanuts, and everyone has a choice to either eat their peanuts or save and replant them. Then, the total production of peanuts in the future will be due to the proportion of peanuts that were replanted today, and the amount of peanuts each person has will be due to their past decisions to save rather than consume. Therefore savings will be equal to investment and investment will be the source of capital income.

I bet you can already see the problem even in this simple model, if we just relax the assumption of equal wealth endowments: Some people have a lot more peanuts than others. Why do some people eat all their peanuts? Well it probably has something to do with the fact they’d starve if they didn’t. Reducing your consumption below the level at which you can survive isn’t “thrifty”, it’s suicidal. (And if you think this is a strawman, the IMF has literally told Third World countries that their problem is they need to save more. Here they are arguing that in Ghana.) In fact, economic growth leads to saving, not the other way around. Most Americans aren’t starving, and could probably stand to save more than we do, but honestly it might not be good if we did—everyone trying to save more can lead to the Paradox of Thrift and cause a recession.

Even worse, in that model world, there is only capital income. There is no such thing as labor income, only the number of peanuts you grow from last year’s planting. If we now add in labor income, what happens? Well, peanuts don’t work anymore… let’s try robots. You have a certain number of robots, and you can either use the robots to do things you need (including somehow feeding you, I guess), or you can use them to build more robots to use later. You can also build more robots yourself. Then the “zero capital tax” argument amounts to saying that the government should take some of your robots for public use if you made them yourself, but not if they were made by other robots you already had.

In order for that argument to carry through, you need to say that there was no such thing as an initial capital endowment; all robots that exist were either made by their owners or saved from previous construction. If there is anyone who simply happened to be born with more robots, or has more because they stole them from someone else (or, more likely, both, they inherited from someone who stole), the argument falls apart.

And even then you need to think about the incentives: If capital income is really all from savings, then taxing capital income provides an incentive to spend. Is that a bad thing? I feel like it isn’t; the economy needs spending. In the robot toy model, we’re giving people a reason to use their robots to do actual stuff, instead of just leaving them to make more robots. That actually seems like it might be a good thing, doesn’t it? More stuff gets done that helps people, instead of just having vast warehouses full of robots building other robots in the hopes that someday we can finally use them for something. Whereas, taxing labor income may give people an incentive not to work, which is definitely going to reduce economic output. More precisely, higher taxes on labor would give low-wage workers an incentive to work less, and give high-wage workers an incentive to work more, which is a major part of the justification of progressive income taxes. A lot of the models intended to illustrate the Chamley-Judd Theorem assume that taxes have an effect on capital but no effect on labor, which is kind of begging the question.

Another thought that occurred to me is: What if the robots in the warehouse are all destroyed by a war or an earthquake? And indeed the possibility of sudden capital destruction would be a good reason not to put everything into investment. This is generally modeled as “uninsurable depreciation risk”, but come on; of course it’s uninsurable. All real risk is uninsurable in the aggregate. Insurance redistributes resources from those who have them but don’t need them to those who suddenly find they need them but don’t have them. This actually does reduce the real risk in utility, but it certainly doesn’t reduce the real risk in terms of goods. Stephen Colbert made this point very well: “Obamacare needs the premiums of healthier people to cover the costs of sicker people. It’s a devious con that can only be described as—insurance.” (This suggests that Stephen Colbert understands insurance better than many economists.) Someone has to make that new car that you bought using your insurance when you totaled the last one. Insurance companies cannot create cars or houses—or robots—out of thin air. And as Piketty and Saez point out, uninsurable risk undermines the Chamley-Judd Theorem. Unlike all these other economists, Piketty and Saez actually understand capital and inequality.
Sumner hand-waves that point away by saying we should just institute a one-time transfer of wealth to equalized the initial distribution, as though this were somehow a practically (not to mention politically) feasible alternative. Ultimately, yes, I’d like to see something like that happen; restore the balance and then begin anew with a just system. But that’s exceedingly difficult to do, while raising the tax rate on capital gains is very easy—and furthermore if we leave the current stock market and derivatives market in place, we will not have a just system by any stretch of the imagination. Perhaps if we can actually create a system where new wealth is really due to your own efforts, where there is no such thing as inheritance of riches (say a 100% estate tax above $1 million), no such thing as poverty (a basic income), no speculation or arbitrage, and financial markets that actually have a single real interest rate and offer all the credit that everyone needs, maybe then you can say that we should not tax capital income.

Until then, we should tax capital income, probably at least as much as we tax labor income.

The moral—and economic—case for progressive taxation

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JDN 2456935 PDT 09:44.

