income effect

Is a job guarantee better than a basic income?

pnrj ethics, futurism, inequality, macroeconomics, market failure, public policy , , , , , , , , , , , ,

Aug 5 JDN 2458336

In previous posts I’ve written about both the possibilities and challenges involved in creating a universal basic income. Today I’d like to address what I consider the most serious counter-argument against a basic income, an alternative proposal known as a job guarantee.

Whereas a basic income is literally just giving everyone free money, a job guarantee entails offering everyone who wants to work a job paid by the government. They’re not necessarily contradictory, but I’ve noticed a clear pattern: While basic income proponents are generally open to the idea of a job guarantee on the side, job guarantee proponents are often vociferously opposed to a basic income—even calling it “sinister”. I think the reason for this is that we see jobs as irrelevant, so we’re okay with throwing them in if you feel you must, while they see jobs as essential, so they meet any attempt to remove them with overwhelming resistance.

Where a basic income is extremely simple and could be implemented by a single act of the legislature, a job guarantee is considerably more complicated. The usual proposal for a job guarantee involves federal funding but local implementation, which is how most of our social welfare system is implemented—and why social welfare programs are so much better in liberal states like California than in conservative states like Mississippi, because California actually believes in what it’s implementing and Mississippi doesn’t. Anyone who wants a job guarantee needs to take that aspect seriously: In the places where poverty is worst, you’re offering control over the policy to the very governments that made poverty worst—and whether it is by malice or incompetence, what makes you think that won’t continue?

Another argument that I think job guarantee proponents don’t take seriously enough is the concern about “make-work”. They insist that a job guarantee is not “make-work”, but real work that’s just somehow not being done. They seem to think that there are a huge number of jobs that we could just create at the snap of a finger, which would be both necessary and useful on the one hand, and a perfect match for the existing skills of the unemployed population on the other hand. If that were the case, we would already be creating those jobs. It doesn’t even require a particularly strong faith in capitalism to understand this: If there is a profit to be made at hiring people to do something, there is probably already a business hiring people to do that. I don’t think of myself as someone with an overriding faith in capitalism, but a lot of the socialist arguments for job guarantees make me feel that way by comparison: They seem to think that there’s this huge untapped reserve of necessary work that the market is somehow failing to provide, and I’m just not seeing it.

There are public goods projects which aren’t profitable but would still be socially beneficial, like building rail lines and cleaning up rivers. But proponents of a job guarantee don’t seem to understand that these are almost all highly specialized jobs at our level of technology. We don’t need a bunch of people with shovels. We need engineers and welders and ecologists.

If you propose using people with shovels where engineers would be more efficient, that is make-work, whether you admit it or not. If you’re making people work in a less-efficient way in order to create jobs, then the jobs you are creating are fake jobs that aren’t worth creating. The line is often credited to Milton Friedman, but actually said first by William Aberhart in 1935:

Taking up the policy of a public works program as a solution for unemployment, it was criticized as a plan that took no account of the part that machinery played in modern construction, with a road-making machine instanced as an example. He saw, said Mr. Aberhart, work in progress at an airport and was told that the men were given picks and shovels in order to lengthen the work, to which he replied why not give them spoons and forks instead of picks and shovels if the object was to lengthen out the task.

I’m all for spending more on building rail lines and cleaning up rivers, but that’s not an anti-poverty program. The people who need the most help are precisely the ones who are least qualified to work on these projects: Children, old people, people with severe disabilities. Job guarantee proponents either don’t understand this fact or intentionally ignore it. If you aren’t finding jobs for 7-year-olds with autism and 70-year-olds with Parkinson’s disease, this program will not end poverty. And if you are, I find it really hard to believe that these are real, productive jobs and not useless “make-work”. A basic income would let the 7-year-olds stay in school and the 70-year-olds live in retirement homes—and keep them both out of poverty.

Another really baffling argument for a job guarantee over basic income is that a basic income would act as a wage subsidy, encouraging employers to reduce wages. That’s not how a basic income works. Not at all. A basic income would provide a pure income effect, necessarily increasing wage demands. People would not be as desperate for work, so they’d be more comfortable turning down unreasonable wage offers. A basic income would also incentivize some people to leave the labor force by retiring or going back to school; the reduction in labor supply would further increase wages. The Earned Income Tax Credit is in many respects similar to a wage subsidy. While superficially it might seem similar, a basic income would have the exact opposite effect.

