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 5: Who really pays the tax?

JDN 2457359

I think all the pieces are now in place to really talk about tax incidence.

In earlier posts I discussed how taxes have important downsides, then talked about how taxes can distort prices, then explained that taxes are actually what gives money its value. In the most recent post in the series, I used supply and demand curves to show precisely how taxes create deadweight loss.

Now at last I can get to the fundamental question: Who really pays the tax?

The common-sense answer would be that whoever writes the check to the government pays the tax, but this is almost completely wrong. It is right about one aspect, a sort of political economy notion, which is that if there is any trouble collecting the tax, it’s generally that person who is on the hook to pay it. But especially in First World countries, most taxes are collected successfully almost all the time. Tax avoidance—using loopholes to reduce your tax burden—is all over the place, but tax evasion—illegally refusing to pay the tax you owe—is quite rare. And for this political economy argument to hold, you really need significant amounts of tax evasion and enforcement against it.

The real economic answer is that the person who pays the tax is the person who bears the loss in surplus. In essence, the person who bears the tax is the person who is most unhappy about it.

In the previous post in this series, I explained what surplus is, but it bears a brief repetition. Surplus is the value you get from purchases you make, in excess of the price you paid to get them. It’s measured in dollars, because that way we can read it right off the supply and demand curve. We should actually be adjusting for marginal utility of wealth and measuring in QALY, but that’s a lot harder so it rarely gets done.

In the graphs I drew in part 4, I already talked about how the deadweight loss is much greater if supply and demand are elastic than if they are inelastic. But in those graphs I intentionally set it up so that the elasticities of supply and demand were about the same. What if they aren’t?

Consider what happens if supply is very inelastic, but demand is very elastic. In fact, to keep it simple, lets suppose that supply is perfectly inelastic, but demand is perfectly elastic. This means that supply elasticity is 0, but demand elasticity is infinite.

The zero supply elasticity means that the worker would actually be willing to work up to their maximum hours for nothing, but is unwilling to go above that regardless of the wage. They have a specific amount of hours they want to work, regardless of what they are paid.

The infinite demand elasticity means that each hour of work is worth exactly the same amount the employer, with no diminishing returns. They have a specific wage they are willing to pay, regardless of how many hours it buys.

Both of these are quite extreme; it’s unlikely that in real life we would ever have an elasticity that is literally zero or infinity. But we do actually see elasticities that get very low or very high, and qualitatively they act the same way.

So let’s suppose as before that the wage is $20 and the number of hours worked is 40. The supply and demand graph actually looks a little weird: There is no consumer surplus whatsoever.

incidence_infinite_notax_surplus

Each hour is worth $20 to the employer, and that is what they shall pay. The whole graph is full of producer surplus; the worker would have been willing to work for free, but instead gets $20 per hour for 40 hours, so they gain a whopping $800 in surplus.

incidence_infinite_tax_surplus

Now let’s implement a tax, say 50% to make it easy. (That’s actually a huge payroll tax, and if anybody ever suggested implementing that I’d be among the people pulling out a Laffer curve to show them why it’s a bad idea.)

Normally a tax would push the demand wage higher, but in this case $20 is exactly what they can afford, so they continue to pay exactly the same as if nothing had happened. This is the extreme example in which your “pre-tax” wage is actually your pre-tax wage, what you’d get if there hadn’t been a tax. This is the only such example—if demand elasticity is anything less than infinity, the wage you see listed as “pre-tax” will in fact be higher than what you’d have gotten in the absence of the tax.

The tax revenue is therefore borne entirely by the worker; they used to take home $20 per hour, but now they only get $10. Their new surplus is only $400, precisely 40% lower. The extra $400 goes directly to the government, which makes this example unusual in another way: There is no deadweight loss. The employer is completely unaffected; their surplus goes from zero to zero. No surplus is destroyed, only moved. Surplus is simply redistributed from the worker to the government, so the worker bears the entirety of the tax. Note that this is true regardless of who actually writes the check; I didn’t even have to include that in the model. Once we know that there was a tax imposed on each hour of work, the market prices decided who would bear the burden of that tax.

