Just how rich is rich?

May 26 JDN 2458630

I think if there is one single thing I would like more people to know about economics, it is the sheer magnitude of global inequality. Most people seem to have no idea just how rich some people are—and how poor so many others are. They have a vision in their head of what “rich” and “poor” are, and their “rich” is a low-level Wall Street trader making $400,000 a year (the kind of people Gordon Gekko mocks in the film), and “poor” is someone who lives under a bridge in New York City. (They’re both New Yorkers, I guess. New Yorkers seem to be the iconic Americans, which is honestly more representative than you might think—80% of Americans live in urban or suburban areas.)

If we take a global perspective, this is not what “rich” and “poor” truly mean.

In next week’s post I’ll talk about what “poor” means. It’s really appallingly bad. We have to leave the First World in order to find it; many people here are poor, but not that poor. It’s so bad that I think once you really understand it, it can’t but change your whole outlook on the world. But I’m saving that for next week.

This week, I’ll talk about what “rich” really means in today’s world. We needn’t leave the United States, for the top 3 and 6 of the top 10 richest people in the world live here. And they are all White men, by the way, though Carlos Slim and Amancio Ortega are at least Latino.

Going down the list of billionaires ranked by wealth, you have to get down to 15th place before encountering a woman, and it’s really worse than that, because Francoise Bettencourt (15), Alice Walton (17), Jacqueline Mars (33), Yang Huiyan (42), Susan Klatton (46), Laurena Powell-Jobs (54), Abigail Johnson (71), and Iris Fontbona (74) are all heirs. The richest living woman who didn’t simply inherit from her father or husband is actually Gina Rinehart, the 75th richest person in the world. (And note that, while also in some sense an heir, Queen Elizabeth is not on that list; in fact, she’s nowhere near the richest people in the world. She’s not in the top 500.)

You have to get to 20th place before encountering someone non-White (Ma Huateng), and all the way down to 65th before encountering someone not White or East Asian (the Hinduja brothers). Not one of the top 100 richest people is Black.

Just how rich are these people? Well, there’s a meme going around saying that Jeff Bezos could afford to buy every homeless person in the world a house at median market price and still, with just what’s left over, be a multi-billionaire among the top 100 richest people in the world.

And that meme is completely correct. The math checks out.

There are about 554,000 homeless people in the US at any given time.

The median sale price of a currently existing house in the US is about $253,000.

Multiply those two numbers together, and you get $140 billion.

And Jeff Bezos has net wealth of $157 billion.

This means that he would still have $17 billion left after buying all those houses. The 100th richest person in the world has $13 billion, so Jeff Bezos would still be higher than that.

Even $17 billion is enough to spend over $2 million every single day—over $20 per second—and never run out of money as long as the dividends keep paying out.

Jeff Bezos in fact made so much in dividends and capital gains this past quarter that he was taking in as much money as the median Amazon employee’s annual salary—which is more than what I make as a grad student, and only slightly less than the median US individual incomeevery nine seconds. Yes, you read that correctly: Nine (9) seconds. In the time it took you to read this paragraph, Jeff Bezos probably received more in capital gains than you will make this whole year. And if not (because you’re relatively rich or you read quickly), I’m sure he will have in the time it takes you to read this whole post.

When Mitt Romney ran for President, a great deal was made of his net wealth of over $250 million. This is indeed very rich, richer than anyone really needs or probably deserves. But compared to the world’s richest, this is pocket change. Jeff Bezos gets that much in dividends and capital gains every day. Bill Gates could give away that much every day for a year and still not run out of money. (He doesn’t quite give that much, but he does give a lot.)

I grew up in Ann Arbor, Michigan. Ann Arbor is a medium-sized city of about 120,000 people (230th in the US by population), and relatively well-off (median household income about 16% higher than the US median). Nevertheless, if Jeff Bezos wanted to, he could give every single person in Ann Arbor the equivalent of 30 years of their income—over a million dollars each—and still have enough money left to be among the world’s 100 richest people.

