Koch

The difference between price, cost, and value

pnrj core principles, critique of neoclassical economics, heuristics and biases, market failure, public policy , , , , , , , , , , , , , , , , , , , , , , , , , , , , ,

JDN 2457559

This topic has been on the voting list for my Patreons for several months, but it never quite seems to win the vote. Well, this time it did. I’m glad, because I was tempted to do it anyway.

“Price”, “cost”, and “value”; the words are often used more or less interchangeably, not only by regular people but even by economists. I’ve read papers that talked about “rising labor costs” when what they clearly meant was rising wages—rising labor prices. I’ve read papers that tried to assess the projected “cost” of climate change by using the prices of different commodity futures. And hardly a day goes buy that I don’t see a TV commercial listing one (purely theoretical) price, cutting it in half (to the actual price), and saying they’re now giving you “more value”.

As I’ll get to, there are reasons to think they would be approximately the same for some purposes. Indeed, they would be equal, at the margin, in a perfectly efficient market—that may be why so many economists use them this way, because they implicitly or explicitly assume efficient markets. But they are fundamentally different concepts, and it’s dangerous to equate them casually.

Price

Price is exactly what you think it is: The number of dollars you must pay to purchase something. Most of the time when we talk about “cost” or “value” and then give a dollar figure, we’re actually talking about some notion of price.

Generally we speak in terms of nominal prices, which are the usual concept of prices in actual dollars paid, but sometimes we do also speak in terms of real prices, which are relative prices of different things once you’ve adjusted for overall inflation. “Inflation-adjusted price” can be a somewhat counter-intuitive concept; if a good’s (nominal) price rises, but by less than most other prices have risen, its real price has actually fallen.

You also need to be careful about just what price you’re looking at. When we look at labor prices, for example, we need to consider not only cash wages, but also fringe benefits and other compensation such as stock options. But other than that, prices are fairly straightforward.

Cost

Cost is probably not at all what you think it is. The real cost of something has nothing to do with money; saying that a candy bar “costs $2” or a computer “costs $2,000” is at best a somewhat sloppy shorthand and at worst a fundamental distortion of what cost is and why it matters. No, those are prices. The cost of a candy bar is the toil of children in cocoa farms in Cote d’Ivoire. The cost of a computer is the ecological damage and displaced indigenous people caused by coltan mining in Congo.

The cost of something is the harm that it does to human well-being (or for that matter to the well-being of any sentient being). It is not measured in money but in “the sweat of our laborers, the genius of our scientists, the hopes of our children” (to quote Eisenhower, who understood real cost better than most economists). There is also opportunity cost, the real cost we pay not by what we did, but by what we didn’t do—what we could have done instead.

This is important precisely because while costs should always be reduced when possible, prices can in fact be too low—and indeed, artificially low prices of goods due to externalities are probably the leading reason why humanity bears so many excess real costs. If the price of that chocolate bar accurately reflected the suffering of those African children (perhaps by—Gasp! Paying them a fair wage?), and the price of that computer accurately reflected the ecological damage of those coltan mines (a carbon tax, at least?), you might not want to buy them anymore; in which case, you should not have bought them. In fact, as I’ll get to once I discuss value, there is reason to think that even if you would buy them at a price that accurately reflected the dollar value of the real cost to their producers, we would still buy more than we should.

There is a point at which we should still buy things even though people get hurt making them; if you deny this, stop buying literally anything ever again. We don’t like to think about it, but any product we buy did cause some person, in some place, some degree of discomfort or unpleasantness in production. And many quite useful products will in fact cause death to a nonzero number of human beings.

For some products this is only barely true—it’s hard to feel bad for bestselling authors and artists who sell their work for millions, for whatever toil they may put into their work, whatever their elevated suicide rate (which is clearly endogenous; people aren’t randomly assigned to be writers), they also surely enjoy it a good deal of the time, and even if they didn’t, their work sells for millions. But for many products it is quite obviously true: A certain proportion of roofers, steelworkers, and truck drivers will die doing their jobs. We can either accept that, recognizing that it’s worth it to have roofs, steel, and trucking—and by extension, industrial capitalism, and its whole babies not dying thing—or we can give up on the entire project of human civilization, and go back to hunting and gathering; even if we somehow managed to avoid the direct homicide most hunter-gatherers engage in, far more people would simply die of disease or get eaten by predators.