By Jove, we’ve actually found an example in which it’s fair to say “the government is taking my hard-earned money!” (I’m fairly certain if you replied to such people with “So you think your supply elasticity is zero but your employer’s demand elasticity is infinite?” you would be met with blank stares or worse.)

This is however quite an extreme case. Let’s try a more realistic example, where supply elasticity is very small, but not zero, and demand elasticity is very high, but not infinite. I’ve made the demand elasticity -10 and the supply elasticity 0.5 for this example.

incidence_supply_notax_surplus

Before the tax, the wage was $20 for 40 hours of work. The worker received a producer surplus of $700. The employer received a consumer surplus of only $80. The reason their demand is so elastic is that they are only barely getting more from each hour of work than they have to pay.

Total surplus is $780.

incidence_supply_tax_surplus

After the tax, the number of hours worked has dropped to 35. The “pre-tax” (demand) wage has only risen to $20.25. The after-tax (supply) wage the worker actually receives has dropped all the way to $10. The employer’s surplus has only fallen to $65.63, a decrease of $14.37 or 18%. Meanwhile the worker’s surplus has fallen all the way to $325, a decrease of $275 or 46%. The employer does feel the tax, but in both absolute and relative terms, the worker feels the tax much more than the employer does.

The tax revenue is $358.75, which means that the total surplus has been reduced to $749.38. There is now $30.62 of deadweight loss. Where both elasticities are finite and nonzero, deadweight loss is basically inevitable.

In this more realistic example, the burden was shared somewhat, but it still mostly fell on the worker, because the worker had a much lower elasticity. Let’s try turning the tables and making demand elasticity low while supply elasticity is high—in fact, once again let’s illustrate by using the extreme case of zero versus infinity.

In order to do this, I need to also set a maximum wage the employer is willing to pay. With nonzero elasticity, that maximum sort of came out automatically when the demand curve hits zero; but when elasticity is zero, the line is parallel so it never crosses. Let’s say in this case that the maximum is $50 per hour.

(Think about why we didn’t need to set a minimum wage for the worker when supply was perfectly inelastic—there already was a minimum, zero.)

incidence_infinite2_notax_surplus

This graph looks deceptively similar to the previous; basically all that has happened is the supply and demand curves have switched places, but that makes all the difference. Now instead of the worker getting all the surplus, it’s the employer who gets all the surplus. At their maximum wage of $50, they are getting $1200 in surplus.

Now let’s impose that same 50% tax again.

incidence_infinite2_tax_surplus

The worker will not accept any wage less than $20, so the demand wage must rise all the way to $40. The government will then receive $800 in revenue, while the employer will only get $400 in surplus. Notice again that the deadweight loss is zero. The employer will now bear the entire burden of the tax.

In this case the “pre-tax” wage is basically meaningless; regardless of the value of the tax the worker would receive the same amount, and the “pre-tax” wage is really just an accounting mechanism the government uses to say how large the tax is. They could just as well have said, “Hey employer, give us $800!” and the outcome would be the same. This is called a lump-sum tax, and they don’t work in the real world but are sometimes used for comparison. The thing about a lump-sum tax is that it doesn’t distort prices in any way, so in principle you could use it to redistribute wealth however you want. But in practice, there’s no way to implement a lump-sum tax that would be large enough to raise sufficient revenue but small enough to be affordable by the entire population. Also, a lump-sum tax is extremely regressive, hurting the poor tremendously while the rich feel nothing. (Actually the closest I can think of to a realistic lump-sum tax would be a basic income, which is essentially a negative lump-sum tax.)

I could keep going with more examples, but the basic argument is the same.

In general what you will find is that the person who bears a tax is the person who has the most to lose if less of that good is sold. This will mean their supply or demand is very inelastic and their surplus is very large.

