The Efficient Roulette Hypothesis

2022-11-282022-11-20 pnrj core principles, critique of neoclassical economics, financial advice, market failure, public policy behavioral finance, deregulation, efficiency, Efficient Market Hypothesis, gambling, motte and bailey, prediction market, roulette

Nov 27 JDN 2459911

The efficient market hypothesis is often stated in several different ways, and these are often treated as equivalent. There are at least three very different definitions of it that people seem to use interchangeably:

Market prices are optimal and efficient.
Market prices aggregate and reflect all publicly-available relevant information.
Market prices are difficult or impossible to predict.

The first reading, I will call the efficiency hypothesis, because, well, it is what we would expect a phrase like “efficient market hypothesis” to mean. The ordinary meaning of those words would imply that we are asserting that market prices are in some way optimal or near-optimal, that markets get prices “right” in some sense at least the vast majority of the time.

The second reading I’ll call the information hypothesis; it implies that market prices are an information aggregation mechanism which automatically incorporates all publicly-available information. This already seems quite different from efficiency, but it seems at least tangentially related, since information aggregation could be one useful function that markets serve.

The third reading I will call the unpredictability hypothesis; it says simply that market prices are very difficult to predict, and so you can’t reasonably expect to make money by anticipating market price changes far in advance of everyone else. But as I’ll get to in more detail shortly, that doesn’t have the slightest thing to do with efficiency.

The empirical data in favor of the unpredictability hypothesis is quite overwhelming. It’s exceedingly hard to beat the market, and for most people, most of the time, the smartest way to invest is just to buy a diversified portfolio and let it sit.

The empirical data in favor of the information hypothesis is mixed, but it’s at least plausible; most prices do seem to respond to public announcements of information in ways we would expect, and prediction markets can be surprisingly accurate at forecasting the future.

The empirical data in favor of the efficiency hypothesis, on the other hand, is basically nonexistent. On the one hand this is a difficult hypothesis to test directly, since it isn’t clear what sort of benchmark we should be comparing against—so it risks being not even wrong. But if you consider basically any plausible standard one could try to set for how an efficient market would run, our actual financial markets in no way resemble it. They are erratic, jumping up and down for stupid reasons or no reason at all. They are prone to bubbles, wildly overvaluing worthless assets. They have collapsed governments and ruined millions of lives without cause. They have resulted in the highest-paying people in the world doing jobs that accomplish basically nothing of genuine value. They are, in short, a paradigmatic example of what inefficiency looks like.

Yet, we still have economists who insist that “the efficient market hypothesis” is a proven fact, because the unpredictability hypothesis is clearly correct.

I do not think this is an accident. It’s not a mistake, or an awkwardly-chosen technical term that people are misinterpreting.

This is a motte and bailey doctrine.

Motte-and-bailey was a strategy in medieval warfare. Defending an entire region is very difficult, so instead what was often done was constructing a small, highly defensible fortification—the motte—while accepting that the land surrounding it—the bailey—would not be well-defended. Most of the time, the people stayed on the bailey, where the land was fertile and it was relatively pleasant to live. But should they be attacked, they could retreat to the motte and defend themselves until the danger was defeated.

A motte-and-bailey doctrine is an analogous strategy used in argumentation. You use the same words for two different versions of an idea: The motte is a narrow, defensible core of your idea that you can provide strong evidence for, but it isn’t very strong and may not even be interesting or controversial. The bailey is a broad, expansive version of your idea that is interesting and controversial and leads to lots of significant conclusions, but can’t be well-supported by evidence.

The bailey is the efficiency hypothesis: That market prices are optimal and we are fools to try to intervene or even regulate them because the almighty Invisible Hand is superior to us.

The motte is the unpredictability hypothesis: Market prices are very hard to predict, and most people who try to make money by beating the market fail.

By referring to both of these very different ideas as “the efficient market hypothesis”, economists can act as if they are defending the bailey, and prescribe policies that deregulate financial markets on the grounds that they are so optimal and efficient; but then when pressed for evidence to support their beliefs, they can pivot to the motte, and merely show that markets are unpredictable. As long as people don’t catch on and recognize that these are two very different meanings of “the efficient market hypothesis”, then they can use the evidence for unpredictability to support their goal of deregulation.

Yet when you look closely at this argument, it collapses. Unpredictability is not evidence of efficiency; if anything, it’s the opposite. Since the world doesn’t really change on a minute-by-minute basis, an efficient system should actually be relatively predictable in the short term. If prices reflected the real value of companies, they would change only very gradually, as the fortunes of the company change as a result of real-world events. An earthquake or a discovery of a new mine would change stock prices in relevant industries; but most of the time, they’d be basically flat. The occurrence of minute-by-minute or even second-by-second changes in prices basically proves that we are not tracking any genuine changes in value.

Roulette wheels are extremely unpredictable by design—by law, even—and yet no one would accuse them of being an efficient way of allocating resources. If you bet on roulette wheels and try to beat the house, you will almost surely fail, just as you would if you try to beat the stock market—and dare I say, for much the same reasons?

So if we’re going to insist that “efficiency” just means unpredictability, rather than actual, you know, efficiency, then we should all speak of the Efficient Roulette Hypothesis. Anything we can’t predict is now automatically “efficient” and should therefore be left unregulated.

How we measure efficiency affects our efficiency

2020-06-212020-06-14 pnrj core principles, development economics, ethics carbon emissions, charity, effective altruism, efficiency, GiveWell, QALY

Jun 21 JDN 2459022

Suppose we are trying to minimize carbon emissions, and we can afford one of the two following policies to improve fuel efficiency:

Policy A will replace 10,000 cars that average 25 MPG with hybrid cars that average 100 MPG.
Policy B will replace 5,000 diesel trucks that average 5 MPG with turbocharged, aerodynamic diesel trucks that average 10 MPG.

Assume that both cars and trucks last about 100,000 miles (in reality this of course depends on a lot of factors), and diesel and gas pollute about the same amount per gallon (this isn’t quite true, but it’s close). Which policy should we choose?

It seems obvious: Policy A, right? 10,000 vehicles, each increasing efficiency by 75 MPG or a factor of 4, instead of 5,000 vehicles, each increasing efficiency by only 5 MPG or a factor of 2.

