Defending yourself defends others

Mar 10 JDN 2458553

There’s a meme going around the feminist community that is very well-intentioned, but dangerously misguided. I first encountered it as a tweet, though it may have originated elsewhere:

If you’re promoting changes to women’s behaviour to “prevent” rape, you’re really saying “make sure he rapes the other girl”.

The good intention here is that we need to stop blaming victims. Victim-blaming is ubiquitous, and especially common and harmful in the case of sexual assault. If someone assaults you—or robs you, or abuses you—it is never your fault.

But I fear that there is a baby being thrown out with this bathwater: While failing to defend yourself doesn’t make it your fault, being able to defend yourself can still make you safer.

And, just as importantly, it can make others safer too. The game theory behind that is the subject of this post.

For purposes of the theory, it doesn’t matter what the crime is. So let’s set aside the intense emotional implications of sexual assault and suppose the crime is grand theft auto.

Some cars are defended—they have a LoJack system installed that will allow them to be recovered and the thieves to be prosecuted. (Don’t suppose it’s a car alarm; those don’t work.)

Other cars are not defended—once stolen, they may not be recovered.

There are two cases to consider: Defense that is visible, and defense that is invisible.

Let’s start by assuming that the defense is visible: When choosing which car to try to steal, the thieves can intentionally pick one that doesn’t have a LoJack installed. (This doesn’t work well for car theft, but it’s worth considering for the general question of self-defense. The kind of clothes you wear, the way you carry yourself, how many people are with you, and overall just how big and strong you look are visible signs of a capacity for self-defense.)

In that case, the game is one of perfect information: First each car owner chooses whether or not to install a LoJack at some cost L (in real life, about $700), and then thieves see which cars are equipped and then choose which car to steal.

Let’s say the probability of a car theft being recovered and prosecuted if it’s defended is p, and the probability of it being recovered if it’s not defended is q; p > q. In the real world, about half of stolen cars are recovered—but over 90% of LoJack-equipped vehicles are recovered, so p = 0.9 and q = 0.5.

Then let’s say the cost of being caught and prosecuted is C. This is presumably quite high: If you get convicted, you could spend time in prison. But maybe the car will be recovered and the thief won’t be convicted. Let’s ballpark that at about $30,000.

Finally, the value of successfully stealing a car is V. The average price of a used car in the US is about $20,000, so V is probably close to that.

If no cars are defended, what will the thieves choose? Assuming they are risk-neutral (car thieves don’t seem like very risk averse folks, in general), the expected benefit of stealing a car is V – q C. With the parameters above, that’s (20000)-(0.5)(30000) = $5,000. The thieves will choose a car at random and steal it.

If some cars are defended and some are not, what will the thieves choose? They will avoid the defended cars and steal one of the undefended cars.

But what if all cars are defended? Now the expected benefit is V – p C, which is (20000)-(0.9)(30000) = -$7,000. The thieves will not steal any cars at all. (This is actually the unique subgame-perfect equilibrium: Everyone installs a LoJack and no cars get stolen. Of course, that assumes perfect rationality.)

Yet that isn’t so impressive; everyone defending themselves results in everyone being defended? That sounds tautological. Expecting everyone to successfully defend themselves all the time sounds quite unreasonable. This might be what people have in mind when they say things like the quote above: It’s impossible for everyone to be defended always.

But it turns out that we don’t actually need that. Things get a lot more interesting when we assume that self-defense can be invisible. It would be very hard to know whether a car has a LoJack installed without actually opening it up, and there are many other ways to defend yourself that are not so visible—such as knowing techniques of martial arts or using a self-defense phone app.

Now the game has imperfect information. The thieves don’t know whether you have chosen to defend your car or not.

We need to add a couple more parameters. First is the number of cars per thief n. Then we need the proportion of cars that are defended. Let’s call it d. Then with probability d a given car is defended, and with probability 1-d it is not.

The expected value of stealing a car for the thieves is now this: V – p d C – q (1-d) C. If this is positive, they will steal a car; if it is negative, they will not.

Knowing this, should you install a LoJack? Remember that it costs you L to do so.

What’s the probability your car will be stolen? If they are stealing cars at all, the probability of your car being one stolen is 1/n. If that happens, you will have an expected loss of (1-p)V if you have a LoJack, or (1-q)V if you don’t. The difference between those is (p-q)V.

So your expected benefit of having a LoJack is (p-q)V/n – L. With the parameters above, that comes to: (0.9-0.5)(20000)/n – (700) = 8000/n – 700. So if there are no more than 11 cars per thief, this is positive and you should buy a LoJack. If there are 12 or more cars per thief, you’re better off taking your chances.

This only applies if the thieves are willing to steal at all. And then the interesting question is whether V – p d C – q (1-d) C is positive. For these parameters, that’s (20000) – (0.9)(30000)d – (0.5)(30000) + (0.5)(30000)d = 5000 – 12000 d. Notice that if we substitute in d=0 we get back $5,000, and at d=1 we get back -$7,000, just as before. There is a critical value of d at which the thieves aren’t sure whether to try or not: d* = 5/12 = 0.42.

Assuming that a given car is worth defending if it would be stolen (n <= 11), the equilibrium is actually when precisely d* of the cars are defended and 1-d* are not. Any less than this, and there is an undefended car that would be worth defending. Any more than this, and the thieves aren’t going to try to steal anything, so why bother defending?

Of course this is a very stylized model: In particular, we assumed that all cars are equally valuable and equally easy to steal, which is surely not true in real life.

Yet this model is still enough to make the most important point: Since presumably we do not value the welfare of the car thieves, it could happen that people choosing on their own would not defend their cars, but society as a whole would be better off if they did.

The net loss to society from a stolen car is (1-q)V if the car was not defended, or (1-p)V if it was. But if the thieves don’t steal any cars at all, the net loss to society is zero. The cost of defending a proportion d* of all cars is n d* L.

So if we are currently at d = 0, society is currently losing (1-q)V. We could eliminate this cost entirely by paying n d* L to defend a sufficient number of cars. Suppose n = 30. Then this total cost is (30)(5/12)(700) = $8,750. The loss from cars being stolen was (0.5)(20000) = $10,000. So it would be worth it, from society’s perspective, to randomly install LoJack systems in 42% of cars.

But for any given car owner, it would not be worth it; the expected benefit is 8000/30 – 700 = -$433. (I guess we could ask how much you’re willing to pay for “peace of mind”.)

Where does the extra benefit go? To all the other car owners. By defending your car, you are raising d and thereby lowering the expected payoff for a car thief. There is a positive externality; this is a public good. You get some of that benefit yourself, but others also share in that benefit.

This brings me at last to the core message of this post:

Self-defense is a public good.

The better each person defends themselves, the riskier it becomes for criminals to try to victimize anyone. Never feel guilty for trying to defend yourself; you are defending everyone else at the same time. In fact, you should consider taking actions to defend yourself even when you aren’t sure it’s worth it for you personally: That positive externality may be large enough to make your actions worthwhile for society as a whole.