Inversely, the person who doesn’t feel the tax is the person who has the least to lose if the good stops being sold. That will mean their supply or demand is very elastic and their surplus is very small.
Once again, it really does not matter how the tax is collected. It could be taken entirely from the employer, or entirely from the worker, or shared 50-50, or 60-40, or whatever. As long as it actually does get paid, the person who will actually feel the tax depends upon the structure of the market, not the method of tax collection. Raising “employer contributions” to payroll taxes won’t actually make workers take any more home; their “pre-tax” wages will simply be adjusted downward to compensate. Likewise, raising the “employee contribution” won’t actually put more money in the pockets of the corporation, it will just force them to raise wages to avoid losing employees. The actual amount that each party must contribute to the tax isn’t based on how the checks are written; it’s based on the elasticities of the supply and demand curves.

And that’s why I actually can’t get that strongly behind corporate taxes; even though they are formally collected from the corporation, they could simply be hurting customers or employees. We don’t actually know; we really don’t understand the incidence of corporate taxes. I’d much rather use income taxes or even sales taxes, because we understand the incidence of those.

Tax incidence revisited, part 4: Surplus and deadweight loss

JDN 2457355

I’ve already mentioned the fact that taxation creates deadweight loss, but in order to understand tax incidence it’s important to appreciate exactly how this works.

Deadweight loss is usually measured in terms of total economic surplus, which is a strange and deeply-flawed measure of value but relatively easy to calculate.

Surplus is based upon the concept of willingness-to-pay; the value of something is determined by the maximum amount of money you would be willing to pay for it.

This is bizarre for a number of reasons, and I think the most important one is that people differ in how much wealth they have, and therefore in their marginal utility of wealth. $1 is worth more to a starving child in Ghana than it is to me, and worth more to me than it is to a hedge fund manager, and worth more to a hedge fund manager than it is to Bill Gates. So when you try to set what something is worth based on how much someone will pay for it, which someone are you using?

People also vary, of course, in how much real value a good has to them: Some people like dark chocolate, some don’t. Some people love spicy foods and others despise them. Some people enjoy watching sports, others would rather read a book. A meal is worth a lot more to you if you haven’t eaten in days than if you just ate half an hour ago. That’s not actually a problem; part of the point of a market economy is to distribute goods to those who value them most. But willingness-to-pay is really the product of two different effects: The real effect, how much utility the good provides you; and the wealth effect, how your level of wealth affects how much you’d pay to get the same amount of utility. By itself, willingness-to-pay has no means of distinguishing these two effects, and actually I think one of the deepest problems with capitalism is that ultimately capitalism has no means of distinguishing these two effects. Products will be sold to the highest bidder, not the person who needs it the most—and that’s why Americans throw away enough food to end world hunger.

But for today, let’s set that aside. Let’s pretend that willingness-to-pay is really a good measure of value. One thing that is really nice about it is that you can read it right off the supply and demand curves.

When you buy something, your consumer surplus is the difference between your willingness-to-pay and how much you actually did pay. If a sandwich is worth $10 to you and you pay $5 to get it, you have received $5 of consumer surplus.

When you sell something, your producer surplus is the difference between how much you were paid and your willingness-to-accept, which is the minimum amount of money you would accept to part with it. If making that sandwich cost you $2 to buy ingredients and $1 worth of your time, your willingness-to-accept would be $3; if you then sell it for $5, you have received $2 of producer surplus.

Total economic surplus is simply the sum of consumer surplus and producer surplus. One of the goals of an efficient market is to maximize total economic surplus.

Let’s return to our previous example, where a 20% tax raised the original wage from $22.50 and thus resulted in an after-tax wage of $18.

Before the tax, the supply and demand curves looked like this:

equilibrium_notax

Consumer surplus is the area below the demand curve, above the price, up to the total number of goods sold. The basic reasoning behind this is that the demand curve gives the willingness-to-pay for each good, which decreases as more goods are sold because of diminishing marginal utility. So what this curve is saying is that the first hour of work was worth $40 to the employer, but each following hour was worth a bit less, until the 10th hour of work was only worth $35. Thus the first hour gave $40-$20 = $20 of surplus, while the 10th hour only gave $35-$20 = $15 of surplus.