Broadly speaking, there are three ways a tax system can be arranged: It can be flat, in which every person pays the same tax rate; it can be regressive, in which people with higher incomes pay lower rates; or it can be progressive, in which case people with higher incomes pay higher rates.

There are certain benefits to a flat tax: Above all, it’s extremely easy to calculate. It’s easy to determine how much revenue a given tax rate will raise; multiply the rate times your GDP. It’s also easy to determine how much a given person should owe; multiply the rate times their income. This also makes the tax withholding process much easier; a fixed proportion can be withheld from all income everyone makes without worrying about how much they made before or are expected to make later. If your goal is minimal bureaucracy, a flat tax does have something to be said for it.

A regressive tax, on the other hand, is just as complicated as a progressive tax but has none of the benefits. It’s unfair because you’re actually taking more from people who can afford the least. (Note that this is true even if the rich actually pay a higher total; the key point, which I will explain in detail shortly, is that a dollar is worth more to you if you don’t have very many.) There is basically no reason you would ever want to have a regressive tax system—and yet, all US states have regressive tax systems. This is mainly because they rely upon sales taxes, which are regressive because rich people spend a smaller portion of what they have. If you make $10,000 per year, you probably spend $9,500 (you may even spend $15,000 and rack up the difference in debt!). If you make $50,000, you probably spend $40,000. But if you make $10 million, you probably only spend $4 million. Since sales taxes only tax on what you spend, the rich effectively pay a lower rate. This could be corrected to some extent by raising the sales tax on luxury goods—say a 20% rate on wine and a 50% rate on yachts—but this is awkward and very few states even try. Not even my beloved California; they fear drawing the ire of wineries and Silicon Valley.

The best option is to make the tax system progressive. Thomas Piketty has been called a “Communist” for favoring strongly progressive taxation, but in fact most Americans—including Republicans—agree that our tax system should be progressive. (Most Americans also favor cutting the Department of Defense rather than Medicare. This then raises the question: Why isn’t Congress doing that? Why aren’t people voting in representatives to Congress who will do that?) Most people judge whether taxes are fair based on what they themselves pay—which is why, in surveys, the marginal rate on the top 1% is basically unrelated to whether people think taxes are too high, even though that one bracket is the critical decision in deciding any tax system—you can raise about 20% of your revenue by hurting about 1% of your people. In a typical sample of 1,000 respondents, only about 10 are in the top 1%. If you want to run for Congress, the implication is clear: Cut taxes on all but the top 1%, raise them enormously on the top 0.1%, 0.01%, and 0.001%, and leave the 1% the same. People will feel that you’ve made the taxes more fair, and you’ve also raised more revenue. In other words, make the tax system more progressive.

The good news on this front is that the US federal tax system is progressive—barely. Actually the US tax system is especially progressive over the whole distribution—by some measures the most progressive in the world—but the problem is that it’s not nearly progressive enough at the very top, where the real money is. The usual measure based on our Gini coefficient ignores the fact that Warren Buffett pays a lower rate than his secretary. The Gini is based on population, and billionaires are a tiny portion of the population—but they are not a tiny portion of the money. Net wealth of the 400 richest people (the top 0.0001%) adds up to about $2 trillion (13% of our $15 trillion GDP, or about 4% of our $54 trillion net wealth). It also matters of course how you spend your tax revenue; even though Sweden’s tax system is no more progressive than ours and their pre-tax inequality is about the same, their spending is much more targeted at reducing inequality.

Progressive taxation is inherently more fair, because the value of a dollar decreases the more you have. We call this diminishing marginal utility of wealth. There is a debate within the cognitive economics literature about just how quickly the marginal utility of wealth decreases. On the low end, Easterlin argues that it drops off extremely fast, becoming almost negligible as low as $75,000 per year. This paper is on the high end, arguing that marginal utility decreases “only” as the logarithm of how much you have. That’s what I’ll use in this post, because it’s the most conservative reasonable estimate. I actually think the truth is somewhere in between, with marginal utility decreasing about exponentially.

Logarithms are also really easy to work with, once you get used to them. So let’s say that the amount of happiness (utility) U you get from an amount of income I is like this: U = ln(I)

Now let’s suppose the IRS comes along and taxes your money at a rate r. We must have r < 1, or otherwise they’re trying to take money you don’t have. We don’t need to have r > 0; r < 0 would just mean that you receive more in transfers than you lose in taxes. For the poor we should have r < 0.

Now your happiness is U = ln((1-r)I).