Of course, we should have safety standards; but the benefits of higher safety must be carefully weighed against the potential costs of inefficiency, unemployment, and poverty. Safety regulations can reduce some real costs and increase others, even if they almost always increase prices. A good balance is struck when real cost is minimized, where any additional regulation would increase inefficiency more than it improves safety.

Actually OSHA are unsung heroes for their excellent performance at striking this balance, just as EPA are unsung heroes for their balance in environmental regulations (and that whole cutting crime in half business). If activists are mad at you for not banning everything bad and business owners are mad at you for not letting them do whatever they want, you’re probably doing it right. Would you rather people saved from fires, or fires prevented by good safety procedures? Would you rather murderers imprisoned, or boys who grow up healthy and never become murderers? If an ounce of prevention is worth a pound of cure, why does everyone love firefighters and hate safety regulators?So let me take this opportunity to say thank you, OSHA and EPA, for doing the jobs of firefighters and police way better than they do, and unlike them, never expecting to be lauded for it.

And now back to our regularly scheduled programming. Markets are supposed to reflect costs in prices, which is why it’s not totally nonsensical to say “cost” when you mean “price”; but in fact they aren’t very good at that, for reasons I’ll get to in a moment.

Value

Value is how much something is worth—not to sell it (that’s the price again), but to use it. One of the core principles of economics is that trade is nonzero-sum, because people can exchange goods that they value differently and thereby make everyone better off. They can’t price them differently—the buyer and the seller must agree upon a price to make the trade. But they can value them differently.

To see how this works, let’s look at a very simple toy model, the simplest essence of trade: Alice likes chocolate ice cream, but all she has is a gallon of vanilla ice cream. Bob likes vanilla ice cream, but all he has is a gallon of chocolate ice cream. So Alice and Bob agree to trade their ice cream, and both of them are happier.

We can measure value in “willingness-to-pay” (WTP), the highest price you’d willingly pay for something. That makes value look more like a price; but there are several reasons we must be careful when we do that. The obvious reason is that WTP is obviously going to vary based on overall inflation; since $5 isn’t worth as much in 2016 as it was in 1956, something with a WTP of $5 in 1956 would have a much higher WTP in 2016. The not-so-obvious reason is that money is worth less to you the more you have, so we also need to take into account the effect of wealth, and the marginal utility of wealth. The more money you have, the more money you’ll be willing to pay in order to get the same amount of real benefit. (This actually creates some very serious market distortions in the presence of high income inequality, which I may make the subject of a post or even a paper at some point.) Similarly there is “willingness-to-accept” (WTA), the lowest price you’d willingly accept for it. In theory these should be equal; in practice, WTA is usually slightly higher than WTP in what’s called endowment effect.

So to make our model a bit more quantitative, we could suppose that Alice values vanilla at $5 per gallon and chocolate at $10 per gallon, while Bob also values vanilla at $5 per gallon but only values chocolate at $4 per gallon. (I’m using these numbers to point out that not all the valuations have to be different for trade to be beneficial, as long as some are.) Therefore, if Alice sells her vanilla ice cream to Bob for $5, both will (just barely) accept that deal; and then Alice can buy chocolate ice cream from Bob for anywhere between $4 and $10 and still make both people better off. Let’s say they agree to also sell for $5, so that no net money is exchanged and it is effectively the same as just trading ice cream for ice cream. In that case, Alice has gained $5 in consumer surplus (her WTP of $10 minus the $5 she paid) while Bob has gained $1 in producer surplus (the $5 he received minus his $4 WTP). The total surplus will be $6 no matter what price they choose, which we can compute directly from Alice’s WTP of $10 minus Bob’s WTA of $4. The price ultimately decides how that total surplus is distributed between the two parties, and in the real world it would very likely be the result of which one is the better negotiator.

The enormous cost of our distorted understanding

(See what I did there?) If markets were perfectly efficient, prices would automatically adjust so that, at the margin, value is equal to price is equal to cost. What I mean by “at the margin” might be clearer with an example: Suppose we’re selling apples. How many apples do you decide to buy? Well, the value of each successive apple to you is lower, the more apples you have (the law of diminishing marginal utility, which unlike most “laws” in economics is actually almost always true). At some point, the value of the next apple will be just barely above what you have to pay for it, so you’ll stop there. By a similar argument, the cost of producing apples increases the more apples you produce (the law of diminishing returns, which is a lot less reliable, more like the Pirate Code), and the producers of apples will keep selling them until the price they can get is only just barely larger than the cost of production. Thus, in the theoretical limit of infinitely-divisible apples and perfect rationality, marginal value = price = marginal cost. In such a world, markets are perfectly efficient and they maximize surplus, which is the difference between value and cost.