Or suppose instead that all the world’s 500 richest people decided to give away all the money they have above $1 billion—so they’d all still be billionaires, but only barely. That $8.7 trillion they have together, minus the $500 billion they’re keeping, would be $8.2 trillion. In fact, let’s say they keep a little more, just to make sure they all have the same ordering: Give each one an extra $1 million for each point they are in the ranking, so that Jeff Bezos would stay on top at $1 B + 500 ($0.001 B) = $1.5 billion, while Bill Gates in second place would have $1 million less, and so on. That would leave us with still over $8 trillion to give away.

How far could that $8 trillion go? Well, suppose we divided it evenly between all 328 million people in the United States. How much would each person receive? Oh, just about $24,000—basically my annual income.

Or suppose instead we spread it out over the entire world: Every single man, woman, and child on the planet Earth gets an equal share. There are 7.7 billion people in the world, so by spreading out $8 trillion between them, each one would get over $1000. For you or I that’s a big enough windfall to feel. For the world’s poorest people, it’s more than they make in several years. It would be life-changing for them. (Actually that’s about what GiveDirectly gives each family—and it is life-changing.)

And let me remind you: This would be leaving them billionaires. They’re just not as much billionaires as before—they only have $1 billion instead of $20 billion or $50 billion or $100 billion. And even $1 billion is obviously enough to live however you want, wherever you want, for the rest of your life, never working another day if you don’t want to. With $1 billion, you can fly in jets (a good one will set you back $20 million), sail in yachts (even a massive 200-footer wouldn’t run much above $200 million), and eat filet mignon at every meal (in fact, at $25 per pound, you can serve it to yourself and a hundred of your friends without breaking a sweat). You can decorate your bedroom with original Jackson Pollock paintings (at $200 million, his most expensive painting is only 20% of your wealth) and bathe in bottles of Dom Perignon (at $400 per liter, a 200-liter bath would cost you about $80,000—even every day that’s only $30 million a year, or maybe half to a third of your capital income). Remember, this is all feasible at just $1 billion—and Jeff Bezos has over a hundred times that. There is no real lifestyle improvement that happens between $1 billion and $157 billion; it’s purely a matter of status and power.

Taking enough to make them mere millionaires would give us another $0.5 trillion to spend (about the GDP of Sweden, one-fourth the GDP of Canada, or 70% of the US military budget).

Do you think maybe these people have too much money?

I’m not saying that we should confiscate all private property. I’m not saying that we should collectivize all industry. I believe in free markets and private enterprise. People should be able to get rich by inventing things and starting businesses.

But should they be able to get that rich? So rich that one man could pay off every mortgage in a whole major city? So rich that the CEO of a company makes what his employees make in a year in less than a minute? So rich that 500 people—enough to fill a large lecture hall—own enough wealth that if it were spread out evenly they could give $1000 to every single person in the world?

If Jeff Bezos had $1.5 million, I’d say he absolutely earned it. Some high-level programmers at Amazon have that much, and they absolutely earned it. If he had $15 million, I’d think maybe he could deserve that, given his contribution to the world. If he had $150 million, I’d find it hard to believe that anyone could really deserve that much, but if it’s part of what we need to make capitalism work, I could live with that.

But Jeff Bezos doesn’t have $1.5 million. He doesn’t have $15 million. He doesn’t have $150 million. He doesn’t have $1.5 billion. He doesn’t even have $15 billion. He has $150 billion. He has over a thousand times the level of wealth at which I was already having to doubt whether any human being could possibly deserve so much money—and once it gets that big, it basically just keeps growing. A stock market crash might drop it down temporarily, but it would come back in a few years.