Again, this does not mean we should blame victims when they are unable to defend themselves. Self-defense is easier for some people than others, and everyone is bound to slip up on occasion. (Also, eternal vigilance can quickly shade over into paranoia.) It is always the perpetrator’s fault.

Our biggest oil subsidy is called the Interstate Highway System


August 13, JDN 2457979

In last week’s post I proposed an infrastructure project that probably sounded quite expensive. $410 billion for maglev lines? We’ve never spent anything like that on infrastructure, have we?

Actually, we have. The Interstate Highway System, in inflation-adjusted dollars, cost $526 billion. Of course, road is a lot cheaper than maglev rail, so that covers a lot more miles than the maglev system I’m proposing.

Of course, the maglev system would produce a lot less carbon emissions and be a great deal safer; while the Interstate Highway System has about 60% (91 log points) fewer traffic fatalities than the road system that came before it, the Shinkansen high-speed rail system in Japan has not had a single passenger fatality in over 50 years and 1 billion passengers. No system built by humans will ever be perfect, but the Shinkansen comes about as close as we’re ever going to get.

Assuming we could even get close to that level of safety, replacing the highway system with high-speed rail would save about 2,000 American lives every year. (Of course, we’d still lose over 30,000 Americans every year to non-interstate car accidents.)

But what I really want to talk about this week is how the Interstate Highway System is in fact an implicit oil subsidy. We currently spend over $140 billion per year in public funds to maintain highways (about one-fourth of which is specifically the Interstate Highway System). For those of you playing along at home, that’s about half what it would take to end world hunger.

The choice to spending this money maintaining highways instead of bike lanes, rail lines, or subway systems makes this spending an implicit subsidy for the car industry and the oil industry.

Of course, that’s only half the story; there’s also the gasoline tax, which is a pretty obvious tax on the oil industry. But the federal gasoline tax only raises about $35 billion per year, and state taxes add up to a comparable amount; so only about half what we spend on highways is actually covered by gasoline taxes. This means that even if you never drive a car, you are paying for the highway system.

Even including the gasoline tax, this means that this implicit oil subsidy may be the largest oil subsidy in the United States. Standard estimates of oil subsidies in the US range around $30 to $40 billion per year. Assuming that 3/4 of the benefit from the $140 billion in highway spending goes to the oil industry (the other 1/4 to the car industry), and then subtracting the roughly $70 billion paid in gasoline taxes leaves about $35 billion per year in net oil subsidy from the Interstate Highway System—which is to say about as much as all other oil subsidies combined.

Moreover, when you do drive on the highway, you usually don’t pay. You pay for gasoline, but that’s quite cheap, especially if your car is at all fuel-efficient; and most of us (in an entirely economically rational way) avoid toll roads when we have the time. Most of what you spend on driving is paying to buy, insure, and maintain your car—because cars are extremely complicated and expensive machines that take an awful lot of knowhow to build. The annual cost of driving a typical midsize sedan 15,000 miles per year is about $8,500. Of that, about $3,000 is depreciation (I’m assuming half the depreciation was inevitable, and the other half was due to mileage), registration fees, and finance charges that just come from owning the vehicle and would still happen even if you hardly ever drove it. This means that your marginal cost of driving is only about $0.36 per mile. (This makes the $0.54 per mile deduction the IRS will give small business owners actually quite generous.) You have a strong economic incentive not to drive at all, but in many places it’s hard to even get by without a car; and once you have one, a substantial portion of the cost is already sunk and you may as well drive it.

Compare this to how we fund public transit. Most of the spending on public transit is privatized, and federal funds for public transit are about 1/6 of federal funds for interstate highways. Then we charge every single passenger for every single trip. Except for the recent transition to transit cards instead of cash, this whole system almost seems designed to minimize the salience of the cost of driving and maximize the salience of the cost of public transit.

We also spend far more on our public transit projects than is really necessary, because corruption and excess bureaucracy in the subcontracting system dramatically raises the price. This is actually rather strange, as overall the US has less corruption than Spain or France, yet we pay substantially more for our infrastructure than they do. Indeed, capital costs per kilometer for US urban rail lines consistently rate above all but the most expensive European projects—notably, usually above that $100 million per mile threshold I estimated for maglev rail done right.

This combination of high prices and low funding means our public transit system provides far worse service. Combined with the fact that the rent is too damn high, this gives Americans some of the longest commute times in the world.
What we should actually be doing of course is taxing the oil industry, at the social cost of carbon—the monetary value of the marginal ecological damage done by extracting and burning oil. If we did this, it would raise the price of gasoline by about $0.20 per gallon; since the $70 billion in gasoline taxes is currently raised by a tax of about $0.50 per gallon, that means we would raise an additional $30 billion from gasoline alone (not quite, as people would reduce their gasoline consumption a little). This means that by not doing this, we are effectively subsidizing oil by an additional $30 billion—making our total oil subsidies over $100 billion per year.

Of course, there is a case to be made that this is not the largest US oil subsidy after all. There is one quite plausible candidate for US oil subsidies that might actually be larger, and that is US military spending. Obviously not all military spending is an oil subsidy; but when you include both the absurd amounts of fuel that tanks and fighter jets consume (the DoD accounts for 93% of all US government fuel consumption!) and the fact that several of our most recent wars were at least partly about securing oil reserves, it’s not hard to see how this might be benefiting the oil industry. Estimating this effect quantitatively is very difficult, but if even 5% of the US military budget amounts to an oil subsidy, that’s over $25 billion per year—just shy of the Interstate Highway System.

“The cake is a lie”: The fundamental distortions of inequality

July 13, JDN 2457583

Inequality of wealth and income, especially when it is very large, fundamentally and radically distorts outcomes in a capitalist market. I’ve already alluded to this matter in previous posts on externalities and marginal utility of wealth, but it is so important I think it deserves to have its own post. In many ways this marks a paradigm shift: You can’t think about economics the same way once you realize it is true.

To motivate what I’m getting at, I’ll expand upon an example from a previous post.

Suppose there are only two goods in the world; let’s call them “cake” (K) and “money” (M). Then suppose there are three people, Baker, who makes cakes, Richie, who is very rich, and Hungry, who is very poor. Furthermore, suppose that Baker, Richie and Hungry all have exactly the same utility function, which exhibits diminishing marginal utility in cake and money. To make it more concrete, let’s suppose that this utility function is logarithmic, specifically: U = 10*ln(K+1) + ln(M+1)

The only difference between them is in their initial endowments: Baker starts with 10 cakes, Richie starts with $100,000, and Hungry starts with $10.

Therefore their starting utilities are:

U(B) = 10*ln(10+1)= 23.98

U(R) = ln(100,000+1) = 11.51

U(H) = ln(10+1) = 2.40

Thus, the total happiness is the sum of these: U = 37.89

Now let’s ask two very simple questions:

1. What redistribution would maximize overall happiness?
2. What redistribution will actually occur if the three agents trade rationally?

If multiple agents have the same diminishing marginal utility function, it’s actually a simple and deep theorem that the total will be maximized if they split the wealth exactly evenly. In the following blockquote I’ll prove the simplest case, which is two agents and one good; it’s an incredibly elegant proof:

Given: for all x, f(x) > 0, f'(x) > 0, f”(x) < 0.