One reasonable argument against a basic income is the possibility that it could cause inflation. This is something that can’t really be tested with small-scale experiments, so we really won’t know for sure until we try it. But there is reason to think that the inflation would be small, as the people removed from the labor force will largely be the ones who are least-productive to begin with. There is a growing body of empirical evidence suggesting that inflationary effects of a basic income would be small. For example, data on cash transfer programs in Mexico show only a small inflationary effect despite large reductions in poverty. The whole reason a basic income looks attractive is that automation technology is now so advanced is that we really don’t need everyone to be working anymore. Productivity is so high now that a policy of universal 40-hour work weeks just doesn’t make sense in the 21st century.

Probably the best argument for a job guarantee over a basic income concerns cost. A basic income is very expensive, there’s no doubt about that; and a job guarantee could be much cheaper. That is something I take very seriously: Saving $1.5 trillion a year is absolutely a good reason. Indeed, I don’t really object to this argument; the calculations are correct. I merely think that a basic income is enough better that its higher cost is justifiable. A job guarantee can eliminate unemployment, but not poverty.

But the argument for a job guarantee that most people seem to be find most compelling concerns meaning. The philosopher John Danaher expressed this one most cogently. Unemployment is an extremely painful experience for most people, far beyond what could be explained simply by their financial circumstances. Most people who win large sums of money in the lottery cut back their hours, but continue working—so work itself seems to have some value. What seems to happen is that when people lose the chance to work, they feel that they have lost a vital source of meaning in their lives.

Yet this raises two more questions:

First, would a job guarantee actually solve that problem?
Second, are there ways we could solve it under a basic income?

With regard to the first question, I want to re-emphasize the fact that a large proportion of these guaranteed jobs necessarily cannot be genuinely efficient production. If efficient production would have created these jobs, we would most likely already have created them. Our society does not suffer from an enormous quantity of necessary work that could be done with the skills already possessed by the unemployed population, which is somehow not getting done—indeed, it is essentially impossible for a capitalist economy with a highly-liquid financial system to suffer such a malady. If the work is so valuable, someone will probably take out a loan to hire someone to do it. If that’s not happening, either the unemployed people don’t have the necessary skills, or the work really can’t be all that productive. There are some public goods projects that would be beneficial but aren’t being done, but that’s a different problem, and the match between the public goods projects that need done and the skills of the unemployed population is extremely poor. Displaced coal miners aren’t useful for maintaining automated photovoltaic factories. Truckers who get replaced by robot trucks won’t be much good for building maglev rails.

With this in mind, it’s not clear to me that people would really be able to find much meaning in a guaranteed job. You can’t be fired, so the fact that you have the job doesn’t mean anyone is impressed by the quality of your work. Your work wasn’t actually necessary, or the private sector would already have hired someone to do it. The government went out of its way to find a job that precisely matched what you happen to be good at, regardless of whether that job was actually accomplishing anything to benefit society. How is that any better than not working at all? You are spending hours of drudgery to accomplish… what, exactly? If our goal was simply to occupy people’s time, we could do that with Netflix or video games.

With regard to the second question, note that a basic income is quite different from other social welfare programs in that everyone gets it. So it’s very difficult to attach a social stigma to receiving basic income payments—it would require attaching the stigma to literally everyone. Much of the lost meaning, I suspect, from being unemployed comes from the social stigma attached.

Now, it’s still possible to attach social stigma to people who only get the basic income—there isn’t much we can do to prevent that. But in the worst-case scenario, this means unemployed people get the same stigma as before but more money. Moreover, it’s much harder to detect a basic income recipient than, say, someone who eats at a soup kitchen or buys food using EBT; since it goes in your checking account, all everyone else sees is you spending money from your debit card, just like everyone else. People who know you personally would probably know; but people who know you personally are also less likely to destroy your well-being by imposing a high stigma. Maybe they’ll pressure you to get off the couch and get a job, but they’ll do so because they genuinely want to help you, not because they think you are “one of those lazy freeloaders”.

And, as BIEN points out, think about retired people: They don’t seem to be so unhappy. Being on basic income is more like being retired than like being unemployed. It’s something everyone gets, not some special handout for “those people”. It’s permanent, so it’s not like you need to scramble to get a job before it goes away. You just get money automatically, so you don’t have to navigate a complex bureaucracy to get it. Controlling for income, retired people don’t seem to be any less happy than working people—so maybe work doesn’t actually provide all that much meaning after all.

I guess I can’t rule out the possibility that people need jobs to find meaning in their lives, but I both hope and believe that this is not generally the case. You can find meaning in your family, your friends, your community, your hobbies. You can still work even if you don’t need to work for a living: Build a shed, mow your lawn, tune up your car, upgrade your computer, write a story, learn a musical instrument, or try your hand at painting.