And it’s not like there’s nothing we could do to spread this wealth around. Some fairly simple changes in how we tax dividends and capital gains would be enough to get a lot of it, and a wealth tax like the one Elizabeth Warren has proposed would help a great deal as well. At the rates people have seriously proposed, these taxes would only really stop their wealth from growing; it wouldn’t meaningfully shrink it.

That could be combined with policy changes about compensation for corporate executives, particularly with regard to stock options, to make it harder to extract such a large proportion of a huge multinational corporation’s wealth into a single individual. We could impose a cap on the ratio between median employee salary (including the entire supply chain!) and total executive compensation (including dividends and capital gains!), say 100 to 1. (Making in 9 seconds what his employees make in a year, Jeff Bezos is currently operating at a ratio of over 3 million to 1.) If you exceed the cap, the remainder is taxed at 100%. This would mean that as a CEO you can still make $100 million a year, but only if your median employee makes $1 million. If your median employee makes $30,000, you’d better keep your own compensation under $3 million, because we’re gonna take the rest.

Is this socialism? I guess maybe it’s democratic socialism, the high-tax, high-spend #ScandinaviaIsBetter welfare state. But it would not be an end to free markets or free enterprise. We’re not collectivizing any industries, let alone putting anyone in guillotines. You could still start a business and make millions or even hundreds of millions of dollars; you’d simply be expected to share that wealth with your employees and our society as a whole, instead of hoarding it all for yourself.

Why does nobody want to become a teacher?

JDN 2457366

The United States is currently suffering a large and growing shortage of qualified teachers, particularly in grades K-12. In some particular areas, this shortage is extremely acute; high schools are not able to teach some courses because there is simply no one qualified to teach them. Science and math teachers are in particularly high demand, because these programs are being expanded even as the people qualified to teach them are shifting over to working at the college level or in the private sector.

Other countries are also suffering severe teacher shortages, including the UK and several other countries in the EU.
The problem is projected to get worse: Enrollments in teacher training are rapidly declining. Meanwhile, because somewhere along the way people got convinced that the problem with education is that our teachers aren’t smart enough (this is completely, totally wrong by the way), standards for becoming a teacher are becoming ever more stringent, narrowing the pool even more.

This is a very serious problem, because education—often called “human capital investment” in economic jargon—is one of the most important investments any society can make. Indeed, it may be the most important, the one factor of production that is absolutely indispensable. If you run out of one raw material, you can make products out of something else. Manual labor can be replaced by machines. If you don’t have enough machines, you can build more. But if you find yourself without anyone who knows how to read and do arithmetic, how are you going to replace that? If we imagine a scenario like being trapped on a desert island or colonizing Mars where we have to start from scratch and we are only allowed to have one factor of production, education is the one we would want to have. (I guess if it’s Mars you do need a certain bare minimum of physical capital, like a spacesuit.)

The teacher shortage is most acute in high-poverty areas, where educational outcomes are terrible. Indeed, the most important cause of the failings of the US education system has always been poverty.

Why are teachers in poor schools so underqualified? Because their working conditions are terrible. Turnover is extremely high because teachers are underpaid, the schools are undersupplied, and their administrators do not support them.

Why are there so many teachers not qualified to teach their subjects? Because people who are qualified can find better jobs in other places. Jobs just as rewarding, that make just as large a contribution to society, which are more pleasant, offer more autonomy, and pay a lot better.

If you are an expert in physics, you could become a physicist and make a median income of $106,000.

If you are an expert in economics, you could become an economist and make a median income of $92,000.

If you are an expert in biology, you could become a biochemist and make a median income of $81,000.

Or, instead of all those things, you could become a high school teacher and make a median income of $55,000. Gee, I wonder which one you’re going to do?

Keep that in mind if it sounds ridiculous to you to pay teachers $100,000 salaries.

Even in wealthy schools, teachers are miserable; I have this on direct testimony from my father, who has taught high school in Ann Arbor for almost 20 years now. There are a lot of teachers who believe in making a difference through education, but quickly become burnt out and leave for better working conditions.