And yet—in fact the correct answer is definitely policy B, because the use of MPG has distorted our perception of what constitutes efficiency. We should have been using the inverse: gallons per hundred miles.

Policy A will replace 10,000 cars that average 4 GPHM with cars that average 1 GPHM.
Policy B will replace 5,000 trucks that average 20 GPHM with trucks that average 10 GPHM.

This means that policy A will save (10,000)(100,000/100)(4-1) = 30 million gallons, while policy B will save (5,000)(100,000/100)(20-10) = 50 million gallons.

A gallon of gasoline produces about 9 kg of CO2 when burned. This means that by choosing the right policy here, we’ll have saved 450,000 tons of CO2—or by choosing the wrong one we would only have saved 270,000.

The simple choice of which efficiency measure to use when making our judgment—GPHM versus MPG—has had a profound effect on the real impact of our choices.

Let’s try applying the same reasoning to charities. Again suppose we can choose one of two policies.

Policy C will move $10 million that currently goes to local community charities which can save one QALY for $1 million to medical-research charities that can save one QALY for $50,000.
Policy D will move $10 million that currently goes to direct-transfer charities which can save one QALY for $1000 to anti-malaria net charities that can save one QALY for $800.

Policy C means moving funds from charities that are almost useless ($1 million per QALY!?) to charities that meet a basic notion of cost-effectiveness (most public health agencies in the First World have a standard threshold of about $50,000 or $100,000 per QALY).

Policy D means moving funds from charities that are already highly cost-effective to other charities that are only a bit more cost-effective. It almost seems pedantic to even concern ourselves with the difference between $1000 per QALY and $800 per QALY.

It’s the same $10 million either way. So, which policy should we pick?

If the lesson you took from the MPG example is that we should always be focused on increasing the efficiency of the least efficient, you’ll get the wrong answer. The correct answer is based on actually using the right measure of efficiency.

Here, it’s not dollars per QALY we should care about; it’s QALY per million dollars.

Policy C will move $10 million from charities which get 1 QALY per million dollars to charities which get 20 QALY per million dollars.
Policy D will move $10 million from charities which get 1000 QALY per million dollars to charities which get 1250 QALY per million dollars.

Multiply that out, and policy C will gain (10)(20-1) = 190 QALY, while policy D will gain (10)(1250-1000) = 2500 QALY. Assuming that “saving a life” means about 50 QALY, this is the difference between saving 4 lives and saving 50 lives.

My intuition actually failed me on this one; before I actually did the math, I had assumed that it would be far more important to move funds from utterly useless charities to ones that meet a basic standard. But it turns out that it’s actually far more important to make sure that the funds being targeted at the most efficient charities are really the most efficient—even apparently tiny differences matter a great deal.

Of course, if we can move that $10 million from the useless charities to the very best charities, that’s the best of all; it would save (10)(1250-1) = 12,490 QALY. This is nearly 250 lives.

In the fuel economy example, there’s no feasible way to upgrade a semitrailer to get 100 MPG. If we could, we totally should; but nobody has any idea how to do that. Even an electric semi probably won’t be that efficient, depending on how the grid produces electricity. (Obviously if the grid were all nuclear, wind, and solar, it would be; but very few places are like that.)

But when we’re talking about charities, this is just money; it is by definition fungible. So it is absolutely feasible in an economic sense to get all the money currently going towards nearly-useless charities like churches and museums and move that money directly toward high-impact charities like anti-malaria nets and vaccines.

Then again, it may not be feasible in a practical or political sense. Someone who currently donates to their local church may simply not be motivated by the same kind of cosmopolitan humanitarianism that motivates Effective Altruism. They may care more about supporting their local community, or be motivated by genuine religious devotion. This isn’t even inherently a bad thing; nobody is a cosmopolitan in everything they do, nor should we be—we have good reasons to care more about our own friends, family, and community than we do about random strangers in foreign countries thousands of miles away. (And while I’m fairly sure Jesus himself would have been an Effective Altruist if he’d been alive today, I’m well aware that most Christians aren’t—and this doesn’t make them “false Christians”.) There might be some broader social or cultural change that could make this happen—but it’s not something any particular person can expect to accomplish.

Whereas, getting people who are already Effective Altruists giving to efficient charities to give to a slightly more efficient charity is relatively easy: Indeed, it’s basically the whole purpose for which GiveWell exists. And there are analysts working at GiveWell right now whose job it is to figure out exactly which charities yield the most QALY per dollar and publish that information. One person doing that job even slightly better can save hundreds or even thousands of lives.

Indeed, I’m seriously considering applying to be one myself—it sounds both more pleasant and more important than anything I’d be likely to get in academia.

I’m not sure environmentalists understand what the word “consumption” means to economists.

2018-02-252018-03-18 pnrj market failure, public policy carbon emissions, carbon tax, China, climate change, consumerism, consumption, Denmark, efficiency, NIPA, ocean seeding, soil sequestration, vegetarian

Feb 25 JDN 2458175

Several times now I’ve heard environmentalists repeat variants of this line: “Capitalist economies depend on consumption; therefore capitalism is incompatible with environmental sustainability.”

A recent example comes from this article on QZ arguing that “conscious consumerism” isn’t viable for protecting the environment:

In short, consumption is the backbone of the American economy—which means individual conscious consumerism is basically bound to fail. “70% of GDP in the US is based on household consumption. So all the systems, the market, the institutions, everything is calibrated to maximize consumption,” Brown told me in a later interview. “The whole marketing industry and advertising invents new needs we didn’t know we had.”

Consumption. You keep using that word… I do not think it means what you think it means.

To be clear, let me say that I basically agree that “conscious consumerism” isn’t good enough. There are a few big things you can do to reduce your carbon footprint, like moving to California (or better yet, Scandinavia), becoming vegetarian, driving a hybrid car (or not driving at all), and not flying on airplanes. Aside from that, your consumer choices are not going to have a large impact. There is a huge amount of greenwashing that goes on—products that present themselves as eco-friendly which really aren’t. And these things by themselves are not enough. A 2012 study by the European Roundtable on Sustainable Consumption and Production found little or no difference in long-run carbon footprint between people who claim to be “green consumers” and people who don’t.