Producer surplus is the area above the supply curve, below the price, again up to the total number of goods sold. The reasoning is the same: If the first hour of work cost $5 worth of time but the 10th hour cost $10 worth of time, the first hour provided $20-$5 = $15 in producer surplus, but the 10th hour only provided $20-$10 = $10 in producer surplus.

Imagine drawing a little 1-pixel-wide line straight down from the demand curve to the price for each hour and then adding up all those little lines into the total area under the curve, and similarly drawing little 1-pixel-wide lines straight up from the supply curve.

surplus

The employer was paying $20 * 40 = $800 for an amount of work that they actually valued at $1200 (the total area under the demand curve up to 40 hours), so they benefit by $400. The worker was being paid $800 for an amount of work that they would have been willing to accept $480 to do (the total area under the supply curve up to 40 hours), so they benefit $320. The sum of these is the total surplus $720.

equilibrium_notax_surplus

After the tax, the employer is paying $22.50 * 35 = $787.50, but for an amount of work that they only value at $1093.75, so their new surplus is only $306.25. The worker is receiving $18 * 35 = $630, for an amount of work they’d have been willing to accept $385 to do, so their new surplus is $245. Even when you add back in the government revenue of $4.50 * 35 = $157.50, the total surplus is still only $708.75. What happened to that extra $11.25 of value? It simply disappeared. It’s gone. That’s what we mean by “deadweight loss”. That’s why there is a downside to taxation.

equilibrium_tax_surplus

How large the deadweight loss is depends on the precise shape of the supply and demand curves, specifically on how elastic they are. Remember that elasticity is the proportional change in the quantity sold relative to the change in price. If increasing the price 1% makes you want to buy 2% less, you have a demand elasticity of -2. (Some would just say “2”, but then how do we say it if raising the price makes you want to buy more? The Law of Demand is more like what you’d call a guideline.) If increasing the price 1% makes you want to sell 0.5% more, you have a supply elasticity of 0.5.

If supply and demand are highly elastic, deadweight loss will be large, because even a small tax causes people to stop buying and selling a large amount of goods. If either supply or demand is inelastic, deadweight loss will be small, because people will more or less buy and sell as they always did regardless of the tax.

I’ve filled in the deadweight loss with brown in each of these graphs. They are designed to have the same tax rate, and the same price and quantity sold before the tax.

When supply and demand are elastic, the deadweight loss is large:

equilibrium_elastic_tax_surplus

But when supply and demand are inelastic, the deadweight loss is small:

equilibrium_inelastic_tax_surplus

Notice that despite the original price and the tax rate being the same, the tax revenue is also larger in the case of inelastic supply and demand. (The total surplus is also larger, but it’s generally thought that we don’t have much control over the real value and cost of goods, so we can’t generally make something more inelastic in order to increase total surplus.)

Thus, all other things equal, it is better to tax goods that are inelastic, because this will raise more tax revenue while producing less deadweight loss.

But that’s not all that elasticity does!

At last, the end of our journey approaches: In the next post in this series, I will explain how elasticity affects who actually ends up bearing the burden of the tax.

Fear not the deficit

JDN 2456984 PST 12:20.

The deficit! It’s big and scary! And our national debt is rising by the second, says a “debt clock” that is literally just linearly extrapolating the trend. You don’t actually think that there are economists marking down every single dollar the government spends and uploading it immediately, do you? We’ve got better things to do. Conservatives will froth at the mouth over how Obama is the “biggest government spender in world history“, which is true if you just look at the dollar amounts, but of course it is; Obama is the president of the richest country in world history. If the government continues to tax at the same rate and spend what it taxes, government spending will be a constant proportion of GDP (which isn’t quite true, but it’s pretty close; there are ups and downs but for the last 40 years or so federal spending is generally in the range 30% to 35% of GDP), and the GDP of the United States is huge, and far beyond that of any other nation not only today, but ever. This is particularly true if you use nominal dollars, but it’s even true if you use inflation-adjusted real GDP. No other nation even gets close to US GDP, which is about to reach $17 trillion a year (unless you count the whole European Union as a nation, in which case it’s a dead heat).