By the magic of logarithms, this is U = ln(I) + ln(1-r).

If r is between 0 and 1, ln(1-r) is negative and you’re losing happiness. (If r < 0, you’re gaining happiness.) The amount of happiness you lose, ln(1-r), is independent of your income. So if your goal is to take a fixed amount of happiness, you should tax at a fixed rate of income—a flat tax.

But that really isn’t fair, is it? If I’m getting 100 utilons of happiness from my money and you’re only getting 2 utilons from your money, then taking that 1 utilon, while it hurts the same—that’s the whole point of utility—leaves you an awful lot worse off than I. It actually makes the ratio between us worse, going from 50 to 1, all the way up to 99 to 1.

Notice how if we had a regressive tax, it would be obviously unfair—we’d actually take more utility from poor people than rich people. I have 100 utilons, you have 2 utilons; the taxes take 1.5 of yours but only 0.5 of mine. That seems frankly outrageous; but it’s what all US states have.

Most of the money you have is ultimately dependent on your society. Let’s say you own a business and made your wealth selling products; it seems like you deserve to have that wealth, doesn’t it? (Don’t get me started on people who inherited their wealth!) Well, in order to do that, you need to have strong institutions of civil government; you need security against invasion; you need protection of property rights and control of crime; you need a customer base who can afford your products (that’s our problem in the Second Depression); you need workers who are healthy and skilled; you need a financial system that provides reliable credit (also a problem). I’m having trouble finding any good research on exactly what proportion of individual wealth is dependent upon the surrounding society, but let’s just say Bill Gates wouldn’t be spending billions fighting malaria in villages in Ghana if he had been born in a village in Ghana. It doesn’t matter how brilliant or determined or hard-working you are, if you live in a society that can’t support economic activity.

In other words, society is giving you a lot of happiness you wouldn’t otherwise have. Because of this, it makes sense that in order to pay for all that stuff society is doing for you (and maintain a stable monetary system), they would tax you according to how much happiness they’re giving you. Hence we shouldn’t tax your money at a constant rate; we should tax your utility at a constant rate and then convert back to money. This defines a new sort of “tax rate” which I’ll call p. Like our tax rate r, p needs to be less than 1, but it doesn’t need to be greater than 0.

Of the U = ln(I) utility you get from your money, you will get to keep U = (1-p) ln(I). Say it’s 10%; then if I have 100 utilons, they take 10 utilons and leave me with 90. If you have 2 utilons, they take 0.2 and leave you with 1.8. The ratio between us remains the same: 50 to 1.

What does this mean for the actual tax rate? It has to be progressive. Very progressive, as a matter of fact. And in particular, progressive all the way up—there is no maximum tax bracket.

The amount of money you had before is just I.

The amount of money you have now can be found as the amount of money I’ that gives you the right amount of utility. U = ln(I’) = (1-p) ln(I). Take the exponential of both sides: I’ = I^(1-p).

The units on this are a bit weird, “dollars to the 0.8 power”? Oddly, this rarely seems to bother economists when they use Cobb-Douglas functions which are like K^(1/3) L^(2/3). It bothers me though; to really make this tax system in practice you’d need to fix the units of measurement, probably using some subsistence level. Say that’s set at $10,000; instead of saying you make $2 million, we’d say you make 200 subsistence levels.

The tax rate you pay is then r = 1 – I’/I, which is r = 1 – I^-p. As I increases, I^-p decreases, so r gets closer and closer to 1. It never actually hits 1 (that would be a 100% tax rate, which hardly anyone thinks is fair), but for very large income is does get quite close.

Here, let’s use some actual numbers. Suppose as I said we make the subsistence level $10,000. Let’s also set p = 0.1, meaning we tax 10% of your utility. Then, if you make the US median individual income, that’s about $30,000 which would be I = 3. US per-capita GDP of $55,000 would be I = 5.5, and so on. I’ll ignore incomes below the subsistence level for now—basically what you want to do there is establish a basic income so that nobody is below the subsistence level.