Moreover, there is a strong positive correlation between a country’s GDP and its carbon footprint. The list of countries with the highest carbon emissions looks a lot like the list of countries with the highest GDP.

But there is still substantial variation in the ratio of GDP to carbon emissions. Scandinavia does extremely well, at over $5,000 per ton (as does France, thanks to nuclear energy), while most European countries make about $3,000 per ton, the US is at about $2,000 per ton, and the very most carbon-intensive economies like China, the UAE, and South Africa only make about $1,000 per ton. China produces more carbon emissions per capita than Denmark despite having only one-third the standard of living (at purchasing power parity). Emissions also vary a great deal by states within the US; California’s per-capita emissions are comparable to France’s, while Wyoming’s are worse than the UAE’s.

This brings me to my main point, which is that economists don’t mean the same thing by the word “consumption” that environmentalists do. The environmentalist meaning might be closer to common usage: When something is consumed, we think of it as being destroyed, despoiled, degraded. (It’s even an archaic euphemism for tuberculosis.) So I can see why you would think that if our economy is 70% “consumption” that must make capitalism terrible for the environment: An economy that is 70% destruction, despoliation, and degradation does sound pretty bad.

But when economists use the word “consumption”, what we actually mean is private household expenditure. Our economy is 70% “consumption” in the sense that 70% of the dollars spent in GDP are spent by private individuals as opposed to corporations or the government. Of the $19.7 trillion of US GDP, $13.6 trillion was personal consumption expenditures. That’s actually 69%, but it’s okay to round up to 70%. The rest is made up of $3.4 trillion in government spending, $3.3 trillion in private investment, and a loss of $0.6 trillion from our trade deficit.

There’s no particular connection between private household expenditure and destruction, despoliation, or degradation. In fact, the most destructive form of GDP is obviously military spending, which is not counted as “consumption” in the National Income and Product Accounts but rather as “government expenditure”. Military spending is almost pure waste from an ecological perspective; it consumes mind-boggling amounts of fossil fuels in addition to causing death and destruction. The US military produces almost as much total carbon emissions as the entire country of Denmark.

In fact, the vast majority of private household expenditure in highly-developed countries is in the form of services—over $9.2 trillion in the US. The top four categories for expenditure on services in the US are housing/utilities, healthcare, finance, and food service. I can at least see how housing and utilities would be related to ecological impact—concrete and steel are very carbon-intensive, as is electricity if you’re not using nuclear or renewables. But healthcare, finance, and food service? When environmentalists point to the fact that 70% of our economy is consumption as evidence of the fundamental unsustainability of capitalism, this amounts to asserting that the reason we can’t prevent global warming is that there are so many nurses, accountants, and waiters.

Of course, most people don’t quite grasp what economists mean when we use the word “consumption”, so it makes for a nice talking point for environmentalists. You can conjure images of degradation and destruction while citing the respected authority of the National Income and Product Accounts. If you were already left-wing otherwise (as most environmentalists are), you can make it seem as though the problem is capitalism itself, the very structure of an economy built upon “consuming” the Earth.

In reality, there is enormous variation between countries in terms of their carbon efficiency, and in fact the most carbon-efficient nations are all those that have the highest degrees of political and economic freedom—which is to say, social democracies. One can debate whether social democracies like Denmark and Sweden are “truly capitalist”, but they definitely have free-market economies with large private sectors. On a global and historical scale, there’s really not that much difference between Denmark and the United States (compare to the USSR, or China, or Burkina Faso, or Medieval Japan, or Classical Rome). And if the US isn’t capitalist, who is?

My advice? Don’t talk about consumption at all. Talk about carbon emissions. Don’t ignore variation in GDP/carbon ratios: If the world copied China, we’d all have a per-capita income of $15,500 and emissions of 7.6 tons of carbon per person per year; but if the world copied Denmark, we’d all have a per-capita income of $51,000 and emissions of 6.8 tons of carbon per person per year. (Granted, even 6.8 is still too high; the targets I’ve seen say we need to be at about 3.0 by 2030. But Denmark has also been trending downward in emissions, so we could copy them on that too.) Reducing our standard of living wouldn’t save us if it meant being like China, and maintaining it wouldn’t hurt us if it meant being like Denmark.

I definitely agree that focusing on consumer choices isn’t good enough. Focus on policy. Carbon taxes, bans on unconventional extraction (e.g. offshore drilling, fracking), heavy investment in solar and nuclear energy, large reforestation projects, research into soil sequestration and ocean seeding. Demand these things from all politicians of all parties at all levels of government always. Don’t take no for an answer—because millions of people will die if we don’t stop climate change.

But I don’t think nurses, accountants, and waiters are the problem—and it doesn’t hurt for people to become vegetarian and buy hybrid cars.

The difference between price, cost, and value

2016-06-182016-06-10 pnrj core principles, critique of neoclassical economics, heuristics and biases, market failure, public policy capitalism, cocoa, coltan, computers, cost, Cote d'Ivoire, efficiency, Eisenhower, endowment effect, EPA, externalities, Gambia, heliocentrism, inequality, Koch, marginal utility, nominal, opportunity cost, OSHA, paradigm shift, Patreon, price, real, San Francisco, transitive, utility, value, wealth, willingness-to-accept, willingness-to-pay

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.

We do not benefit from economic injustice.

2016-03-122016-03-05 pnrj development economics, ethics, public policy, Uncategorized Apple, billionaires, efficiency, exploitation, history, income, income effect, inequality, injustice, iPad, iPod, Japan, Korea, labor, Oprah, Pareto-efficiency, poverty, privilege, slavery, substitution effect, sweatshops, tragedy of the commons

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 19^th 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.

Is marginal productivity fair?

2014-11-012015-04-04 pnrj critique of neoclassical economics Adam Smith, deadweight loss, DeBeers, demand, diamond, efficiency, efficient, Einstein, elasticity, fair, fairness, labor market, marginal, productivity, supply, water, willingness-to-accept

JDN 2456963 PDT 11:11.