Maximize: f(x) + f(A-x) for fixed A

f'(x) – f'(A – x) = 0

f'(x) = f'(A – x)

Since f”(x) < 0, this is a maximum.

Since f'(x) > 0, f is monotonic; therefore f is injective.

x = A – x

QED

This can be generalized to any number of agents, and for multiple goods. Thus, in this case overall happiness is maximized if the cakes and money are both evenly distributed, so that each person gets 3 1/3 cakes and $33,336.66.

The total utility in that case is:

3 * (10 ln(10/3+1) + ln(33,336.66+1)) = 3 * (14.66 + 10.414) = 3 (25.074) =75.22

That’s considerably better than our initial distribution (almost twice as good). Now, how close do we get by rational trade?

Each person is willing to trade up until the point where their marginal utility of cake is equal to their marginal utility of money. The price of cake will be set by the respective marginal utilities.

In particular, let’s look at the trade that will occur between Baker and Richie. They will trade until their marginal rate of substitution is the same.

The actual algebra involved is obnoxious (if you’re really curious, here are some solved exercises of similar trade problems), so let’s just skip to the end. (I rushed through, so I’m not actually totally sure I got it right, but to make my point the precise numbers aren’t important.)
Basically what happens is that Richie pays an exorbitant price of $10,000 per cake, buying half the cakes with half of his money.

Baker’s new utility and Richie’s new utility are thus the same:
U(R) = U(B) = 10*ln(5+1) + ln(50,000+1) = 17.92 + 10.82 = 28.74
What about Hungry? Yeah, well, he doesn’t have $10,000. If cakes are infinitely divisible, he can buy up to 1/1000 of a cake. But it turns out that even that isn’t worth doing (it would cost too much for what he gains from it), so he may as well buy nothing, and his utility remains 2.40.

Hungry wanted cake just as much as Richie, and because Richie has so much more Hungry would have gotten more happiness from each new bite. Neoclassical economists promised him that markets were efficient and optimal, and so he thought he’d get the cake he needs—but the cake is a lie.

The total utility is therefore:

U = U(B) + U(R) + U(H)

U = 28.74 + 28.74 + 2.40

U = 59.88

Note three things about this result: First, it is more than where we started at 37.89—trade increases utility. Second, both Richie and Baker are better off than they were—trade is Pareto-improving. Third, the total is less than the optimal value of 75.22—trade is not utility-maximizing in the presence of inequality. This is a general theorem that I could prove formally, if I wanted to bore and confuse all my readers. (Perhaps someday I will try to publish a paper doing that.)

This result is incredibly radical—it basically goes against the core of neoclassical welfare theory, or at least of all its applications to real-world policy—so let me be absolutely clear about what I’m saying, and what assumptions I had to make to get there.

I am saying that if people start with different amounts of wealth, the trades they would willfully engage in, acting purely under their own self interest, would not maximize the total happiness of the population. Redistribution of wealth toward equality would increase total happiness.

First, I had to assume that we could simply redistribute goods however we like without affecting the total amount of goods. This is wildly unrealistic, which is why I’m not actually saying we should reduce inequality to zero (as would follow if you took this result completely literally). Ironically, this is an assumption that most neoclassical welfare theory agrees with—the Second Welfare Theorem only makes any sense in a world where wealth can be magically redistributed between people without any harmful economic effects. If you weaken this assumption, what you find is basically that we should redistribute wealth toward equality, but beware of the tradeoff between too much redistribution and too little.

Second, I had to assume that there’s such a thing as “utility”—specifically, interpersonally comparable cardinal utility. In other words, I had to assume that there’s some way of measuring how much happiness each person has, and meaningfully comparing them so that I can say whether taking something from one person and giving it to someone else is good or bad in any given circumstance.

This is the assumption neoclassical welfare theory generally does not accept; instead they use ordinal utility, on which we can only say whether things are better or worse, but never by how much. Thus, their only way of determining whether a situation is better or worse is Pareto efficiency, which I discussed in a post a couple years ago. The change from the situation where Baker and Richie trade and Hungry is left in the lurch to the situation where all share cake and money equally in socialist utopia is not a Pareto-improvement. Richie and Baker are slightly worse off with 25.07 utilons in the latter scenario, while they had 28.74 utilons in the former.

Third, I had to assume selfishness—which is again fairly unrealistic, but again not something neoclassical theory disagrees with. If you weaken this assumption and say that people are at least partially altruistic, you can get the result where instead of buying things for themselves, people donate money to help others out, and eventually the whole system achieves optimal utility by willful actions. (It depends just how altruistic people are, as well as how unequal the initial endowments are.) This actually is basically what I’m trying to make happen in the real world—I want to show people that markets won’t do it on their own, but we have the chance to do it ourselves. But even then, it would go a lot faster if we used the power of government instead of waiting on private donations.

Also, I’m ignoring externalities, which are a different type of market failure which in no way conflicts with this type of failure. Indeed, there are three basic functions of government in my view: One is to maintain security. The second is to cancel externalities. The third is to redistribute wealth. The DOD, the EPA, and the SSA, basically. One could also add macroeconomic stability as a fourth core function—the Fed.

One way to escape my theorem would be to deny interpersonally comparable utility, but this makes measuring welfare in any way (including the usual methods of consumer surplus and GDP) meaningless, and furthermore results in the ridiculous claim that we have no way of being sure whether Bill Gates is happier than a child starving and dying of malaria in Burkina Faso, because they are two different people and we can’t compare different people. Far more reasonable is not to believe in cardinal utility, meaning that we can say an extra dollar makes you better off, but we can’t put a number on how much.

And indeed, the difficulty of even finding a unit of measure for utility would seem to support this view: Should I use QALY? DALY? A Likert scale from 0 to 10? There is no known measure of utility that is without serious flaws and limitations.

But it’s important to understand just how strong your denial of cardinal utility needs to be in order for this theorem to fail. It’s not enough that we can’t measure precisely; it’s not even enough that we can’t measure with current knowledge and technology. It must be fundamentally impossible to measure. It must be literally meaningless to say that taking a dollar from Bill Gates and giving it to the starving Burkinabe would do more good than harm, as if you were asserting that triangles are greener than schadenfreude.

Indeed, the whole project of welfare theory doesn’t make a whole lot of sense if all you have to work with is ordinal utility. Yes, in principle there are policy changes that could make absolutely everyone better off, or make some better off while harming absolutely no one; and the Pareto criterion can indeed tell you that those would be good things to do.

But in reality, such policies almost never exist. In the real world, almost anything you do is going to harm someone. The Nuremburg trials harmed Nazi war criminals. The invention of the automobile harmed horse trainers. The discovery of scientific medicine took jobs away from witch doctors. Inversely, almost any policy is going to benefit someone. The Great Leap Forward was a pretty good deal for Mao. The purges advanced the self-interest of Stalin. Slavery was profitable for plantation owners. So if you can only evaluate policy outcomes based on the Pareto criterion, you are literally committed to saying that there is no difference in welfare between the Great Leap Forward and the invention of the polio vaccine.