I know in my own case that I’m not planning on teaching high school, even though I know I’d be very good at it and I’ve always found teaching very rewarding. I’d actually be qualified to teach several subjects, from mathematics to social studies and even including physics and Latin. Any public school would be thrilled to have me—but probably not thrilled enough to pay me as much as I’d get from a university, international institution, or policy think-tank. So it’s hard for me to justify the career decision of going into public education.

The absolute highest-paid teacher in the Ann Arbor Public Schools is paid $109,000 gross—and Ann Arbor is one of the highest-paying school systems in the nation, and not coincidentally also one of the best. Most of the professors at the University of Michigan are paid over $100,000 gross and some are paid over $300,000. (As a public school, the University of Michigan releases all its salaries.)

So, you’re living in Ann Arbor… you have a graduate degree… you want to work in education; you could either start at $40,000 and maybe work your way up to $100,000 by teaching high school, or you could start at $100,000 and maybe work your way up to $300,000 by teaching college. (Admittedly, to teach in college you generally also need to do research work and probably get a PhD; so it’s not quite an equal comparison. But the most-qualified educators would be good at either job.)

Economics, along with most science and math fields, pays particularly well outside education. This senior economist position at the World Bank pays at grade GG, which is a minimum starting net salary of $102,000.
How can we solve our teacher shortage? It’s really quite simple: Offer higher salaries for teachers. If you want the best-qualified people in your classrooms, you must pay salaries that attract the best-qualified people. If you pay substandard salaries, you’re going to attract substandard talent. “Those who can, do; those who can’t, teach” isn’t a law of nature; it’s a result of public policy decisions to keep teachers systematically underpaid.

Most of the time when people say “It’s just ECON 101”, they don’t actually understand economics very well and likely have not actually taken ECON 101. But this really basically is a question of ECON 101: Supply and demand. If you have a shortage of something, not enough people willing to produce it compared to the number of people who want to buy it, you must raise the price.

Would that be expensive? Yes it would. Doubling the salary of every teacher would raise total spending on education by about 75%, because teacher compensation is about three-quarters of education spending. This would raise US K-12 education spending from about $600 billion per year to more like $1.05 trillion per year, an additional $450 billion per year in public spending, or a little less than $1,500 per American per year. That is not a small amount of money; indeed, it’s about three times what we’d need to end world hunger. And this is actually an underestimate, since we also hope to hire more teachers and should also improve facilities while we’re at it. So a truly comprehensive educational reform project could very well double our total spending on K-12 education to $1.2 trillion.

And if you want to go up there on a podium and actually tell people, “It would be nice to improve our educational system, but we simply can’t afford to do it without raising taxes unreasonably high!” then that is absolutely a reasonable argument to make. There are always tradeoffs in life. At some point, maybe it really isn’t worth spending an extra million dollars to educate one more child. (Is it worth an extra million dollars to educate two more children? Based on net present value of earnings, yes. And frankly I don’t think net present value of earnings even gets close to assessing the true value of an education; it’s a very weak lower bound.)

But I am sick and tired of people saying “Education is our highest priority!” and then refusing to actually spend the money it would take to improve our educational system. This is not a question of “finding solutions”; we know what to do. Raise teacher salaries. Improve schools. Buy new textbooks. People just aren’t willing to actually pony up the cash to do it. They want an easy way out, some simple way of making education better that somehow won’t cost anything. But we’ve been searching for that for awhile now—don’t you think we’d have found it by now?

The winner-takes-all effect

JDN 2457054 PST 14:06.

As I write there is some sort of mariachi band playing on my front lawn. It is actually rather odd that I have a front lawn, since my apartment is set back from the road; yet there is the patch of grass, and there is the band playing upon it. This sort of thing is part of the excitement of living in a large city (and Long Beach would seem like a large city were it not right next to the sprawling immensity that is Los Angeles—there are more people in Long Beach than in Cleveland, but there are more people in greater Los Angeles than in Sweden); with a certain critical mass of human beings comes unexpected pieces of culture.