The standard economic equilibrium that is the goal of any neoclassical analysis is based on margins, rather than totals; what matters is not how much you have in all, but how much you get from each new one. This may be easier to understand with specific examples: The price of a product isn’t set by the total utility that you get from using that product; it’s set by the marginal utility that you get from each new unit. The wage of a worker isn’t set by their total value to the company; it’s set by the marginal value they provide with each additional hour of work. Formally, it’s not the value of the function f(x), it’s the derivative of the function, f'(x). (If you don’t know calculus, don’t worry about that last part; it isn’t that important to understand the basic concept.)

This is the standard modern explanation for Adam Smith’s “diamond-water paradox“: Why are diamonds so much more expensive than water, even though water is much more useful? Well, we have plenty of water, so the marginal utility of water isn’t very high; what are you really going to do with that extra liter? But we don’t have a lot of diamonds, so even though diamonds in general aren’t that useful, getting an extra diamond has a lot of benefit. (The units are a bit weird, as George Stigler once used to argue that Smith’s paradox is “meaningless”; but that’s silly. Let’s fix the units at “per kilogram”; a kilogram of diamonds is far, far more expensive than a kilogram of water.)

This explanation is obviously totally wrong, by the way; that’s not why diamonds are expensive. The marginal-utility argument makes sense for cars (or at least ordinary Fords and Toyotas, for reasons you’ll see in a minute), but it doesn’t explain diamonds. Diamonds are expensive for two reasons: First, the absolutely insane monopoly power of the De Beers cartel; as you might imagine, water would be really expensive too if it were also controlled by a single cartel with the power to fix prices and crush competitors. (For awhile De Beers executives had a standing warrant for their arrest in the United States; recently they pled guilty and paid fines—because, as we all know, rich people never go to prison.) And you can clearly see how diamond prices plummeted when the cartel was weakened in the 1980s. But Smith was writing long before DeBeers, and even now that De Beers only controls 40% of the market so we have an oligopoly instead of a monopoly (it’s a step in the right direction I guess), diamonds are still far more expensive than water. The real reason why diamonds are expensive is that diamonds are a Veblen good; you don’t buy diamonds because you actually want to use diamonds (maybe once in awhile, if you want to make a diamond saw or something). You buy diamonds in order to show off how rich you are. And if your goal is to show how rich you are, higher prices are good; you want it to be really expensive, you’re more likely to buy it if it’s really expensive. That’s why the marginal utility argument doesn’t work for Porsches and Ferraris; they’re Veblen goods too. If the price of a Ferrari suddenly dropped to $10,000, people would realize pretty quickly that they are hard to maintain, have very poor suspensions, and get awful gas mileage. It’s not like you can actually drive at 150 mph without getting some serious speeding tickets. (I guess they look nice?) But if the price of a Prius dropped to $10,000, everyone would buy one. For some people diamonds are also a speculation good; they hope to buy them at one price and sell them at a higher price. This is also how most trading in the stock market works, which is why I’m dubious of how well the stock market actually supports real investment. When we’re talking about Veblen goods and speculation goods, the sky is the limit; any price that someone can pay is a price they might sell at.

But all of that is a bit tangential. It’s worth thinking about all the ways that neoclassical theory doesn’t comport with reality, all the cases where price and marginal value become unhinged. But for today I’m going to give the neoclassicists the benefit of the doubt: Suppose it were true. Suppose that markets really were perfectly efficient and everything were priced at its marginal value. Would that even be a good thing?

I tend to focus most of my arguments on why a given part of our economic system deviates from optimal efficiency, because once you can convince economists of that they are immediately willing to try to fix it. But what if we had optimal efficiency? Most economists would say that we’re done, we’ve succeeded, everything is good now. (I am suddenly reminded of the Lego song, “Everything is Awesome.”) This notion is dangerously wrong.

A system could be perfectly efficient and still be horrifically unfair. This is particularly important when we’re talking about labor markets. A diamond or a bottle of water doesn’t have feelings; it doesn’t care what price you sell it at. More importantly it doesn’t have rights. People have feelings; people have rights. (And once again I’m back to Citizens United; a rat is more of a person than any corporation. We should stop calling them “rats” and “fat cats”, for this is an insult to the rodent and feline communities. No, only a human psychopath could ever be quite so corrupt.)

Of course when you sell a product, the person selling it cares how much you pay, but that will either trace back to someone’s labor—and labor markets are still the issue—or it won’t, in which case as far as I’m concerned it really doesn’t matter. If you make money simply by owning things, our society is giving you an enormous gift simply by allowing that capital income to exist; press the issue much more and we’d be well within our rights to confiscate every dime. Unless and until capital ownership is shared across the entire population and we can use it to create a post-scarcity society, capital income will be a necessary evil at best.

So let’s talk about labor markets. If you’ve taken any economics, you have probably seen a great many diagrams like this:

The red line is labor supply, the blue line is labor demand. At the intersection is our glorious efficient market equilibrium, in this case at 7.5 hours of work per day (the x-axis) and $12.50 an hour (the y-axis). The green line is the wage, $12.50 per hour. But let’s stop and think for a moment about what this diagram really means.

What decides that red labor supply line? Do people just arbitrarily decide that they’re going to work 4 hours a day if they get paid $9 an hour, but 8 hours a day if they get paid $13 an hour? No, this line is meant to represent the marginal real cost of working. It’s the monetized value of your work effort and the opportunity cost of what else you could have been doing with your time. It rises because the more hours you work, the more stress it causes you and the more of your life it takes up. Working 4 hours a day, you probably had that time available anyway. Working 8 hours a day, you can fit it in. Working 12 hours a day, now you have no leisure at all. Working 16 hours a day, now you’re having trouble fitting in basic needs like food and sleep. Working 20 hours a day, you eat at work, you don’t get enough sleep, and you’re going to burn yourself out in no time. Why is it a straight line? Because we assume linear relationships to make the math easier. (No, really; that is literally the only reason. We call them “supply and demand curves” but almost always draw and calculate them as straight lines.)

Now let’s consider the blue labor demand line. Is this how much the “job creators” see fit to bestow upon you? No, it’s the marginal value of productivity. The first hour you work each day, you are focused and comfortable, and you can produce a lot of output. The second hour you’re just a little bit fatigued, so you can produce a bit less. By the time you get to hour 8, you’re exhausted, and producing noticeably less output. And if they pushed you past 16 hours, you’d barely produce anything at all. They multiply the amount of products you produce by the price at which they can sell those products, and that’s their demand for your labor. And once again we assume it’s a straight line just to make the math easier.