One way around it (that might actually be a good kludge for now, until we get better at measuring utility) is to broaden the Pareto criterion: We could use a majoritarian criterion, where you care about the number of people benefited versus harmed, without worrying about magnitudes—but this can lead to Tyranny of the Majority. Or you could use the Difference Principle developed by Rawls: find an ordering where we can say that some people are better or worse off than others, and then make the system so that the worst-off people are benefited as much as possible. I can think of a few cases where I wouldn’t want to apply this criterion (essentially they are circumstances where autonomy and consent are vital), but in general it’s a very good approach.

Neither of these depends upon cardinal utility, so have you escaped my theorem? Well, no, actually. You’ve weakened it, to be sure—it is no longer a statement about the fundamental impossibility of welfare-maximizing markets. But applied to the real world, people in Third World poverty are obviously the worst off, and therefore worthy of our help by the Difference Principle; and there are an awful lot of them and very few billionaires, so majority rule says take from the billionaires. The basic conclusion that it is a moral imperative to dramatically reduce global inequality remains—as does the realization that the “efficiency” and “optimality” of unregulated capitalism is a chimera.

Should we give up on growth?

JDN 2457572

Recently I read this article published by the Post Carbon Institute, “How to Shrink the Economy without Crashing It”, which has been going around environmentalist circles. (I posted on Facebook that I’d answer it in more detail, so here goes.)

This is the far left view on climate change, which is wrong, but not nearly as wrong as even the “mainstream” right-wing view that climate change is not a serious problem and we should continue with business as usual. Most of the Republicans who ran for President this year didn’t believe in using government action to fight climate change, and Donald Trump doesn’t even believe it exists.
This core message of the article is clearly correct:

We know this because Global Footprint Network, which methodically tracks the relevant data, informs us that humanity is now using 1.5 Earths’ worth of resources.

We can temporarily use resources faster than Earth regenerates them only by borrowing from the future productivity of the planet, leaving less for our descendants. But we cannot do this for long.

To be clear, “using 1.5 Earths” is not as bad as it sounds; spending is allow to exceed income at times, as long as you have reason to think that future income will exceed future spending, and this is true not just of money but also of natural resources. You can in fact “borrow from the future”, provided you do actually have a plan to pay it back. And indeed there has been some theoretical work by environmental economists suggesting that we are rightly still in the phase of net ecological dissaving, and won’t enter the phase of net ecological saving until the mid-21st century when our technology has made us two or three times as productive. This optimal path is defined by a “weak sustainability” condition where total real wealth never falls over time, so any natural wealth depleted is replaced by at least as much artificial wealth.

Of course some things can’t be paid back; while forests depleted can be replanted, if you drive species to extinction, only very advanced technology could restore them. And we are driving thousands of species to extinction every single year. Even if we should be optimally dissaving, we are almost certainly depleting natural resources too fast, and depleting natural resources that will be difficult if not impossible to later restore. In that sense, the Post Carbon Institute is right: We must change course toward ecological sustainability.

Unfortunately, their specific ideas of how to do so leave much to be desired. Beyond ecological sustainability, they really argue for two propositions: one is radical but worth discussing, but the other is totally absurd.

The absurd claim is that we should somehow force the world to de-urbanize and regress into living in small farming villages. To show this is a bananaman and not a strawman, I quote:

8. Re-localize. One of the difficulties in the transition to renewable energy is that liquid fuels are hard to substitute. Oil drives nearly all transportation currently, and it is highly unlikely that alternative fuels will enable anything like current levels of mobility (electric airliners and cargo ships are non-starters; massive production of biofuels is a mere fantasy). That means communities will be obtaining fewer provisions from far-off places. Of course trade will continue in some form: even hunter-gatherers trade. Re-localization will merely reverse the recent globalizing trade trend until most necessities are once again produced close by, so that we—like our ancestors only a century ago—are once again acquainted with the people who make our shoes and grow our food.

9. Re-ruralize. Urbanization was the dominant demographic trend of the 20th century, but it cannot be sustained. Indeed, without cheap transport and abundant energy, megacities will become increasingly dysfunctional. Meanwhile, we’ll need lots more farmers. Solution: dedicate more societal resources to towns and villages, make land available to young farmers, and work to revitalize rural culture.

First of all: Are electric cargo ships non-starters? The Ford-class aircraft carrier is electric, specifically nuclear. Nuclear-powered cargo ships would raise a number of issues in terms of practicality, safety, and regulation, but they aren’t fundamentally infeasible. Massive efficient production of biofuels is a fantasy as long as the energy to do it is provided by coal power, but not if it’s provided by nuclear. Perhaps this author’s concept of “infeasible” really just means “infeasible if I can’t get over my irrational fear of nuclear power”. Even electric airliners are not necessarily out of the question; NASA has been experimenting with electric aircraft.

The most charitable reading I can give of this (in my terminology of argument “men”, I’m trying to make a banana out of iron), is as promoting slightly deurbanizing and going back to more like say the 1950s United States, with 64% of people in cities instead of 80% today. Even then this makes less than no sense, as higher urbanization is associated with lower per-capita ecological impact, which frankly shouldn’t even be surprising because cities have such huge economies of scale. Instead of everyone needing a car to get around in the suburbs, we can all share a subway system in the city. If that subway system is powered by a grid of nuclear, solar, and wind power, it could produce essentially zero carbon emissions—which is absolutely impossible for rural or suburban transportation. Urbanization is also associated with slower population growth (or even population decline), and indeed the reason population growth is declining is that rising standard of living and greater urbanization have reduced birth rates and will continue to do so as poor countries reach higher levels of development. Far from being a solution to ecological unsustainability, deurbanization would make it worse.

And that’s not even getting into the fact that you would have to force urban white-collar workers to become farmers, because if we wanted to be farmers we already would be (the converse is not as true), and now you’re actually talking about some kind of massive forced labor-shift policy like the Great Leap Forward. Normally I’m annoyed when people accuse environmentalists of being totalitarian communists, but in this case, I think the accusation might be onto something.

Moving on, the radical but not absurd claim is that we must turn away from economic growth and even turn toward economic shrinkage:

One way or another, the economy (and here we are talking mostly about the economies of industrial nations) must shrink until it subsists on what Earth can provide long-term.

[…]

If nothing is done deliberately to reverse growth or pre-adapt to inevitable economic stagnation and contraction, the likely result will be an episodic, protracted, and chaotic process of collapse continuing for many decades or perhaps centuries, with innumerable human and non-human casualties.

I still don’t think this is right, but I understand where it’s coming from, and like I said it’s worth talking about.