China recently passed us if you use purchasing-power-parity, but that really doesn’t mean much, because purchasing-power-parity, or PPP, is a measure of standard of living, not a measure of a nation’s total economic power. If you want to know how well people in a country live, you use GDP per capita (that is, per person) PPP. But if you want to know a country’s capacity to influence the world economy, what matters is so-called real GDP, which is adjusted for inflation and international exchange rates. The difference is that PPP will tell you how many apples a person can buy, but real GDP will tell you how many aircraft carriers a government can build. The US is still doing quite well in that department, thank you; we have 10 of the world’s 20 active aircraft carriers, which is to say as many as everyone else combined. The US has 4% of the world’s population and 24% of the world’s economic output.

In particular, GDP in the US has been growing rather steadily since the Great Recession, and we are now almost recovered from the Second Depression and back to our equilibrium level of unemployment and economic growth. As the economy grows, government spending grows alongside it. Obama has actually presided over a decrease in the proportion of government spending relative to GDP, largely because of all this political pressure to reduce the deficit and stop the growth of the national debt. Under Obama the deficit has dropped dramatically.

But what is the deficit, anyway? And how can the deficit be decreasing if the debt clock keeps ticking up?

The government deficit is simply the difference between total government spending and total government revenue. If the government spends $3.90 trillion and takes in $3.30 trillion, the deficit is going to be $0.60 trillion, or $600 billion. In the rare case that you take in more than you spend, the deficit would be negative; we call that a surplus instead. (This almost never happens.)

Because of the way the US government is financed, the deficit corresponds directly to the national debt, which is the sum of all outstanding loans to the government. Every time the government spends more than it takes in, it makes up the difference by taking out a loan, in the form of a Treasury bond. As long as the deficit is larger than zero, the debt will increase. Think of the debt as where you are, and the deficit as how fast you’re going; you can be slowing down, but you’ll continue to move forward as long as you have some forward momentum.

Who is giving us these loans? You can look at the distribution of bondholders here. About a third of the debt is owned by the federal government itself, which makes it a very bizarre notion of “debt” indeed. Of the rest, 21% is owned by states or the Federal Reserve, so that’s also a pretty weird kind of debt. Only 55% of the total debt is owned by the public, and of those 39% are people and corporations within the United States. That means that only 33% of the national debt is actually owned by foreign people, corporations, or governments. What we actually owe to China is about $1.4 trillion. That’s a lot of money (it’s literally enough to make an endowment that would end world hunger forever), but our total debt is almost $18 trillion, so that’s only 8%.

When most people see these huge figures they panic: “Oh my god, we owe $18 trillion! How will we ever repay that!” Well, first of all, our GDP is $17 trillion, so we only owe a little over one year of income. (I wish I only owed one year of income in student loans….)

But in fact we don’t really owe it at all, and we don’t need to ever repay it. Chop off everything that’s owned by US government institutions (including the Federal Reserve, which is only “quasi-governmental”), and the figure drops down to $9.9 trillion. If by we you mean American individuals and corporations, then obviously we don’t owe back the debt that’s owned by ourselves, so take that off; now you’re looking at $6 trillion. That’s only about 4 months of total US economic output, or less than two years of government revenue.

And it gets better! The government doesn’t need to somehow come up with that money; they don’t even have to raise it in taxes. They can print that money, because the US government has a sovereign currency and the authority to print as much as we want. Really, we have the sovereign currency, because the US dollar is the international reserve currency, the currency that other nations hold in order to make exchanges in foreign markets. Other countries buy our money because it’s a better store of value than their own. Much better, in fact; the US has the most stable inflation rate in the world, and has literally never undergone hyperinflation. Better yet, the last time we had prolonged deflation was the Great Depression. This system is self-perpetuating, because being the international reserve currency also stabilizes the value of your money.