The fact that people agglomerate in this way is actually relevant to today’s topic, which is what I will call the winner-takes-all effect. I actually just finished reading a book called The Winner-Take-All Society, which is particularly horrifying to read because it came out in 1996. That’s almost twenty years ago, and things were already bad; and since then everything it describes has only gotten worse.

What is the winner-takes-all effect? It is the simple fact that in competitive capitalist markets, a small difference in quality can yield an enormous difference in return. The third most popular soda drink company probably still makes drinks that are pretty good, but do you have any idea what it is? There’s Coke, there’s Pepsi, and then there’s… uh… Dr. Pepper, apparently! But I didn’t know that before today and I bet you didn’t either. Now think about what it must be like to be the 15th most popular soda drink company, or the 37th. That’s the winner-takes-all effect.

I don’t generally follow football, but since tomorrow is the Super Bowl I feel some obligation to use that example as well. The highest-paid quarterback is Russell Wilson of the Seattle Seahawks, who is signing onto a five-year contract worth $110 million ($22 million a year). In annual income that will make him pass Jay Cutler of the Chicago Bears who has a seven-year contract worth $127 million ($18.5 million a year). This shift may have something to do with the fact that the Seahawks are in the Super Bowl this year and the Bears are not (they haven’t since 2007). Now consider what life is like for most football players; the median income of football players is most likely zero (at least as far as football-related income), and the median income of NFL players—the cream of the crop already—is $770,000; that’s still very good money of course (more than Krugman makes, actually! But he could make more, if he were willing to sell out to Wall Street), but it’s barely 1/30 of what Wilson is going to be making. To make that million-dollar salary, you need to be the best, of the best, of the best (sir!). That’s the winner-takes-all effect.

To go back to the example of cities, it is for similar reasons that the largest cities (New York, Los Angeles, London, Tokyo, Shanghai, Hong Kong, Delhi) become packed with tens of millions of people while others (Long Beach, Ann Arbor, Cleveland) get hundreds of thousands and most (Petoskey, Ketchikan, Heber City, and hundreds of others you’ve never heard of) get only a few thousand. Beyond that there are thousands of tiny little hamlets that many don’t even consider cities. The median city probably has about 10,000 people in it, and that only because we’d stop calling it a city if it fell below 1,000. If we include every tiny little village, the median town size is probably about 20 people. Meanwhile the largest city in the world is Tokyo, with a greater metropolitan area that holds almost 38 million people—or to put it another way almost exactly as many people as California. Huh, LA doesn’t seem so big now does it? How big is a typical town? Well, that’s the thing about this sort of power-law distribution; the concept of “typical” or “average” doesn’t really apply anymore. Each little piece of the distribution has basically the same shape as the whole distribution, so there isn’t a “typical” size or scale. That’s the winner-takes-all effect.

As they freely admit in the book, it isn’t literally that a single winner takes everything. That is the theoretical maximum level of wealth inequality, and fortunately no society has ever quite reached it. The closest we get in today’s society is probably Saudi Arabia, which recently lost its king—and yes I do mean king in the fullest sense of the word, a man of virtually unlimited riches and near-absolute power. His net wealth was estimated at $18 billion, which frankly sounds low; still even if that’s half the true amount it’s oddly comforting to know that he is still not quite as rich as Bill Gates ($78 billion), who earned his wealth at least semi-legitimately in a basically free society. Say what you will about intellectual property rents and market manipulation—and you know I do—but they are worlds away from what Abdullah’s family did, which was literally and directly robbed from millions of people by the power of the sword. Mostly he just inherited all that, and he did implement some minor reforms, but make no mistake: He was ruthless and by no means willing to give up his absolute power—he beheaded dozens of political dissidents, for example. Saudi Arabia does spread their wealth around a little, such that basically no one is below the UN poverty lines of $1.25 and $2 per day, but about a fourth of the population is below the national poverty line—which is just about the same distribution of wealth as what we have in the US, which actually makes me wonder just how free and legitimate our markets really are.