The biggest mistake here lies in assuming that GDP is directly correlated to natural resource depletion, so that the only way to reduce natural resource depletion is to reduce GDP. This is not even remotely true; indeed, countries vary almost as much in their GDP-per-carbon-emission ratio as they do in their per-capita GDP. As usual, #ScandinaviaIsBetter; Norway and Sweden produce about $8,000 in GDP per ton of carbon, while the US produces only about $2,000 per ton. Both poor and rich countries can be found among both the inefficient and the efficient. Saudi Arabia is very rich and produces about $900 per ton, while Liberia is exceedingly poor and produces about $800 per ton. I already mentioned how Norway produces $8,000 per ton, and they are as rich as Saudi Arabia. Yet above them is Mali, which produces almost $11,000 per ton, and is as poor as Liberia. Other notable facts: France is head and shoulders above the UK and Germany at almost $6000 per ton instead of $4300 and $3600 respectively—because France runs almost entirely on nuclear power.

So the real conclusion to draw from this is not that we need to shrink GDP, but that we need to make GDP more like how they do it in Norway or at least how they do it in France, rather than how we do in the US, and definitely not how they do it in Saudi Arabia. Total world emissions are currently about 36 billion tons per year, producing about $108 trillion in GDP, averaging about $3,000 of GDP per ton of carbon emissions. If we could raise the entire world to the ecological efficiency of Norway, we could double world GDP and still be producing less CO2 than we currently are. Turning the entire planet into a bunch of Norways would indeed raise CO2 output, by about a factor of 2; but it would raise standard of living by a factor of 5, and indeed bring about a utopian future with neither war nor hunger. Compare this to the prospect of cutting world GDP in half, but producing it as inefficiently as in Saudi Arabia: This would actually increase global CO2 emissions, almost as much as turning every country into Norway.

But ultimately we will in fact need to slow down or even end economic growth. I ran a little model for you, which shows a reasonable trajectory for global economic growth.

This graph shows the growth rate in productivity slowly declining, along with a much more rapidly declining GDP growth:

Solow_growth

This graph shows the growth trajectory for total real capital and GDP:

Solow_capital

And finally, this is the long-run trend for GDP graphed on a log scale:

Solow_logGDP

The units are arbitrary, though it’s not unreasonable to imagine them as being years and hundreds of dollars in per-capita GDP. If that is indeed what you imagine them to be, my model shows us the Star Trek future: In about 300 years, we rise from a per-capita GDP of $10,000 to one of $165,000—from a world much like today to a world where everyone is a millionaire.

Notice that the growth rate slows down a great deal fairly quickly; by the end of 100 years (i.e., the end of the 21st century), growth has slowed from its peak over 10% to just over 2% per year. By the end of the 300-year period, the growth rate is a crawl of only 0.1%.

Of course this model is very simplistic, but I chose it for a very specific reason: This is not a radical left-wing environmentalist model involving “limits to growth” or “degrowth”. This is the Solow-Swan model, the paradigm example of neoclassical models of economic growth. It is sometimes in fact called simply “the neoclassical growth model”, because it is that influential. I made one very small change from the usual form, which was to assume that the rate of productivity growth would decline exponentially over time. Since productivity growth is exogenous to the model, this is a very simple change to make; it amounts to saying that productivity-enhancing technology is subject to diminishing returns, which fits recent data fairly well but could be totally wrong if something like artificial intelligence or neural enhancement ever takes off.

I chose this because many environmentalists seem to think that economists have this delusional belief that we can maintain a rate of economic growth equal to today indefinitely. David Attenborough famously said “Anyone who believes in indefinite growth in anything physical, on a physically finite planet, is either mad – or an economist.”

Another physicist argued that if we increase energy consumption 2.3% per year for 400 years, we’d literally boil the Earth. Yes, we would, and no economist I know of believes that this is what will happen. Economic growth doesn’t require energy growth, and we do not think growth can or should continue indefinitely—we just think it can and should continue a little while longer. We don’t think that a world standard of living 1000 times as good as Norway is going to happen; we think that a world standard of living equal to Norway is worth fighting for.

Indeed, we are often the ones trying to explain to leaders that they need to adapt to slower growth rates—this is particularly a problem in China, where nationalism and groupthink seems to have convinced many people in China that 7% annual growth is the result of some brilliant unique feature of the great Chinese system, when it is in fact simply the expected high growth rate for an economy that is very poor and still catching up by establishing a capital base. (It’s not so much what they are doing right now, as what they were doing wrong before. Just as you feel a lot better when you stop hitting yourself in the head, countries tend to grow quite fast after they transition out of horrifically terrible economic policy—and it doesn’t get much more terrible than Mao.) Even a lot of the IMF projections are now believed to be too optimistic, because they didn’t account for how China was fudging the numbers and rapidly depleting natural resources.

Some of the specific policies recommended in the article are reasonable, while others go to far.

1. Energy: cap, reduce, and ration it. Energy is what makes the economy go, and expanded energy consumption is what makes it grow. Climate scientists advocate capping and reducing carbon emissions to prevent planetary disaster, and cutting carbon emissions inevitably entails reducing energy from fossil fuels. However, if we aim to shrink the size of the economy, we should restrain not just fossil energy, but all energy consumption. The fairest way to do that would probably be with tradable energy quotas.

I strongly support cap-and-trade on fossil fuels, but I can’t support it on energy in general, unless we get so advanced that we’re seriously concerned about significantly altering the entropy of the universe. Solar power does not have negative externalities, and therefore should not be taxed or capped.

The shift to renewable energy sources is a no-brainer, and I know of no ecologist and few economists who would disagree.

This one is rich, coming from someone who goes on to argue for nonsensical deurbanization:

However, this is a complicated process. It will not be possible merely to unplug coal power plants, plug in solar panels, and continue with business as usual: we have built our immense modern industrial infrastructure of cities, suburbs, highways, airports, and factories to take advantage of the unique qualities and characteristics of fossil fuels.

How will we make our industrial infrastructure run off a solar grid? Urbanization. When everything is in one place, you can use public transportation and plug everything into the grid. We could replace the interstate highway system with a network of maglev lines, provided that almost everyone lived in major cities that were along those lines. We can’t do that if people move out of cities and go back to being farmers.

Here’s another weird one:

Without continued economic growth, the market economy probably can’t function long. This suggests we should run the transformational process in reverse by decommodifying land, labor, and money.

“Decommodifying money”? That’s like skinning leather or dehydrating water. The whole point of money is that it is a maximally fungible commodity. I support the idea of a land tax to provide a basic income, which could go a long way to decommodifying land and labor; but you can’t decommodify money.

The next one starts off sounding ridiculous, but then gets more reasonable:

4. Get rid of debt. Decommodifying money means letting it revert to its function as an inert medium of exchange and store of value, and reducing or eliminating the expectation that money should reproduce more of itself. This ultimately means doing away with interest and the trading or manipulation of currencies. Make investing a community-mediated process of directing capital toward projects that are of unquestioned collective benefit. The first step: cancel existing debt. Then ban derivatives, and tax and tightly regulate the buying and selling of financial instruments of all kinds.

No, we’re not going to get rid of debt. But should we regulate it more? Absolutely. A ban on derivatives is strong, but shouldn’t be out of the question; it’s not clear that even the most useful derivatives (like interest rate swaps and stock options) bring more benefit than they cause harm.