From this diagram you can calculate what is called employer surplus and worker surplus. Employer surplus is basically the same thing as profit. (It’s not exactly the same for some wonky technical reasons, but for our purposes they may as well be the same.) Worker surplus is a subtler concept; it’s the amount of money you receive minus the monetized value of your cost of working. So if that first hour of work was really easy and you were willing to do it for anything over $5, we take that $5 as your monetized cost of working (your “marginal willingness-to-accept“). Then if you are being paid $12.50 an hour, we infer that you must have gained $7.50 worth of utility from that exchange. (“$7.50 of utility” is a very weird concept, for reasons I’ll get into more in a later post; but it is actually the standard means of estimating utility in neoclassical economics. That’s one of the things I hope to change, actually.)

When you add these up for all the hours worked, the result becomes an integral, which is a formal mathematical way of saying “the area between those two lines”. In this case they are triangles of equal size, so we can just use the old standby A = 1/2*b*h. The area of each triangle is 1/2*7.5*7.5 = $28.13. From each day you work, you make $28.13 in consumer surplus and your employer makes $28.13 in profit.

And that seems fair, doesn’t it? You split it right down the middle. Both of you are better off than you were, and the economic benefits are shared equally. If this were really how labor markets work, that seems like how things ought to be.

But nothing in the laws of economics says that the two areas need to be equal. We tend to draw them that way out of an aesthetic desire for symmetry. But in general they are not, and in some cases they can be vastly unequal.

This happens if we have wildly different elasticities, which is a formal term for the relative rates of change of two things. An elasticity of labor supply of 1 would mean that for a 1% increase in wage you’re willing to work 1% more hours, while an elasticity of 10 would mean that for a 1% increase in wage you’re willing to work 10% more hours. Elasticities can also be negative; a labor demand elasticity of -1 would mean that for a 1% increase in wage your employer is willing to hire you for 1% fewer hours. In the graph above, the elasticity of labor supply is exactly 1. The elasticity of labor demand varies along the curve, but at the equilibrium it is about -1.6. The fact that the profits are shared equally is related to the fact that these two elasticities are close in magnitude but opposite in sign.

But now consider this equilibrium, in which I’ve raised the labor elasticity to 10. Notice that the wage and number of hours haven’t change; it’s still 7.5 hours at $12.50 per hour. But now the profits are shared quite unequally indeed; while the employer still gets $28.13, the value for the worker is only 1/2*7.5*0.75 = $2.81. In real terms this means we’ve switched from a job that starts off easy but quickly gets harder to a job that is hard to start with but never gets much harder than that.

On the other hand what if the supply elasticity is only 0.1? Now the worker surplus isn’t even a triangle; it’s a trapezoid. The area of this trapezoid is 6*12.5+1/2*1.5*12.5 = $84.38. This job starts off easy and fun—so much so that you’d do it for free—but then after 6 hours a day it quickly becomes exhausting and you need to stop.

If we had to guess what these jobs are, my suggestion is that maybe the first one is a research assistant, the second one is a garbage collector, and the third one is a video game tester. And thus, even though they are paid about the same (I think that’s true in real life? They all make about $15 an hour or $30k a year), we all agree that the video game tester job is better than the research assistant job which is better than the garbage collector job—which is exactly what the worker surplus figures are saying.

What about the demand side? Here’s where it gets really unfair. Going back to our research assistant with a supply elasticity of 1, suppose they’re not really that good a researcher. Their output isn’t wrong, but it’s also not very interesting. They can do the basic statistics, but they aren’t very creative and they don’t have a deep intuition for the subject. This might produce a demand elasticity 10 times larger. The worker surplus remains the same, but the employer surplus is much lower. The triangle has an area 1/2*7.5*0.75 = $2.81.

Now suppose that they are the best research assistant ever; let’s say we have a young Einstein. Everything he touches turns to gold, but even Einstein needs his beauty sleep (he actually did sleep about 10 hours a day, which is something I’ve always been delighted to have in common with him), so the total number of work hours still caps out at 7.5. It is entirely possible for the wage equilibrium to be exactly the same as it was for the lousy researcher, making the graph look like this:

You can’t even see the top of the triangle on this scale; it’s literally off the chart. The worker had a lower bound at zero, but there’s no comparable upper bound. (I suppose you could argue the lower bound shouldn’t be there either, since there are kinds of work you’d be willing to do even if you had to pay to do them—like, well, testing video games.) The top of the triangle is actually at about $90, as it turns out, so the area of employer surplus is 1/2*(90-12.5)*7.5 = $290.63. For every day he works, the company gets almost $300, but Einstein himself only gets $28.13 after you include what it costs him to work. (His gross pay is just wage*hours of course, so that’s $93.75.) The total surplus produced is $318.76. Einstein himself only gets a measly 8.9% of that.

So here we have three research assistants, who have very different levels of productivity, getting the same pay. But isn’t pay supposed to reflect productivity? Sort of; it’s supposed to reflect marginal productivity. Because Einstein gets worn out and produces at the same level as the mediocre researcher after 7.5 hours of work, since that’s where the equilibrium is that’s what they both get paid.

Now maybe Einstein should hold back; he could exercise some monopolistic power over his amazing brain. By only offering to work 4 hours a day, he can force the company to pay him at his marginal productivity for 4 hours a day, which turns out to be $49 an hour. Now he makes a gross pay of $196, with a worker surplus of $171.

This diagram is a bit harder to read, so let me walk you through it. The light red and blue lines are the same as before. The darker blue line is the marginal revenue per hour for Einstein, once he factors in the fact that working more hours will mean accepting a lower wage. The optimum for him is when that marginal revenue curve crosses his marginal cost curve, which is the red supply curve. That decides how many hours he will work, namely 4. But that’s not the wage he gets; to find that, we move up vertically along the dark red line until we get the company’s demand curve. That tells us what wage the company is willing to pay for the level of marginal productivity Einstein has at 4 hours per day of work—which is the $49 wage he ends up making shown by the dark green line. The lighter lines show what happens if we have a competitive labor market, while the darker lines show what happens if Einstein exercises monopoly power.