The winner-takes-all effect would really be more accurately described as the “top small fraction takes the vast majority” effect, but that isn’t nearly as catchy, now is it?

There are several different causes that can all lead to this same result. In the book, Robert Frank and Philip Cook argue that we should not attribute the cause to market manipulation, but in fact to the natural functioning of competitive markets. There’s something to be said for this—I used to buy the whole idea that competitive markets are the best, but increasingly I’ve been seeing ways that less competitive markets can make better overall outcomes.

Where they lose me is in arguing that the skyrocketing compensation packages for CEOs are due to their superior performance, and corporations are just being rational in competing for the best CEOs. If that were true, we wouldn’t find that the rank correlation between the CEO’s pay and the company’s stock performance is statistically indistinguishable from zero. Actually even a small positive correlation wouldn’t prove that the CEOs are actually performing well; it could just be that companies that perform well are willing to pay their CEOs more—and stock option compensation will do this automatically. But in fact the correlation is so tiny as to be negligible; corporations would be better off hiring a random person off the street and paying them $50,000 for all the CEO does for their stock performance. If you adjust for the size of the company, you find that having a higher-paid CEO is positively related to performance for small startups, but negatively correlated for large well-established corporations. No, clearly there’s something going on here besides competitive pay for high performance—corruption comes to mind, which you’ll remember was the subject of my master’s thesis.

But in some cases there isn’t any apparent corruption, and yet we still see these enormously unequal distributions of income. Another good example of this is the publishing industry, in which J.K. Rowling can make over $1 billion (she donated enough to charity to officially lose her billionaire status) but most authors make little or nothing, particularly those who can’t get published in the first place. I have no reason to believe that J.K. Rowling acquired this massive wealth by corruption; she just sold an awful lot of booksover 100 million of the first Harry Potter book alone.

But why would she be able to sell 100 million while thousands of authors write books that are probably just as good or nearly so make nothing? Am I just bitter and envious, as Mitt Romney would say? Is J.K. Rowling actually a million times as good an author as I am?

Obviously not, right? She may be better, but she’s not that much better. So how is it that she ends up making a million times as much as I do from writing? It feels like squaring the circle: How can markets be efficient and competitive, yet some people are being paid millions of times as others despite being only slightly more productive?

The answer is simple but enormously powerful: positive feedback.Once you start doing well, it’s easier to do better. You have what economists call an economy of scale. The first 10,000 books sold is the hardest; then the next 10,000 is a little easier; the next 10,000 a little easier still. In fact I suspect that in many cases the first 10% growth is harder than the second 10% growth and so on—which is actually a much stronger claim. For my sales to grow 10% I’d need to add like 20 people. For J.K. Rowling’s sales to grow 10% she’d need to add 10 million. Yet it might actually be easier for J.K. Rowling to add 10 million than for me to add 20. If not, it isn’t much harder. Suppose we tried by just sending out enticing tweets. I have about 100 Twitter followers, so I’d need 0.2 sales per follower; she has about 4 million, so she’d need an average of 2.5 sales per follower. That’s an advantage for me, percentage-wise—but if we have the same uptake rate I sell 20 books and she sells 800,000.