If you need to be taking orders from a corporation five days a week in order to have meaning in your life, you have bigger problems. I think what has happened to many people is that employment has so drained their lives of the real sources of meaning that they cling to it as the only thing they have left. But in fact work is not the cure to your ennui—it is the cause of it. Finally being free of the endless toil that has plagued humanity since the dawn of our species will give you the chance to reconnect with what really matters in life. Show your children that you love them in person, to their faces, instead of in this painfully indirect way of “providing for” them by going to work every day. Find ways to apply your skills in volunteering or creating works of art, instead of in endless drudgery for the profit of some faceless corporation.

We do not benefit from economic injustice.

pnrj development economics, ethics, public policy, Uncategorized , , , , , , , , , , , , , , , , , , , , ,

JDN 2457461

Recently I think I figured out why so many middle-class White Americans express so much guilt about global injustice: A lot of people seem to think that we actually benefit from it. Thus, they feel caught between a rock and a hard place; conquering injustice would mean undermining their own already precarious standard of living, while leaving it in place is unconscionable.

The compromise, is apparently to feel really, really guilty about it, constantly tell people to “check their privilege” in this bizarre form of trendy autoflagellation, and then… never really get around to doing anything about the injustice.

(I guess that’s better than the conservative interpretation, which seems to be that since we benefit from this, we should keep doing it, and make sure we elect big, strong leaders who will make that happen.)

So let me tell you in no uncertain words: You do not benefit from this.

If anyone does—and as I’ll get to in a moment, that is not even necessarily true—then it is the billionaires who own the multinational corporations that orchestrate these abuses. Billionaires and billionaires only stand to gain from the exploitation of workers in the US, China, and everywhere else.

How do I know this with such certainty? Allow me to explain.

First of all, it is a common perception that prices of goods would be unattainably high if they were not produced on the backs of sweatshop workers. This perception is mistaken. The primary effect of the exploitation is simply to raise the profits of the corporation; there is a secondary effect of raising the price a moderate amount; and even this would be overwhelmed by the long-run dynamic effect of the increased consumer spending if workers were paid fairly.

Let’s take an iPad, for example. The price of iPads varies around the world in a combination of purchasing power parity and outright price discrimination; but the top model almost never sells for less than $500. The raw material expenditure involved in producing one is about $370—and the labor expenditure? Just $11. Not $110; $11. If it had been $110, the price could still be kept under $500 and turn a profit; it would simply be much smaller. That is, even if prices are really so elastic that Americans would refuse to buy an iPad at any more than $500 that would still mean Apple could still afford to raise the wages they pay (or rather, their subcontractors pay) workers by an order of magnitude. A worker who currently works 50 hours a week for $10 per day could now make $10 per hour. And the price would not have to change; Apple would simply lose profit, which is why they don’t do this. In the absence of pressure to the contrary, corporations will do whatever they can to maximize profits.

Now, in fact, the price probably would go up, because Apple fans are among the most inelastic technology consumers in the world. But suppose it went up to $600, which would mean a 1:1 absorption of these higher labor expenditures into price. Does that really sound like “Americans could never afford this”? A few people right on the edge might decide they couldn’t buy it at that price, but it wouldn’t be very many—indeed, like any well-managed monopoly, Apple knows to stop raising the price at the point where they start losing more revenue than they gain.

Similarly, half the price of an iPhone is pure profit for Apple, and only 2% goes into labor. Once again, wages could be raised by an order of magnitude and the price would not need to change.

Apple is a particularly obvious example, but it’s quite simple to see why exploitative labor cannot be the source of improved economic efficiency. Paying workers less does not make them do better work. Treating people more harshly does not improve their performance. Quite the opposite: People work much harder when they are treated well. In addition, at the levels of income we’re talking about, small improvements in wages would result in substantial improvements in worker health, further improving performance. Finally, substitution effect dominates income effect at low incomes. At very high incomes, income effect can dominate substitution effect, so higher wages might result in less work—but it is precisely when we’re talking about poor people that it makes the least sense to say they would work less if you paid them more and treated them better.

At most, paying higher wages can redistribute existing wealth, if we assume that the total amount of wealth does not increase. So it’s theoretically possible that paying higher wages to sweatshop workers would result in them getting some of the stuff that we currently have (essentially by a price mechanism where the things we want get more expensive, but our own wages don’t go up). But in fact our wages are most likely too low as well—wages in the US have become unlinked from productivity, around the time of Reagan—so there’s reason to think that a more just system would improve our standard of living also. Where would all the extra wealth come from? Well, there’s an awful lot of room at the top.

The top 1% in the US own 35% of net wealth, about as much as the bottom 95%. The 400 billionaires of the Forbes list have more wealth than the entire African-American population combined. (We’re double-counting Oprah—but that’s it, she’s the only African-American billionaire in the US.) So even assuming that the total amount of wealth remains constant (which is too conservative, as I’ll get to in a moment), improving global labor standards wouldn’t need to pull any wealth from the middle class; it could get plenty just from the top 0.01%.