The company still does pretty well on this deal; they now make an employer surplus of $82. Now, of the total $253 of economic surplus being made, Einstein takes 69%. It’s his brain, so him taking most of the benefit seems fair.

But you should notice something: This result is inefficient! There’s a whole triangle between 4 and 7.5 hours that nobody is getting; it’s called the deadweight loss. In this case it is $65.76, the difference between the total surplus in the efficient equilibrium and the inefficient equilibrium. In real terms, this means that research doesn’t get done because Einstein held back in order to demand a higher wage. That’s research that should be done—its benefit exceeds its cost—but nobody is doing it. Well now, maybe that doesn’t seem so fair after all. It seems selfish of him to not do research that needs done just so he can get paid more for what he does.

If Einstein has monopoly power, he gets a fair share but the market is inefficient. Removing Einstein’s monopoly power by some sort of regulation would bring us back to efficiency, but it would give most of his share to the company instead. Neither way seems right.

How do we solve this problem? I’m honestly not sure. First of all, we rarely know the actual supply and demand elasticities, and when we do it’s generally after painstaking statistical work to determine the aggregate elasticities, which aren’t even what we’re talking about here. These are individual workers.

Notice that the problem isn’t due to imperfect information; the company knows full well that Einstein is a golden goose, but they aren’t going to pay him any more than they have to.

We could just accept it, I suppose. As long as the productive work gets done, we could shrug our shoulders and not worry about the fact that corporations are capturing most of the value from the hard work of our engineers and scientists. That seems to be the default response, perhaps because it’s the easiest. But it sure doesn’t seem fair to me.

One solution might be for the company to voluntarily pay Einstein more, or offer him some sort of performance bonus. I wouldn’t rule out this possibility entirely, but this would require the company to be unusually magnanimous. This won’t happen at most corporations. It might happen for researchers at a university, where the administrators are fellow academics. Or it might happen to a corporate executive because other corporate executives feel solidarity for their fellow corporate executives.

That sort of solidarity is most likely why competition hasn’t driven down executive salaries. Theoretically shareholders would have an incentive to choose boards of directors who are willing to work for $20 an hour and elect CEOs who are willing to work for $30 an hour; but in practice old rich White guys feel solidarity with other old rich White guys, and even if there isn’t any direct quid pro quo there is still a general sense that because we are “the same kind of people” we should all look out for each other—and that’s how you get $50 million salaries. And then of course there’s the fact that even publicly-traded companies often have a handful of shareholders who control enough of the shares to win any vote.

In some industries, we don’t need to worry about this too much because productivity probably doesn’t really vary that much; just how good can a fry cook truly be? But this is definitely an issue for a lot of scientists and engineers, particularly at entry-level positions. Some scientists are an awful lot better than other scientists, but they still get paid the same.

Much more common however is the case where the costs of working vary. Some people may have few alternatives, so their opportunity cost is low, driving their wage down; but that doesn’t mean they actually deserve a lower wage. Or they may be disabled, making it harder to work long hours; but even though they work so much harder their pay is the same, so their net benefit is much smaller. Even though they aren’t any more productive, it still seems like they should be paid more to compensate them for that extra cost of working. At the other end are people who start in a position of wealth and power; they have a high opportunity cost because they have so many other options, so it may take very high pay to attract them; but why do they deserve to be paid more just because they have more to start with?

Another option would be some sort of redistribution plan, where we tax the people who are getting a larger share and give it to those who are getting a smaller share. The problem here arises in how exactly you arrange the tax. A theoretical “lump sum tax” where we just figure out the right amount of money and say “Person A: Give $217 to person B! No, we won’t tell you why!” would be optimally efficient because there’s no way it can distort markets if nobody sees it coming; but this is not something we can actually do in the real world. (It also seems a bit draconian; the government doesn’t even tax activities, they just demand arbitrary sums of money?) We’d have to tax profits, or sales, or income; and all of these could potentially introduce distortions and make the market less efficient.

We could offer some sort of publicly-funded performance bonus, and for scientists actually we do; it’s called the Nobel Prize. If you are truly the best of the best of the best as Einstein was, you may have a chance at winning the Nobel and getting $1.5 million. But of course that has to be funded somehow, and it only works for the very very top; it doesn’t make much difference to Jane Engineer who is 20% more productive than her colleagues.

I don’t find any of these solutions satisfying. This time I really can’t offer a good solution. But I think it’s important to keep the problem in mind. It’s important to always remember that “efficient” does not mean “fair”, and being paid at marginal productivity isn’t the same as being paid for overall productivity.

Pareto Efficiency: Why we need it—and why it’s not enough

2014-09-132015-05-09 pnrj core principles, critique of neoclassical economics, Top 10 things to know about economics cardinal, cognitive, economics, efficiency, ethics, game theory, happiness, Krugman, Nash, nonzero-sum, ordinal, Pareto, preference, Rawls, utility, voting, zero-sum

JDN 2456914 PDT 11:45.

I already briefly mentioned the concept in an earlier post, but Pareto-efficiency is so fundamental to both ethics and economics I decided I would spent some more time on explaining exactly what it’s about.

This is the core idea: A system is Pareto-efficient if you can’t make anyone better off without also making someone else worse off. It is Pareto-inefficient if the opposite is true, and you could improve someone’s situation without hurting anyone else.

Improving someone’s situation without harming anyone else is called a Pareto-improvement. A system is Pareto-efficient if and only if there are no possible Pareto-improvements.

Zero-sum games are always Pareto-efficient. If the game is about how we distribute the same $10 between two people, any dollar I get is a dollar you don’t get, so no matter what we do, we can’t make either of us better off without harming the other. You may have ideas about what the fair or right solution is—and I’ll get back to that shortly—but all possible distributions are Pareto-efficient.