If you have only a handful of book sales like I do, those sales are static; but once you cross that line into millions of sales, it’s easy for that to spread into tens or even hundreds of millions. In the particular case of books, this is because it spreads by word-of-mouth; say each person who reads a book recommends it to 10 friends, and you only read a book if at least 2 of your friends recommended it. In a city of 100,000 people, if you start with 50 people reading it, odds are that most of those people don’t have friends that overlap and so you stop at 50. But if you start at 50,000, there is bound to be a great deal of overlap; so then that 50,000 recruits another 10,000, then another 10,000, and pretty soon the whole 100,000 have read it. In this case we have what are called network externalitiesyou’re more likely to read a book if your friends have read it, so the more people there are who have read it, the more people there are who want to read it. There’s a very similar effect at work in social networks; why does everyone still use Facebook, even though it’s actually pretty awful? Because everyone uses Facebook. Less important than the quality of the software platform (Google Plus is better, and there are some third-party networks that are likely better still) is the fact that all your friends and family are on it. We all use Facebook because we all use Facebook? We all read Harry Potter books because we all read Harry Potter books? The first rule of tautology club is…

Languages are also like this, which is why I can write this post in English and yet people can still read it around the world. English is the winner of the language competition (we call it the lingua franca, as weird as that is—French is not the lingua franca anymore). The losers are those hundreds of New Guinean languages you’ve never heard of, many of which are dying. And their distribution obeys, once again, a power-law. (Individual words actually obey a power-law as well, which makes this whole fractal business delightfully ever more so.)
Network externalities are not the only way that the winner-takes-all effect can occur, though I think it is the most common. You can also have economies of scale from the supply side, particularly in the case of information: Recording a song is a lot of time and effort, but once you record a song, it’s trivial to make more copies of it. So that first recording costs a great deal, while every subsequent recording costs next to nothing. This is probably also at work in the case of J.K. Rowling and the NFL; the two phenomena are by no means mutually exclusive. But clearly the sizes of cities are due to network externalities: It’s quite expensive to live in a big city—no supply-side economy of scale—but you want to live in a city where other people live because that’s where friends and family and opportunities are.

The most worrisome kind of winner-takes-all effect is what Frank and Cook call deep pockets: Once you have concentration of wealth in a few hands, those few individuals can now choose their own winners in a much more literal sense: the rich can commission works of art from their favorite artists, exacerbating the inequality among artists; worse yet they can use their money to influence politicians (as the Kochs are planning on spending $900 million—$3 for every person in America—to do in 2016) and exacerbate the inequality in the whole system. That gives us even more positive feedback on top of all the other positive feedbacks.

Sure enough, if you run the standard neoclassical economic models of competition and just insert the assumption of economies of scale, the result is concentration of wealth—in fact, if nothing about the rules prevents it, the result is a complete monopoly. Nor is this result in any sense economically efficient; it’s just what naturally happens in the presence of economies of scale.

Frank and Cook seem most concerned about the fact that these winner-take-all incomes will tend to push too many people to seek those careers, leaving millions of would-be artists, musicians and quarterbacks with dashed dreams when they might have been perfectly happy as electrical engineers or high school teachers. While this may be true—next week I’ll go into detail about prospect theory and why human beings are terrible at making judgments based on probability—it isn’t really what I’m most concerned about. For all the cost of frustrated ambition there is also a good deal of benefit; striving for greatness does not just make the world better if we succeed, it can make ourselves better even if we fail. I’d strongly encourage people to have backup plans; but I’m not going to tell people to stop painting, singing, writing, or playing football just because they’re unlikely to make a living at it. The one concern I do have is that the competition is so fierce that we are pressured to go all in, to not have backup plans, to use performance-enhancing drugs—they may carry awful risks, but they also work. And it’s probably true, actually, that you’re a bit more likely to make it all the way to the top if you don’t have a backup plan. You’re also vastly more likely to end up at the bottom. Is raising your probability of being a bestselling author from 0.00011% to 0.00012% worth giving up all other career options? Skipping chemistry class to practice football may improve your chances of being an NFL quarterback from 0.000013% to 0.000014%, but it will also drop your chances of being a chemical engineer from 95% (a degree in chemical engineering almost guarantees you a job eventually) to more like 5% (it’s hard to get a degree when you flunk all your classes).