This is why it’s so aggravating to me when people say things like “the government can’t afford that” or “the government is broke” or “that money needs to come from somewhere”. No, the government can’t be broke! No, the money doesn’t have to come from somewhere! The US government is the somewhere from which the world’s money comes. If there is one institution in the world that can never, ever be broke, it is the US government. This gives our government an incredible amount of power—combine that with our aforementioned enormous GDP and fleet of aircraft carriers, and you begin to see why the US is considered a global hegemon.

To be clear: I’m not suggesting we eliminate all taxes and just start printing money to pay for everything. Taxes are useful, and we should continue to have them—ideally we would make them more progressive than they presently are. But it’s important to understand why taxes are useful; it’s really not that they are “paying for” government services. It’s actually more that they are controlling the money supply. The government creates money by spending, then removes money by taxing; in this way we maintain a stable growth of the money supply that allows us to keep the economy running smoothly and maintain inflation at a comfortable level. Taxes also allow the government to redistribute income from those who have it and save it to those who need it and will spend it—which is all the more reason for them to be progressive. But in theory we could eliminate all taxes without eliminating government services; it’s just that this would cause a surge in inflation. It’s a bad idea, but by no means impossible.

When we have a deficit, the national debt increases. This is not a bad thing. This is a fundamental misconception that I hope to disabuse you of: Government debt is not like household debt or corporate debt. When people say things like “we need to stop spending outside our means” or “we shouldn’t put wars on the credit card”, they are displaying a fundamental misunderstanding of what government debt is. The government simply does not operate under the same kind of credit constraints as you and I.

First, the government controls its own interest rates, and they are always very low—typically the lowest in the entire economy. That already gives it a lot more power over its debt than you or I have over our own.

Second, the government has no reason to default, because they can always print more money. That’s probably why bondholders tolerate the fact that the government sets its own interest rates; sure, it only pays 0.5%, but it definitely pays that 0.5%.

Third, government debt plays a role in the functioning of global markets; one of the reasons why China is buying up so much of our debt is so that they can keep the dollar high in value and thus maintain their trade surplus. (This is why whenever someone says something like, “The government needs to stop going further into debt, just like how I tightened my belt and paid off my mortgage!” I generally reply, “So when was the last time someone bought your debt in order to prop up your currency?”) This is also why we can’t get rid of our trade deficit and maintain a “strong dollar” at the same time; anyone who wants to do that may feel patriotic, but they are literally talking nonsense. The stronger the dollar, the higher the trade deficit.

Fourth, as I already hinted at above, the government doesn’t actually need debt at all. Government debt, like taxation, is not actually a source of funding; it is a tool of monetary policy. (If you’re going to quote one sentence from this post, it should be the previous; that basically sums up what I’m saying.) Even without raising taxes or cutting spending, the government could choose not to issue bonds, and instead print cash. You could make a sophisticated economic argument for how this is really somehow “issuing debt with indefinite maturity at 0% interest”; okay, fine. But it’s not what most people think of when they think of debt. (In fact, sophisticated economic arguments can go quite the opposite way: there’s a professor at Harvard I may end up working with—if I get into Harvard for my PhD of course—who argues that the federal debt and deficit are literally meaningless because they can be set arbitrarily by policy. I think he goes too far, but I see his point.) This is why many economists were suggesting that in order to get around ridiculous debt-ceiling intransigence Obama could simply Mint the Coin.

Government bonds aren’t really for the benefit of the government, they’re for the benefit of society. They allow the government to ensure that there is always a perfectly safe investment that people can buy into which will anchor interest rates for the rest of the economy. If we ever did actually pay off all the Treasury bonds, the consequences could be disastrous.