But in the real world of course, none of those assumptions are true. No product is infinitely divisible (though the gasoline in a car is obviously a lot more divisible than the car itself). No one is perfectly rational. And worst of all, we’re not measuring value in the same units. As a result, there is basically no reason to think that markets are optimizing anything; their optimization mechanism is setting two things equal that aren’t measured the same way, like trying to achieve thermal equilibrium by matching the temperature of one thing in Celsius to the temperature of other things in Fahrenheit.

An implicit assumption of the above argument that didn’t even seem worth mentioning was that when I set value equal to price and set price equal to cost, I’m setting value equal to cost; transitive property of equality, right? Wrong. The value is equal to the price, as measured by the buyer. The cost is equal to the price, as measured by the seller.

If the buyer and seller have the same marginal utility of wealth, no problem; they are measuring in the same units. But if not, we convert from utility to money and then back to utility, using a different function to convert each time. In the real world, wealth inequality is massive, so it’s wildly implausible that we all have anything close to the same marginal utility of wealth. Maybe that’s close enough if you restrict yourself to middle-class people in the First World; so when a tutoring client pays me, we might really be getting close to setting marginal value equal to marginal cost. But once you include corporations that are owned by billionaires and people who live on $2 per day, there’s simply no way that those price-to-utility conversions are the same at each end. For Bill Gates, a million dollars is a rounding error. For me, it would buy a house, give me more flexible work options, and keep me out of debt, but not radically change the course of my life. For a child on a cocoa farm in Cote d’Ivoire, it could change her life in ways she can probably not even comprehend.

The market distortions created by this are huge; indeed, most of the fundamental flaws in capitalism as we know it are ultimately traceable to this. Why do Americans throw away enough food to feed all the starving children in Africa? Marginal utility of wealth. Why are Silicon Valley programmers driving the prices for homes in San Francisco higher than most Americans will make in their lifetimes? Marginal utility of wealth. Why are the Koch brothers spending more on this year’s elections than the nominal GDP of the Gambia? Marginal utility of wealth. It’s the sort of pattern that once you see it suddenly seems obvious and undeniable, a paradigm shift a bit like the heliocentric model of the solar system. Forget trade barriers, immigration laws, and taxes; the most important market distortions around the world are all created by wealth inequality. Indeed, the wonder is that markets work as well as they do.

The real challenge is what to do about it, how to reduce this huge inequality of wealth and therefore marginal utility of wealth, without giving up entirely on the undeniable successes of free market capitalism. My hope is that once more people fully appreciate the difference between price, cost, and value, this paradigm shift will be much easier to make; and then perhaps we can all work together to find a solution.

What really scares me

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JDN 2457327

Today is Halloween, so in the spirit of the holiday I thought I’d talk about things that are scary. Not things like zombies and witches and vampires; those things aren’t real (though people do still believe in them in many parts of the world). And maybe that’s part of the point; maybe Halloween is meant to “scare” us like a roller coaster, where we feel some of the epinephrine rush of fear but deep down we know we are safe.

But today I’m going to talk about things that are actually scary, things that are not safe deep down. I could talk about the Republican debate earlier this week, but maybe I shouldn’t get too scary.

In fiction there is whatever sort of ending the author wants to make, usually a happy one. Even tragic endings are written to be meaningful and satisfying. But in real life any sort of ending is possible. I could be driving down the street tomorrow and a semi truck could blindside me and kill me on impact. There’s no satisfying tragedy there, no comeuppance for my hubris or tragic flaw in my character leading to my doom—but this sort of thing kills over 30,000 Americans each year.

But are car accidents really scary? The way they kill just about anyone at random is scary. But there is a clear limit to how much damage they can do. No society has ever been wiped off the face of the Earth because of traffic accidents. There is no way for traffic accidents to risk the survival of the human race itself.

This brings me to the first thing that is really scary: Climate change. Human societies have been wiped off the face of the Earth due to local ecological collapses. The classic example is Easter Island, which did have an ecological collapse, but also suffered greatly from European invaders. Recent evidence suggests that the Vikings fell apart because glaciation broke their trade networks. Jared Diamond argues that a large number of ancient societies have fallen due to ecological collapse.