Frank and Cook offer a solution that I think is basically right; they call it positional arms control agreements. By analogy with arms control agreements between nations—and what is war, if not the ultimate winner-takes-all contest?—they propose that we use taxation and regulation policy to provide incentives to make people compete less fiercely for the top positions. Some of these we already do: Performance-enhancing drugs are banned in professional sports, for instance. Even where there are no regulations, we can use social norms: That’s why it’s actually a good thing that your parents rarely support your decision to drop out of school and become a movie star.

That’s yet another reason why progressive taxation is a good idea, as if we needed another; by paring down those top incomes it makes the prospect of winning big less enticing. If NFL quarterbacks only made 10 times what chemical engineers make instead of 300 times, people would be a lot more hesitant to give up on chemical engineering to become a quarterback. If top Wall Street executives only made 50 times what normal people make instead of 5000, people with physics degrees might go back to actually being physicists instead of speculating on stock markets.

There is one case where we might not want fewer people to try, and that is entrepreneurship. Most startups fail, and only a handful go on to make mind-bogglingly huge amounts of money (often for no apparent reason, like the Snuggie and Flappy Bird), yet entrepreneurship is what drives the dynamism of a capitalist economy. We need people to start new businesses, and right now they do that mainly because of a tiny chance of a huge benefit. Yet we don’t want them to be too unrealistic in their expectations: Entrepreneurs are much more optimistic than the general population, but the most successful entrepreneurs are a bit less optimistic than other entrepreneurs. The most successful strategy is to be optimistic but realistic; this outperforms both unrealistic optimism and pessimism. That seems pretty intuitive; you have to be confident you’ll succeed, but you can’t be totally delusional. Yet it’s precisely the realistic optimists who are most likely to be disincentivized by a reduction in the top prizes.

Here’s my solution: Let’s change it from a tiny change of a huge benefit to a large chance of a moderately large benefit. Let’s reward entrepreneurs for trying—with standards for what constitutes a really serious, good attempt rather than something frivolous that was guaranteed to fail. Use part of the funds from the progressive tax as a fund for angel grants, provided to a large number of the most promising entrepreneurs. It can’t be a million-dollar prize for the top 100. It needs to be more like a $50,000 prize for the top 100,000 (which would cost $5 billion a year, affordable for the US government). It should be paid at the proposal phase; the top 100,000 business plans receive the funding and are under no obligation to repay it. It has to be enough money that someone can rationally commit themselves to years of dedicated work without throwing themselves into poverty, and it has to be confirmed money so that they don’t have to worry about throwing themselves into debt. As for the upper limit, it only needs to be small enough that there is still an incentive for the business to succeed; but even with a 99% tax Mark Zuckerberg would still be a millionaire, so the rewards for success are high indeed.

The good news is that we actually have such a system to some extent. For research scientists rather than entrepreneurs, NSF grants are pretty close to what I have in mind, but at present they are a bit too competitive: 8,000 research grants with a median of $130,000 each and a 20% acceptance rate isn’t quite enough people—the acceptance rate should be higher, since most of these proposals are quite worthy. Still, it’s close, and definitely a much better incentive system than what we have for entrepreneurs; there are almost 12 million entrepreneurs in the United States, starting 6 million businesses a year, 75% of which fail before they can return their venture capital. Those that succeed have incomes higher than the general population, with a median income of around $70,000 per year, but most of this is accounted for by the fact that entrepreneurs are more educated and talented than the general population. Once you factor that in, successful entrepreneurs have about 50% more income on average, but their standard deviation of income is also 60% higher—so some are getting a lot and some are getting very little. Since 75% fail, we’re talking about a 25% chance of entering an income distribution that’s higher on average but much more variable, and a 75% chance of going through a period with little or no income at all—is it worth it? Maybe, maybe not. But if you could get a guaranteed $50,000 for having a good idea—and let me be clear, only serious proposals that have a good chance of success should qualify—that deal sounds an awful lot better.