Where Pareto-efficiency gets interesting is in nonzero-sum games. The most famous and most important such game is the so-called Prisoner’s Dilemma; I don’t like the standard story to set up the game, so I’m going to give you my own. Two corporations, Alphacomp and Betatech, make PCs. The computers they make are of basically the same quality and neither is a big brand name, so very few customers are going to choose on anything except price. Combining labor, materials, equipment and so on, each PC costs each company $300 to manufacture a new PC, and most customers are willing to buy a PC as long as it’s no more than $1000. Suppose there are 1000 customers buying. Now the question is, what price do they set? They would both make the most profit if they set the price at $1000, because customers would still buy and they’d make $700 on each unit, each making $350,000. But now suppose Alphacomp sets a price at $1000; Betatech could undercut them by making the price $999 and sell twice as many PCs, making $699,000. And then Alphacomp could respond by setting the price at $998, and so on. The only stable end result if they are both selfish profit-maximizers—the Nash equilibrium—is when the price they both set is $301, meaning each company only profits $1 per PC, making $1000. Indeed, this result is what we call in economics perfect competition. This is great for consumers, but not so great for the companies.

If you focus on the most important choice, $1000 versus $999—to collude or to compete—we can set up a table of how much each company would profit by making that choice (a payoff matrix or normal form game in game theory jargon).

A: $999

A: $1000

B: $999

A:$349k

B:$349k

A:$0

B:$699k

B: $1000

A:$699k

B:$0

A:$350k

B:$350k

Obviously the choice that makes both companies best-off is for both companies to make the price $1000; that is Pareto-efficient. But it’s also Pareto-efficient for Alphacomp to choose $999 and the other one to choose $1000, because then they sell twice as many computers. We have made someone worse off—Betatech—but it’s still Pareto-efficient because we couldn’t give Betatech back what they lost without taking some of what Alphacomp gained.

There’s only one option that’s not Pareto-efficient: If both companies charge $999, they could both have made more money if they’d charged $1000 instead. The problem is, that’s not the Nash equilibrium; the stable state is the one where they set the price lower.

This means that only case that isn’t Pareto-efficient is the one that the system will naturally trend toward if both compal selfish profit-maximizers. (And while most human beings are nothing like that, most corporations actually get pretty close. They aren’t infinite, but they’re huge; they aren’t identical, but they’re very similar; and they basically are psychopaths.)

In jargon, we say the Nash equilibrium of a Prisoner’s Dilemma is Pareto-inefficient. That one sentence is basically why John Nash was such a big deal; up until that point, everyone had assumed that if everyone acted in their own self-interest, the end result would have to be Pareto-efficient; Nash proved that this isn’t true at all. Everyone acting in their own self-interest can doom us all.

It’s not hard to see why Pareto-efficiency would be a good thing: if we can make someone better off without hurting anyone else, why wouldn’t we? What’s harder for most people—and even most economists—to understand is that just because an outcome is Pareto-efficient, that doesn’t mean it’s good.

I think this is easiest to see in zero-sum games, so let’s go back to my little game of distributing the same $10. Let’s say it’s all within my power to choose—this is called the ultimatum game. If I take $9 for myself and only give you $1, is that Pareto-efficient? It sure is; for me to give you any more, I’d have to lose some for myself. But is it fair? Obviously not! The fair option is for me to go fifty-fifty, $5 and $5; and maybe you’d forgive me if I went sixty-forty, $6 and $4. But if I take $9 and only offer you $1, you know you’re getting a raw deal.

Actually as the game is often played, you have the choice the say, “Forget it; if that’s your offer, we both get nothing.” In that case the game is nonzero-sum, and the choice you’ve just taken is not Pareto-efficient! Neoclassicists are typically baffled at the fact that you would turn down that free $1, paltry as it may be; but I’m not baffled at all, and I’d probably do the same thing in your place. You’re willing to pay that $1 to punish me for being so stingy. And indeed, if you allow this punishment option, guess what? People aren’t as stingy! If you play the game without the rejection option, people typically take about $7 and give about $3 (still fairer than the $9/$1, you may notice; most people aren’t psychopaths), but if you allow it, people typically take about $6 and give about $4. Now, these are pretty small sums of money, so it’s a fair question what people might do if $100,000 were on the table and they were offered $10,000. But that doesn’t mean people aren’t willing to stand up for fairness; it just means that they’re only willing to go so far. They’ll take a $1 hit to punish someone for being unfair, but that $10,000 hit is just too much. I suppose this means most of us do what Guess Who told us: “You can sell your soul, but don’t you sell it too cheap!”

Now, let’s move on to the more complicated—and more realistic—scenario of a nonzero-sum game. In fact, let’s make the “game” a real-world situation. Suppose Congress is debating a bill that would introduce a 70% marginal income tax on the top 1% to fund a basic income. (Please, can we debate that, instead of proposing a balanced-budget amendment that would cripple US fiscal policy indefinitely and lead to a permanent depression?)

This tax would raise about 14% of GDP in revenue, or about $2.4 trillion a year (yes, really). It would then provide, for every man, woman and child in America, a $7000 per year income, no questions asked. For a family of four, that would be $28,000, which is bound to make their lives better.

But of course it would also take a lot of money from the top 1%; Mitt Romney would only make $6 million a year instead of $20 million, and Bill Gates would have to settle for $2.4 billion a year instead of $8 billion. Since it’s the whole top 1%, it would also hurt a lot of people with more moderate high incomes, like your average neurosurgeon or Paul Krugman, who each make about $500,000 year. About $100,000 of that is above the cutoff for the top 1%, so they’d each have to pay about $70,000 more than they currently do in taxes; so if they were paying $175,000 they’re now paying $245,000. Once taking home $325,000, now only $255,000. (Probably not as big a difference as you thought, right? Most people do not seem to understand how marginal tax rates work, as evinced by “Joe the Plumber” who thought that if he made $250,001 he would be taxed at the top rate on the whole amount—no, just that last $1.)

You can even suppose that it would hurt the economy as a whole, though in fact there’s no evidence of that—we had tax rates like this in the 1960s and our economy did just fine. The basic income itself would inject so much spending into the economy that we might actually see more growth. But okay, for the sake of argument let’s suppose it also drops our per-capita GDP by 5%, from $53,000 to $50,300; that really doesn’t sound so bad, and any bigger drop than that is a totally unreasonable estimate based on prejudice rather than data. For the same tax rate might have to drop the basic income a bit too, say $6600 instead of $7000.