Yet for the first time we are now facing rapid global climate change, and it is our own doing. (As the vast majority of climate scientists agree.) We are already seeing its effects in flooding, wildfires, droughts, and hurricanes. Positive feedbacks are created, such as heat waves leading to more air conditioning, which draws more electricity that releases more carbon. Even as management of fishing improves, fisheries are still being depleted—because their waters are becoming too warm for the native fish.

Just yesterday the United Nations released a report showing that current promises of reduced carbon emissions will not be sufficient—even if they are followed through, which such promises often aren’t. The goal was to keep warming under 2 C; but it looks like we are looking at more like 2.7 C. That 0.7-degree difference may not seem like much, but in fact it means thousands or even millions of additional deaths. Most of the economic damage will be done to countries near the equator—which is also where the most impoverished people tend to live. The Global Humanitarian Forum estimates that global warming is already killing 300,000 people each year and causing over $100 billion in economic damage.

Meanwhile, there is a campaign of disinformation about climate change, funneled through secretive “dark money” processes (Why are these even allowed!?), including Exxon corporation, which has known for 30 years that they were contributing to climate change but actively suppressed that knowledge in order to avoid regulation. Koch Industries has also funded a great deal of climate change denialism. West Virginia recently tried to alter their science textbooks to remove references to climate change because they considered the scientific facts to be “too political”. Supposedly serious “think tanks” with conservative ideologies twist data in order to support their claims. Rather than be caught lying or denying science, most of the Republican presidential candidates are avoiding talking about the subject altogether.
There is good news, however: More Americans than ever recognize that climate change is real. 7% changed their minds in just the last few months. Even a lot of Republican politicians are finally coming around.

What else is scary? Nuclear war, a Black Swan. This is the most probable way humanity could destroy ourselves; the probability of nuclear war in the next 50 years has been estimated as high as 10%. Every day that goes by with nuclear weapons at the ready is like pulling the trigger in a game of Russian Roulette. We don’t really know how to estimate the probability with any precision; but even 0.1% per year would be a 10% chance over the next century.

There’s good news on this front as well: Slowly but surely, the world is disarming its nuclear weapons. From a peak of 60,000 nuclear weapons in 1986, we are now down to about 10,000. But we shouldn’t get too comfortable, as the estimated number necessary to trigger a global nuclear winter with catastrophic consequences is only about 100. India or Pakistan alone probably has enough to do that. The US or Russia has enough to do it 40 times over. We will need to continue our current disarmament trend for another 30 years before no single nation has enough weapons to trigger a nuclear winter.

Then there’s one more class of scary Black Swans: Mass extinction events. In particular, I’m talking about the Yellowstone Supervolcano, which could erupt at any moment, and the possibility of a large asteroid impact which could destroy cities or even wipe out all life on the surface of the Earth. We are 99.989% sure that TV135 will not do this; but in that 0.02% chance, it would hit with the force of 2500 megatons—50 times larger than any nuclear weapon ever built. Smaller (“smaller”) sub-megaton impacts are actually remarkably common; we average about two per year. If one ever hit a major city, it would be comparable to the Hiroshima nuclear bombing. The Yellowstone supervolcano would not be as catastrophic as a planet-scouring impact, but it would be comparable to a nuclear war and nuclear winter.

With asteroids, there are actually clear things we could do to improve our chances. Above all, we could invest in space exploration and astronomy. With better telescopes and more tracking stations we could see them coming; with better long-range rockets we might be able to deflect them before they get here. A number of different deflection proposals are being studied right now. This is actually the best reason I can think of to keep at least some nuclear weapons on standby; a large nuclear blast positioned at the right place could be effective at destroying an asteroid or deflecting it enough to miss us.

With Yellowstone, there really isn’t much we can do; all we can do at this point is continue to research the supervolcano and try to find ways to reduce the probability of its eruption. It is currently estimated at a just over 1 in 1 million chance of erupting any given year, but that’s a very rough estimate. Fracking near Yellowstone is currently banned, and I think it should stay that way until we have a very clear idea of what would happen. (It’s actually possible it could reduce the probability of eruption, in which case we should start fracking like crazy.)

Forget the zombie apocalypse. I’m scared of the supervolcano apocalypse.

The winner-takes-all effect

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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 books—over 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 externalities—you’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.