The next proposal, to reform our monetary system so that it is no longer based on debt, is one I broadly agree with, though you need to be clear about how you plan to do that. Positive Money’s plan to make central banks democratically accountable, establish full-reserve banking, and print money without trying to hide it in arcane accounting mechanisms sounds pretty good to me. Going back to the gold standard or something would be a terrible idea. The article links to a couple of “alternative money theorists”, but doesn’t explain further.

Sooner or later, we absolutely will need to restructure our macroeconomic policy so that 4% or even 2% real growth is no longer the expectation in First World countries. We will need to ensure that constant growth isn’t necessary to maintain stability and full employment.

But I believe we can do that, and in any case we do not want to stop global growth just yet—far from it. We are now on the verge of ending world hunger, and if we manage to do it, it will be from economic growth above all else.

The difference between price, cost, and value

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.

Do we always want to internalize externalities?

JDN 2457437

I often talk about the importance of externalitiesa full discussion in this earlier post, and one of their important implications, the tragedy of the commons, in another. Briefly, externalities are consequences of actions incurred upon people who did not perform those actions. Anything I do affecting you that you had no say in, is an externality.

Usually I’m talking about how we want to internalize externalities, meaning that we set up a system of incentives to make it so that the consequences fall upon the people who chose the actions instead of anyone else. If you pollute a river, you should have to pay to clean it up. If you assault someone, you should serve jail time as punishment. If you invent a new technology, you should be rewarded for it. These are all attempts to internalize externalities.

But today I’m going to push back a little, and ask whether we really always want to internalize externalities. If you think carefully, it’s not hard to come up with scenarios where it actually seems fairer to leave the externality in place, or perhaps reduce it somewhat without eliminating it.

For example, suppose indeed that someone invents a great new technology. To be specific, let’s think about Jonas Salk, inventing the polio vaccine. This vaccine saved the lives of thousands of people and saved millions more from pain and suffering. Its value to society is enormous, and of course Salk deserved to be rewarded for it.

But we did not actually fully internalize the externality. If we had, every family whose child was saved from polio would have had to pay Jonas Salk an amount equal to what they saved on medical treatments as a result, or even an amount somehow equal to the value of their child’s life (imagine how offended people would get if you asked that on a survey!). Those millions of people spared from suffering would need to each pay, at minimum, thousands of dollars to Jonas Salk, making him of course a billionaire.

And indeed this is more or less what would have happened, if he had been willing and able to enforce a patent on the vaccine. The inability of some to pay for the vaccine at its monopoly prices would add some deadweight loss, but even that could be removed if Salk Industries had found a way to offer targeted price vouchers that let them precisely price-discriminate so that every single customer paid exactly what they could afford to pay. If that had happened, we would have fully internalized the externality and therefore maximized economic efficiency.

But doesn’t that sound awful? Doesn’t it sound much worse than what we actually did, where Jonas Salk received a great deal of funding and support from governments and universities, and lived out his life comfortably upper-middle class as a tenured university professor?

Now, perhaps he should have been awarded a Nobel Prize—I take that back, there’s no “perhaps” about it, he definitely should have been awarded a Nobel Prize in Medicine, it’s absurd that he did not—which means that I at least do feel the externality should have been internalized a bit more than it was. But a Nobel Prize is only 10 million SEK, about $1.1 million. That’s about enough to be independently wealthy and live comfortably for the rest of your life; but it’s a small fraction of the roughly $7 billion he could have gotten if he had patented the vaccine. Yet while the possible world in which he wins a Nobel is better than this one, I’m fairly well convinced that the possible world in which he patents the vaccine and becomes a billionaire is considerably worse.

Internalizing externalities makes sense if your goal is to maximize total surplus (a concept I explain further in the linked post), but total surplus is actually a terrible measure of human welfare.

Total surplus counts every dollar of willingness-to-pay exactly the same across different people, regardless of whether they live on $400 per year or $4 billion.

It also takes no account whatsoever of how wealth is distributed. Suppose a new technology adds $10 billion in wealth to the world. As far as total surplus, it makes no difference whether that $10 billion is spread evenly across the entire planet, distributed among a city of a million people, concentrated in a small town of 2,000, or even held entirely in the bank account of a single man.

Particularly a propos of the Salk example, total surplus makes no distinction between these two scenarios: a perfectly-competitive market where everything is sold at a fair price, and a perfectly price-discriminating monopoly, where everything is sold at the very highest possible price each person would be willing to pay.

This is a perfectly-competitive market, where the benefits are more or less equally (in this case exactly equally, but that need not be true in real life) between sellers and buyers:

elastic_supply_competitive_labeled

This is a perfectly price-discriminating monopoly, where the benefits accrue entirely to the corporation selling the good:

elastic_supply_price_discrimination

In the former case, the company profits, consumers are better off, everyone is happy. In the latter case, the company reaps all the benefits and everyone else is left exactly as they were. In real terms those are obviously very different outcomes—the former being what we want, the latter being the cyberpunk dystopia we seem to be hurtling mercilessly toward. But in terms of total surplus, and therefore the kind of “efficiency” that is maximize by internalizing all externalities, they are indistinguishable.

In fact (as I hope to publish a paper about at some point), the way willingness-to-pay works, it weights rich people more. Redistributing goods from the poor to the rich will typically increase total surplus.

Here’s an example. Suppose there is a cake, which is sufficiently delicious that it offers 2 milliQALY in utility to whoever consumes it (this is a truly fabulous cake). Suppose there are two people to whom we might give this cake: Richie, who has $10 million in annual income, and Hungry, who has only $1,000 in annual income. How much will each of them be willing to pay?

Well, assuming logarithmic marginal utility of wealth (which is itself probably biasing slightly in favor of the rich), 1 milliQALY is about $1 to Hungry, so Hungry will be willing to pay $2 for the cake. To Richie, however, 1 milliQALY is about $10,000; so he will be willing to pay a whopping $20,000 for this cake.

What this means is that the cake will almost certainly be sold to Richie; and if we proposed a policy to redistribute the cake from Richie to Hungry, economists would emerge to tell us that we have just reduced total surplus by $19,998 and thereby committed a great sin against economic efficiency. They will cajole us into returning the cake to Richie and thus raising total surplus by $19,998 once more.

This despite the fact that I stipulated that the cake is worth just as much in real terms to Hungry as it is to Richie; the difference is due to their wildly differing marginal utility of wealth.

Indeed, it gets worse, because even if we suppose that the cake is worth much more in real utility to Hungry—because he is in fact hungry—it can still easily turn out that Richie’s willingness-to-pay is substantially higher. Suppose that Hungry actually gets 20 milliQALY out of eating the cake, while Richie still only gets 2 milliQALY. Hungry’s willingness-to-pay is now $20, but Richie is still going to end up with the cake.

Now, if your thought is, “Why would Richie pay $20,000, when he can go to another store and get another cake that’s just as good for $20?” Well, he wouldn’t—but in the sense we mean for total surplus, willingness-to-pay isn’t just what you’d actually be willing to pay given the actual prices of the goods, but the absolute maximum price you’d be willing to pay to get that good under any circumstances. It is instead the marginal utility of the good divided by your marginal utility of wealth. In this sense the cake is “worth” $20,000 to Richie, and “worth” substantially less to Hungry—but not because it’s actually worth less in real terms, but simply because Richie has so much more money.