Fifth, the government does not have a credit limit; they can always issue more debt (unless Congress is filled with idiots who won’t raise the debt ceiling!). The US government is the closest example in the world to what neoclassical economists call a perfect credit market. A perfect credit market is like an ideal rational agent; these sort of things only exist in an imaginary world of infinite identical psychopaths. A perfect credit market would have perfect information, zero transaction cost, zero default risk, and an unlimited quantity of debt; with no effort at all you could take out as much debt as you want and everyone would know that you are always guaranteed to pay it back. This is in most cases an utterly absurd notion—but in the case of the US government it’s actually pretty close.

Okay, now that I’ve deluged you with reasons why the national debt is fundamentally different from a household mortgage or corporate bond, let’s get back to talking about the deficit. As I mentioned earlier, the deficit is almost always positive; the government is almost always spending more money than it takes in. Most people think that is a bad thing; it is not.

It would be bad for a corporation to always run a deficit, because then it would never make a profit. But the government is not a for-profit corporation. It would be bad for an individual to always run a deficit, because eventually they would go bankrupt. But the government is not an individual.

In fact, the government running a deficit is necessary for both corporations to make profits and individuals to gain net wealth! The government is the reason why our monetary system is nonzero-sum.

This is actually so easy to see that most people who learn about it react with shock, assuming that it can’t be right. There can’t be some simple and uncontroversial equation that shows that government deficits are necessary for profits and savings. Actually, there is; and the fact that we don’t talk about this more should tell you something about the level of sophistication in our economic discourse.

Individuals do work, get paid wages W. (This also includes salaries and bonuses; it’s all forms of labor income.) They also get paid by government spending, G, and pay taxes, T. Let’s pretend that all taxing and spending goes to people and not corporations. This is pretty close to true, especially since corporations as big as Boeing frequently pay nothing in taxes. Corporate subsidies, while ridiculous, are also a small portion of spending—no credible estimate is above $300 billion a year, or less than 10% of the budget. (Without that assumption the equation has a couple more terms, but the basic argument doesn’t change.) People use their money to buy consumption goods, C. What they don’t spend they save, S.

S = (W + G – T) – C

I’m going to rearrange this for reasons that will soon become clear:

S = (W – C) + (G – T)

I’ll also subtract investment I from both sides, again for reasons that will become clear:

S – I = (W – C – I) + (G – T)

Corporations hire workers and pay them W. They make consumption goods which are then sold for C. They also sell to foreign companies and buy from foreign companies, exporting X and importing M. Since we have a trade deficit, this means that X < M. Finally, they receive investment I that comes in the form of banks creating money through loans (yes, banks can create money). Most of our monetary policy is in the form of trying to get banks to create more money by changing interest rates. Only when desperate do we actually create the money directly (I’m not sure why we do it this way). In any case, this yields a total net profit P.

P = C + I – W + (X – M)

Now, if the economy is functioning well, we want profits and savings to both be positive—both people and corporations will have more money on average next year then they had this year. This means that S > 0 and P > 0. We also don’t want the banks loaning out more money than people save—otherwise people go ever further into debt—so we actually want S > I, or S – I > 0. If S – I > 0, people are paying down their debts and gaining net wealth. If S – I < 0, people are going further into debt and losing net wealth. In a well-functioning economy we want people to be gaining net wealth.

In order to have P > 0, because X – M < 0 we need to have C + I > W. People have to spend more on consumption and investment than they are paid in wages—have to, absolutely have to, as a mathematical law—in order for corporations to make a profit.

But then if C + I > W, W – C – I < 0, which means that the first term of the savings equation is negative. In order for savings to be positive, it must be—again as a mathematical law—that G – T > 0, which means that government spending exceeds taxes. In order for both corporations to profit and individuals to save at the same time, the government must run a deficit.