In surveys, most Americans are willing to pay more for goods in order to improve labor standards—and the amounts that people are willing to pay, while they may seem small (on the order of 10% to 20% more), are in fact clearly enough that they could substantially increase the wages of sweatshop workers. The biggest problem is that corporations are so good at covering their tracks that it’s difficult to know whether you are really supporting higher labor standards. The multiple layers of international subcontractors make things even more complicated; the people who directly decide the wages are not the people who ultimately profit from them, because subcontractors are competitive while the multinationals that control them are monopsonists.

But for now I’m not going to deal with the thorny question of how we can actually regulate multinational corporations to stop them from using sweatshops. Right now, I just really want to get everyone on the same page and be absolutely clear about cui bono. If there is a benefit at all, it’s not going to you and me.

Why do I keep saying “if”? As so many people will ask me: “Isn’t it obvious that if one person gets less money, someone else must get more?” If you’ve been following my blog at all, you know that the answer is no.

On a single transaction, with everything else held constant, that is true. But we’re not talking about a single transaction. We’re talking about a system of global markets. Indeed, we’re not really talking about money at all; we’re talking about wealth.

By paying their workers so little that those workers can barely survive, corporations are making it impossible for those workers to go out and buy things of their own. Since the costs of higher wages are concentrated in one corporation while the benefits of higher wages are spread out across society, there is a Tragedy of the Commons where each corporation acting in its own self-interest undermines the consumer base that would have benefited all corporations (not to mention people who don’t own corporations). It does depend on some parameters we haven’t measured very precisely, but under a wide range of plausible values, it works out that literally everyone is worse off under this system than they would have been under a system of fair wages.

This is not simply theoretical. We have empirical data about what happened when companies (in the US at least) stopped using an even more extreme form of labor exploitation: slavery.

Because we were on the classical gold standard, GDP growth in the US in the 19th century was extremely erratic, jumping up and down as high as 10 lp and as low as -5 lp. But if you try to smooth out this roller-coaster business cycle, you can see that our growth rate did not appear tobe slowed by the ending of slavery:

US_GDP_growth_1800s

 

Looking at the level of real per capita GDP (on a log scale) shows a continuous growth trend as if nothing had changed at all:

US_GDP_per_capita_1800s

In fact, if you average the growth rates (in log points, averaging makes sense) from 1800 to 1860 as antebellum and from 1865 to 1900 as postbellum, you find that the antebellum growth rate averaged 1.04 lp, while the postbellum growth rate averaged 1.77 lp. Over a period of 50 years, that’s the difference between growing by a factor of 1.7 and growing by a factor of 2.4. Of course, there were a lot of other factors involved besides the end of slavery—but at the very least it seems clear that ending slavery did not reduce economic growth, which it would have if slavery were actually an efficient economic system.

This is a different question from whether slaveowners were irrational in continuing to own slaves. Purely on the basis of individual profit, it was most likely rational to own slaves. But the broader effects on the economic system as a whole were strongly negative. I think that part of why the debate on whether slavery is economically inefficient has never been settled is a confusion between these two questions. One side says “Slavery damaged overall economic growth.” The other says “But owning slaves produced a rate of return for investors as high as manufacturing!” Yeah, those… aren’t answering the same question. They are in fact probably both true. Something can be highly profitable for individuals while still being tremendously damaging to society.

I don’t mean to imply that sweatshops are as bad as slavery; they are not. (Though there is still slavery in the world, and some sweatshops tread a fine line.) What I’m saying is that showing that sweatshops are profitable (no doubt there) or even that they are better than most of the alternatives for their workers (probably true in most cases) does not show that they are economically efficient. Sweatshops are beneficent exploitation—they make workers better off, but in an obviously unjust way. And they only make workers better off compared to the current alternatives; if they were replaced with industries paying fair wages, workers would obviously be much better off still.

And my point is, so would we. While the prices of goods would increase slightly in the short run, in the long run the increased consumer spending by people in Third World countries—which soon would cease to be Third World countries, as happened in Korea and Japan—would result in additional trade with us that would raise our standard of living, not lower it. The only people it is even plausible to think would be harmed are the billionaires who own our multinational corporations; and yet even they might stand to benefit from the improved efficiency of the global economy.

No, you do not benefit from sweatshops. So stop feeling guilty, stop worrying so much about “checking your privilege”—and let’s get out there and do something about it.

The moral—and economic—case for progressive taxation

pnrj public policy, Top 10 things to know about economics , , , , , , , , , , , , , ,

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.