Even economists often equate these two, implicitly assuming that we are spending our money up to the point where our marginal willingness-to-pay is the actual price we choose to pay; but in general our willingness-to-pay is higher than the price if we are willing to buy the good at all. The consumer surplus we get from goods is in fact equal to the difference between willingness-to-pay and actual price paid, summed up over all the goods we have purchased.

Internalizing all externalities would definitely maximize total surplus—but would it actually maximize happiness? Probably not.

If you asked most people what their marginal utility of wealth is, they’d have no idea what you’re talking about. But most people do actually have an intuitive sense that a dollar is worth more to a homeless person than it is to a millionaire, and that’s really all we mean by diminishing marginal utility of wealth.

I think the reason we’re uncomfortable with the idea of Jonas Salk getting $7 billion from selling the polio vaccine, rather than the same number of people getting the polio vaccine and Jonas Salk only getting the $1.1 million from a Nobel Prize, is that we intuitively grasp that after that $1.1 million makes him independently wealthy, the rest of the money is just going to sit in some stock account and continue making even more money, while if we’d let the families keep it they would have put it to much better use raising their children who are now protected from polio. We do want to reward Salk for his great accomplishment, but we don’t see why we should keep throwing cash at him when it could obviously be spent in better ways.

And indeed I think this intuition is correct; great accomplishments—which is to say, large positive externalities—should be rewarded, but not in direct proportion. Maybe there should be some threshold above which we say, “You know what? You’re rich enough now; we can stop giving you money.” Or maybe it should simply damp down very quickly, so that a contribution which is worth $10 billion to the world pays only slightly more than one that is worth $100 million, but a contribution that is worth $100,000 pays considerably more than one which is only worth $10,000.

What it ultimately comes down to is that if we make all the benefits incur to the person who did it, there aren’t any benefits anymore. The whole point of Jonas Salk inventing the polio vaccine (or Einstein discovering relativity, or Darwin figuring out natural selection, or any great achievement) is that it will benefit the rest of humanity, preferably on to future generations. If you managed to fully internalize that externality, this would no longer be true; Salk and Einstein and Darwin would have become fabulously wealthy, and then somehow we’d all have to continue paying into their estates or something an amount equal to the benefits we received from their discoveries. (Every time you use your GPS, pay a royalty to the Einsteins. Every time you take a pill, pay a royalty to the Darwins.) At some point we’d probably get fed up and decide we’re no better off with them than without them—which is exactly by construction how we should feel if the externality were fully internalized.

Internalizing negative externalities is much less problematic—it’s your mess, clean it up. We don’t want other people to be harmed by your actions, and if we can pull that off that’s fantastic. (In reality, we usually can’t fully internalize negative externalities, but we can at least try.)

But maybe internalizing positive externalities really isn’t so great after all.

Tax Incidence Revisited, Part 1: The downside of taxes

JDN 2457345 EST 22:02

As I was writing this, it was very early (I had to wake up at 04:30) and I was groggy, because we were on an urgent road trip to Pennsylvania for the funeral of my aunt who died quite suddenly a few days ago. I have since edited this post more thoroughly to minimize the impact of my sleep deprivation upon its content. Actually maybe this is a good thing; the saying goes, “write drunk, edit sober” and sleep deprivation and alcohol have remarkably similar symptoms, probably because alcohol is GABA-ergic and GABA is involved in sleep regulation.

Awhile ago I wrote a long post on tax incidence, but the primary response I got was basically the online equivalent of a perplexed blank stare. Struck once again by the Curse of Knowledge, I underestimated the amount of background knowledge necessary to understand my explanation. But tax incidence is very important for public policy, so I really would like to explain it.

Therefore I am now starting again, slower, in smaller pieces. Today’s piece is about the downsides of taxation in general, why we don’t just raise taxes as high as we feel like and make the government roll in dough.

To some extent this is obvious; if income tax were 100%, why would anyone bother working for a salary? You might still work for fulfillment, or out of a sense of duty, or simply because you enjoy what you do—after all, most artists and musicians are hardly in it for the money. But many jobs are miserable and not particularly fulfilling, yet still need to get done. How many janitors or bus drivers work purely for the sense of fulfillment it gives them? Mostly they do it to pay the bills—and if income tax were 100%, it wouldn’t anymore. The formal economy would basically collapse, and then nobody would end up actually paying that 100% tax—so the government would actually get very little revenue, if any.

At the other end of the scale, it’s kind of obvious that if your taxes are all 0% you don’t get any revenue. This is actually more feasible than it may sound; provided you spend only a very small amount (say, 4% of GDP, though that’s less than any country actually spends—maybe you could do 6% like Bangladesh) and you can still get people to accept your currency, you could, in principle, have a government that funds its spending entirely by means of printing money, and could do this indefinitely. In practice, that has never been done, and the really challenging part is getting people to accept your money if you don’t collect taxes in it. One of the more counter-intuitive aspects of modern monetary theory (or perhaps I should capitalize it, Modern Monetary Theory, though the part I agree with is not that different from standard Keynesian theory) is that taxation is the primary mechanism by which money acquires its value.

And then of course with intermediate tax rates such as 20%, 30%, and 50% that actual countries actually use, we do get some positive amount of revenue.

Everything I’ve said so far may seem pretty obvious. Yeah, usually taxes raise revenue, but if you taxed at 0% or 100% they wouldn’t; so what?

Well, this leads to quite an important result. Assuming that tax revenue is continuous (which isn’t quite true, but since we can collect taxes in fractions of a percent and pay in pennies, it’s pretty close), it follows directly from the Extreme Value Theorem that there is in fact a revenue-maximizing tax rate. Both below and above that tax rate, the government takes in less total money. These theorems don’t tell us what the revenue-maximizing rate is; but they tell us that it must exist, somewhere between 0% and 100%.

Indeed, it follows that there is what we call the Laffer Curve, a graph of tax revenue as a function of tax rate, and it is in fact a curve, as opposed to the straight line it would be if taxes had no effect on the rest of the economy.

Very roughly, it looks something like this (the blue curve is my sketch of the real-world Laffer curve, while the red line is what it would be if taxes had no distortionary effects):

Laffer_curve

Now, the Laffer curve has been abused many times; in particular, it’s been used to feed into the “trickle-down” “supply-sideReaganomics that has been rightly derided as “voodoo economics” by serious economists. Jeb Bush (or should I say, Jeb!) and Marco Rubio would have you believe that we are on the right edge of the Laffer curve, and we could actually increase tax revenue by cutting taxes, particularly on capital gains and incomes at the top 1%; that’s obviously false. We tried that, it didn’t work. Even theoretically we probably should have known that it wouldn’t; but now that we’ve actually done the experiment and it failed, there should be no serious doubt anymore.