There is one other way, actually, and that’s for X – M to be positive, meaning you run a trade surplus. But right now we don’t, and moreover, the world as a whole necessarily cannot. For the world as a whole, X = M. This will remain true at least until we colonize other planets. This means that in order for both corporate profits and individual savings to be positive worldwide, overall governments worldwide must spend more than they take in. It has to be that way, otherwise the equations simply don’t balance.

You can also look at it another way by adding the equations for S – I and P:

S – I + P = (G – T) + (X – M)

Finally, you can also derive this a third way. This is your total GDP which we usually call Y (“yield”, I think?); it’s equal to consumption plus investment plus government spending, plus net exports:

Y = C + I + G + (X – M)

It’s also equal to consumption plus profit plus saving plus taxes:

Y = C + P + S + T

So those two things must be the same:

C + S + T + P = C + I + G + (X – M)

Canceling and rearranging we get:

(S – I) + P = (G – T) + (X – M)

The sum of saving minus investment (which we can sort of think of as “net saving”) plus profit is equal to the sum of the government deficit and the trade surplus. (Usually you don’t see P in this sectoral balances equation because no distinction is made between consumers and corporations and P is absorbed into S.)

From the profit equation:

W = C + I + (X – M) – P

Put that back into our GDP equation:

Y = W + P + G

GDP is wages plus profits plus government spending.

That’s a lot of equations; simple equations, but yes, equations. Lots of people are scared by equations. So here, let me try to boil it down to a verbal argument. When people save and corporations make profits, money gets taken out of circulation. If no new money is added, the money supply will decrease as a result; this shrinks the economy (mathematically it must absolutely shrink it in nominal terms; theoretically it could cause deflation and not reduce real output, but in practice real output always goes down because deflation causes its own set of problems). New money can be created by banks, but the mechanism of creation requires that people go further into debt. This is unstable, and eventually people can’t borrow anymore and the whole financial system comes crashing down. The better way, then, is for the government to create new money. Yes, as we currently do things, this means the government will go further into debt; but that’s all right, because the government can continue to increase its debt indefinitely without having to worry about hitting a ceiling and making everything fall apart. We could also just print money instead, and in fact I think in many cases this is what we should do—but for whatever reason people always freak out when you suggest such a thing, invariably mentioning Zimbabwe. (And yes, Zimbabwe is in awful shape; but they didn’t just print money to cover a reasonable amount of deficit spending. They printed money to line their own pockets, and it was thousands of times more than what I’m suggesting. Also Zimbabwe has a much smaller economy; $1 trillion is 5% of US GDP, but it’s 8,000% of Zimbabwe’s. I’m suggesting we print maybe 4% of GDP; at the peak of the hyperinflation they printed something more like 100,000%.)

One last thing before I go. If investment suddenly drops, net saving will go up. If the government deficit and trade deficit remain constant, profits must go down. This drives firms into bankruptcy, driving wages down as well. This makes GDP fall—and you get a recession. A similar effect would occur if consumption suddenly drops. In both cases people will be trying to increase their net wealth, but in fact they won’t be able to—this is what’s called the paradox of thrift. You actually want to increase the government deficit under these circumstances, because then you will both add to GDP directly and allow profits and wages to go back up and raise GDP even further. Because GDP has gone down, tax income will go down, so if you insist on balancing the budget, you’ll cut spending and only make things worse.

Raising the government deficit generally increases economic growth. From these simple equations it looks like you could raise GDP indefinitely, but these are nominal figures—actual dollar amounts—so after a certain point all you’d be doing is creating inflation. Where exactly that point is depends on how your economy is performing relative to its potential capacity. In a recession you are far below capacity, so that’s just the time to spend. You’d only want a budget surplus if you actually thought you were above long-run capacity, because you’re depleting natural resources or causing too much inflation or something like that. And indeed, we hardly ever see budget surpluses.

So that, my dear reader, is why we don’t need to fear the deficit. Government debt is nothing like other forms of debt; profits and savings depend upon the government spending more than it takes in; deficits are highly beneficial during recessions; and the US government is actually in a unique position to never worry about defaulting on its debt.