So, this is not a Pareto-improvement; we’re making some people better off, but others worse off. In fact, the way economists usually estimate Pareto-efficiency based on so-called “economic welfare”, they really just count up the total number of dollars and divide by the number of people and call it a day; so if we lose 5% in GDP they would register this as a Pareto-loss. (Yes, that’s a ridiculous way to do it for obvious reasons—$1 to Mitt Romney isn’t worth as much as it is to you and me—but it’s still how it’s usually done.)

But does that mean that it’s a bad idea? Not at all. In fact, if you assume that the real value—the utility—of a dollar decreases exponentially with each dollar you have, this policy could almost double the total happiness in US society. If you use a logarithm instead, it’s not quite as impressive; it’s only about a 20% improvement in total happiness—in other words, “only” making as much difference to the happiness of Americans from 2014 to 2015 as the entire period of economic growth from 1900 to 2000.

If right now you’re thinking, “Wow! Why aren’t we doing that?” that’s good, because I’ve been thinking the same thing for years. And maybe if we keep talking about it enough we can get people to start voting on it and actually make it happen.

But in order to make things like that happen, we must first get past the idea that Pareto-efficiency is the only thing that matters in moral decisions. And once again, that means overcoming the standard modes of thinking in neoclassical economics.

Something strange happened to economics in about 1950. Before that, economists from Marx to Smith to Keynes were always talking about differences in utility, marginal utility of wealth, how to maximize utility. But then economists stopped being comfortable talking about happiness, deciding (for reasons I still do not quite grasp) that it was “unscientific”, so they eschewed all discussion of the subject. Since we still needed to know why people choose what they do, a new framework was created revolving around “preferences”, which are a simple binary relation—you either prefer it or you don’t, you can’t like it “a lot more” or “a little more”—that is supposedly more measurable and therefore more “scientific”. But under this framework, there’s no way to say that giving a dollar to a homeless person makes a bigger difference to them than giving the same dollar to Mitt Romney, because a “bigger difference” is something you’ve defined out of existence. All you can say is that each would prefer to receive the dollar, and that both Mitt Romney and the homeless person would, given the choice, prefer to be Mitt Romney. While both of these things are true, it does seem to be kind of missing the point, doesn’t it?

There are stirrings of returning to actual talk about measuring actual (“cardinal”) utility, but still preferences (so-called “ordinal utility”) are the dominant framework. And in this framework, there’s really only one way to evaluate a situation as good or bad, and that’s Pareto-efficiency.

Actually, that’s not quite right; John Rawls cleverly came up with a way around this problem, by using the idea of “maximin”—maximize the minimum. Since each would prefer to be Romney, given the chance, we can say that the homeless person is worse off than Mitt Romney, and therefore say that it’s better to make the homeless person better off. We can’t say how much better, but at least we can say that it’s better, because we’re raising the floor instead of the ceiling. This is certainly a dramatic improvement, and on these grounds alone you can argue for the basic income—your floor is now explicitly set at the $6600 per year of the basic income.

But is that really all we can say? Think about how you make your own decisions; do you only speak in terms of strict preferences? I like Coke more than Pepsi; I like massages better than being stabbed. If preference theory is right, then there is no greater distance in the latter case than the former, because this whole notion of “distance” is unscientific. I guess we could expand the preference over groups of goods (baskets as they are generally called), and say that I prefer the set “drink Pepsi and get a massage” to the set “drink Coke and get stabbed”, which is certainly true. But do we really want to have to define that for every single possible combination of things that might happen to me? Suppose there are 1000 things that could happen to me at any given time, which is surely conservative. In that case there are 2^1000 = 10^300 possible combinations. If I were really just reading off a table of unrelated preference relations, there wouldn’t be room in my brain—or my planet—to store it, nor enough time in the history of the universe to read it. Even imposing rational constraints like transitivity doesn’t shrink the set anywhere near small enough—at best maybe now it’s 10^20, well done; now I theoretically could make one decision every billion years or so. At some point doesn’t it become a lot more parsimonious—dare I say, more scientific—to think that I am using some more organized measure than that? It certainly feels like I am; even if couldn’t exactly quantify it, I can definitely say that some differences in my happiness are large and others are small. The mild annoyance of drinking Pepsi instead of Coke will melt away in the massage, but no amount of Coke deliciousness is going to overcome the agony of being stabbed.

And indeed if you give people surveys and ask them how much they like things or how strongly they feel about things, they have no problem giving you answers out of 5 stars or on a scale from 1 to 10. Very few survey participants ever write in the comments box: “I was unable to take this survey because cardinal utility does not exist and I can only express binary preferences.” A few do write 1s and 10s on everything, but even those are fairly rare. This “cardinal utility” that supposedly doesn’t exist is the entire basis of the scoring system on Netflix and Amazon. In fact, if you use cardinal utility in voting, it is mathematically provable that you have the best possible voting system, which may have something to do with why Netflix and Amazon like it. (That’s another big “Why aren’t we doing this already?”)

If you can actually measure utility in this way, then there’s really not much reason to worry about Pareto-efficiency. If you just maximize utility, you’ll automatically get a Pareto-efficient result; but the converse is not true because there are plenty of Pareto-efficient scenarios that don’t maximize utility. Thinking back to our ultimatum game, all options are Pareto-efficient, but you can actually prove that the $5/$5 choice is the utility-maximizing one, if the two players have the same amount of wealth to start with. (Admittedly for those small amounts there isn’t much difference; but that’s also not too surprising, since $5 isn’t going to change anybody’s life.) And if they don’t—suppose I’m rich and you’re poor and we play the game—well, maybe I should give you more, precisely because we both know you need it more.

Perhaps even more significant, you can move from a Pareto-inefficient scenario to a Pareto-efficient one and make things worse in terms of utility. The scenario in which the top 1% are as wealthy as they can possibly be and the rest of us live on scraps may in fact be Pareto-efficient; but that doesn’t mean any of us should be interested in moving toward it (though sadly, we kind of are). If you’re only measuring in terms of Pareto-efficiency, your attempts at improvement can actually make things worse. It’s not that the concept is totally wrong; Pareto-efficiency is, other things equal, good; but other things are never equal.

So that’s Pareto-efficiency—and why you really shouldn’t care about it that much.

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Human Economics

Cognitive development economics: Understanding the mind in order to feed the world

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