I made a table of tax rates and after-tax incomes that would result:

Pre-tax income Tax rate After-tax income
$10,000 0.0% $10,000
$20,000 6.7% $18,661
$30,000 10.4% $26,879
$40,000 12.9% $34,822
$50,000 14.9% $42,567
$60,000 16.4% $50,158
$70,000 17.7% $57,622
$80,000 18.8% $64,980
$90,000 19.7% $72,247
$100,000 20.6% $79,433
$1,000,000 36.9% $630,957
$10,000,000 49.9% $5,011,872
$100,000,000 60.2% $39,810,717
$1,000,000,000 68.4% $316,227,766

What if that’s not enough revenue? We could raise to p = 0.2:

Pre-tax income Tax rate After-tax income
$10,000 0.0% $10,000
$20,000 12.9% $17,411
$30,000 19.7% $24,082
$40,000 24.2% $30,314
$50,000 27.5% $36,239
$60,000 30.1% $41,930
$70,000 32.2% $47,433
$80,000 34.0% $52,780
$90,000 35.6% $57,995
$100,000 36.9% $63,096
$1,000,000 60.2% $398,107
$10,000,000 74.9% $2,511,886
$100,000,000 84.2% $15,848,932
$1,000,000,000 90.0% $100,000,000

The richest 400 people in the US have a combined net wealth of about $2.2 trillion. If we assume that billionaires make about a 10% return on their net wealth, this 90% rate would raise over $200 billion just from those 400 billionaires alone, enough to pay all interest on the national debt. Let me say that again: This tax system would raise enough money from a group of people who could fit in a large lecture hall to provide for servicing the national debt. And it could do so indefinitely, because we are only taxing the interest, not the principal.

And what if that’s still not enough? We could raise it even further, to p = 0.3. Now the tax rates look a bit high for most people, but not absurdly so—and notice how the person at the poverty line is still paying nothing, as it should be. The millionaire is unhappy with 75%, but the billionaire is really unhappy with his 97% rate. But the government now has plenty of money.

Pre-tax income Tax rate After-tax income
$10,000 0.0% $10,000
$20,000 18.8% $16,245
$30,000 28.1% $21,577
$40,000 34.0% $26,390
$50,000 38.3% $30,852
$60,000 41.6% $35,051
$70,000 44.2% $39,045
$80,000 46.4% $42,871
$90,000 48.3% $46,555
$100,000 49.9% $50,119
$1,000,000 74.9% $251,189
$10,000,000 87.4% $1,258,925
$100,000,000 93.7% $6,309,573
$1,000,000,000 96.8% $31,622,777

Is it fair to tax the super-rich at such extreme rates? Well, why wouldn’t it be? They are living fabulously well, and most of their opportunity to do so is dependent upon living in our society. It’s actually not at all unreasonable to think that over 97% of the wealth a billionaire has is dependent upon society in this way—indeed, I think it’s unreasonable to imagine that it’s any less than 99.9%. If you say that the portion a billionaire receives from society is less than 99.9%, you are claiming that it is possible to become a millionaire while living on a desert island. (Remember, 0.1% of $1 billion is $1 million.) Forget the money system; do you really think that anything remotely like a millionaire standard of living is possible from catching your own fish and cutting down your own trees?Another fun fact is that this tax system will not change the ordering of income at all. If you were the 37,824th richest person yesterday, you will be the 37,824th richest person today; you’ll just have a lot less money while you do so. And if you were the 300,120,916th richest person, you’ll still be the 300,120,916th person, and probably still have the same amount of money you did before (or even more, if the basic income is doled out on tax day).

And these figures, remember, are based on a conservative estimate of how quickly the marginal utility of wealth decreases. I’m actually pretty well convinced that it’s much faster than that, in which case even these tax rates may not be progressive enough.

Many economists worry that taxes reduce the incentive to work. If you are taxed at 30%, that’s like having a wage that’s 30% lower. It’s not hard to imagine why someone might not work as much if they were being paid 30% less.

But there are actually two effects here. One is the substitution effect: a higher wage gives you more reason to work. The other is the income effect: having more money means that you can meet your needs without working as much.

For low incomes, the substitution effect dominates; if your pay rises from $12,000 a year to $15,000, you’re probably going to work more, because you get paid more to work and you’re still hardly wealthy enough to rest on your laurels.

For moderate incomes, the effects actually balance quite well; people who make $40,000 work about the same number of hours as people who make $50,000.

For high incomes, the income effect dominates; if your pay rises from $300,000 to $400,000, you’re probably going to work less, because you can pay all your bills while putting in less work.

So if you want to maximize work incentives, what should you do? You want to raise the wages of poor people and lower the wages of rich people. In other words, you want very low—or negative—taxes on the lower brackets, and very high taxes on the upper brackets. If you’re genuinely worried about taxes distorting incentives to work, you should be absolutely in favor of progressive taxation.

In conclusion: Because money is worth less to you the more of it you have, in order to take a fixed proportion of the happiness, we should be taking an increasing proportion of the money. In order to be fair in terms of real utility, taxes should be progressive. And this would actually increase work incentives.