No, we are on the left side of the Laffer curve, where increasing taxes increases revenue, much as you’d intuitively expect. It doesn’t quite increase one-to-one, because adding more taxes does make the economy less efficient; but from where we currently stand, a 1% increase in taxes leads to about a 0.9% increase in revenue (actually estimated as between 0.78% and 0.99%).

Denmark may be on the right side of the Laffer curve, where they could raise more revenue by decreasing tax rates (even then I’m not so sure). But Denmark’s tax rates are considerably higher than ours; while in the US we pay about 27% of GDP in taxes, folks in Denmark pay 49% of GDP in taxes.

The fact remains, however, that there is a Laffer curve, and no serious economist would dispute this. Increasing taxes does in fact create distortions in the economy, and as a result raising tax rates does not increase revenue in a one-to-one fashion. When calculating the revenue from a new tax, you must include not only the fact that the government will get an increased portion, but also that the total amount of income will probably decrease.

Now, I must say probably, because it does depend on what exactly you are taxing. If you tax something that is perfectly inelastic—the same amount of it is going to be made and sold no matter what—then total income will remain exactly the same after the tax. It may be distributed differently, but the total won’t change. This is one of the central justifications for a land tax; land is almost perfectly inelastic, so taxing it allows us to raise revenue without reducing total income.

In fact, there are certain kinds of taxes which increase total income, which makes them basically no-brainer taxes that should always be implemented if at all feasible. These are Pigovian taxes, which are taxes on products with negative externalities; when a product causes harm to other people (the usual example is pollution of air and water), taxing that product equal to the harm caused provides a source of government revenue that also increases the efficiency of the economy as a whole. If we had a tax on carbon emissions that was used to fund research into sustainable energy, this would raise our total GDP in the long run. Taxes on oil and natural gas are not “job killing”; they are job creating. This is why we need a carbon tax, a higher gasoline tax, and a financial transaction tax (to reduce harmful speculation); it’s also why we already have high taxes on alcohol and tobacco.

The alcohol tax is one of the great success stories of Pigouvian taxation.The alcohol tax is actually one of the central factors holding our crime rate so low right now. Another big factor is overall economic growth and anti-poverty programs. The most important factor, however, is lead, or rather the lack thereof; environmental regulations reducing pollutants like lead and mercury from the environment are the leading factor in reducing crime rates over the last generation. Yes, that’s right—our fall in crime had little to do with state police, the FBI, the DEA, or the ATF; our most effective crime-fighting agency is the EPA. This is really not that surprising, as a cognitive economist. Most crime is impulsive and irrational, or else born of economic desperation. Rational crime that it would make sense to punish harshly as a deterrent is quite rare (well, except for white-collar crime, which of course we don’t punish harshly enough—I know I harp on this a lot, but HSBC laundered money for terrorists). Maybe crime would be more common if we had no justice system in place at all, but making our current system even harsher accomplishes basically nothing. Far better to tax the alcohol that leads good people to bad decisions.

It also matters whom you tax, though one of my goals in this tax incidence series is to explain why that doesn’t mean quite what most people think it does. The person who writes the check to the government is not necessarily the person who really pays the tax. The person who really pays is the one whose net income ends up lower after the tax is implemented. Often these are the same person; but often they aren’t, for fundamental reasons I’m hoping to explain.

For now, it’s worth pointing out that a tax which primarily hits the top 1% is going to have a very different impact on the economy than one which hits the entire population. Because of the income and substitution effects, poor people tend to work less as their taxes go up, but rich people tend to work more. Even within income brackets, a tax that hits doctors and engineers is going to have a different effect than a tax that hits bankers and stock traders, and a tax that hits teachers is going to have a different effect than a tax that hits truck drivers. A tax on particular products or services will reduce demand for those products or services, which is good if that’s what you’re trying to do (such as alcohol) but not so good if it isn’t.

So, yes, there are cases where raising taxes can actually increase, or at least not reduce, total income. These are the exception, however; as a general rule, in a Pirate Code sort of way, taxes reduce total income. It’s not simply that income goes down for everyone but the government (which would again be sort of obvious); income goes down for everyone including the government. The difference is simply lost, wasted away by a loss in economic efficiency. We call that difference deadweight loss, and for a poorly-designed tax it can actually far exceed the revenue received.

I think an extreme example may help to grasp the intuition: Suppose we started taxing cars at 200,000%, so that a typical new car costs something like $40 million with taxes. (That’s not a Lamborghini, mind you; that’s a Honda Accord.) What would happen? Nobody is going to buy cars anymore. Overnight, you’ve collapsed the entire auto industry. Dozens of companies go bankrupt, thousands of employees get laid off, the economy immediately falls into recession. And after all that, your car tax will raise no revenue at all, because not a single car will sell. It’s just pure deadweight loss.

That’s an intentionally extreme example; most real-world taxes in fact create less deadweight loss than they raise in revenue. But most real-world taxes do in fact create deadweight loss, and that’s a good reason to be concerned about any new tax.

In general, higher taxes create lower total income, or equivalently higher deadweight loss. All other things equal, lower taxes are therefore better.

What most Americans don’t seem to quite grasp is that all other things are not equal. That tax revenue is central to the proper functioning of our government and our monetary system. We need a certain amount of taxes in order to ensure that we can maintain a stable currency and still pay for things like Medicare, Social Security, and the Department of Defense (to name our top three budget items).

Alternatively, we could not spend so much on those things, and that is a legitimate question of public policy. I personally think that Medicare and Social Security are very good things (and I do have data to back that up—Medicare saves thousands of lives), but they aren’t strictly necessary for basic government functioning; we could get rid of them, it’s just that it would be a bad idea. As for the defense budget, some kind of defense budget is necessary for national security, but I don’t think I’m going out on a very big limb here when I say that one country making 40% of all world military spending probably isn’t.

We can’t have it both ways; if you want Medicare, Social Security, and the Department of Defense, you need to have taxes. “Cutting spending” always means cutting spending on something—so what is it you want to cut? A lot of people seem to think that we waste a huge amount of money on pointless bureaucracy, pork-barrel spending, or foreign aid; but that’s simply not true. All government administration is less than 1% of the budget, and most of it is necessary; earmarks are also less than 1%; foreign aid is also less than 1%. Since our deficit is about 15% of spending, we could eliminate all of those things and we’d barely put a dent in it.

Americans don’t like taxes; I understand that. It’s basically one of our founding principles, in fact, though “No taxation without representation” seems to have mutated of late into simply “No taxation”, or maybe “Read my lips, no new taxes!” It’s never pleasant to see that chunk taken out of your paycheck before you even get it. (Though one thing I hope to explain in this series is that these figures are really not very meaningful; there’s no particular reason to think you’d have made the same gross salary if those taxes hadn’t been present.)

There are in fact sound economic reasons to keep taxes low. The Laffer Curve is absolutely a real thing, even though most of its applications are wrong. But sometimes we need taxes to be higher, and that’s a tradeoff we have to make.We need to have a serious public policy discussion about where our priorities lie, not keep trading sound-bytes about “cutting wasteful spending” and “job-killing tax hikes”.