How not to do financial transaction tax

JDN 2457520

I strongly support the implementation of a financial transaction tax; like a basic income, it’s one of those economic policy ideas that are so brilliantly simple it’s honestly a little hard to believe how incredibly effective they are at making the world a better place. You mean we might be able to end stock market crashes just by implementing this little tax that most people will never even notice, and it will raise enough revenue to pay for food stamps? Yes, a financial transaction tax is that good.

So, keep that in mind when I say this:

TruthOut’s proposal for a financial transaction tax is somewhere between completely economically illiterate and outright insane.

They propose a 10% transaction tax on stocks and a 1% transaction tax on notional value of derivatives, then offer a “compromise” of 5% on stocks and 0.5% on derivatives. They make a bunch of revenue projections based on these that clearly amount to nothing but multiplying the current amount of transactions by the tax rate, which is so completely wrong we now officially have a left-wing counterpart to trickle-down voodoo economics.

Their argument is basically like this (I’m paraphrasing): “If we have to pay 5% sales tax on groceries, why shouldn’t you have to pay 5% on stocks?”

But that’s not how any of this works.

Demand for most groceries is very inelastic, especially in the aggregate. While you might change which groceries you’ll buy depending on their respective prices, and you may buy in bulk or wait for sales, over a reasonably long period (say a year) across a large population (say all of Michigan or all of the US), total amount of spending on groceries is extremely stable. People only need a certain amount of food, and they generally buy that amount and then stop.

So, if you implement a 5% sales tax that applies to groceries (actually sales tax in most states doesn’t apply to most groceries, but honestly it probably should—offset the regressiveness by providing more social services), people would just… spend about 5% more on groceries. Probably a bit less than that, actually, since suppliers would absorb some of the tax; but demand is much less elastic for groceries than supply, so buyers would bear most of the incidence of the tax. (It does not matter how the tax is collected; see my tax incidence series for further explanation of why.)

Other goods like clothing and electronics are a bit more elastic, so you’d get some deadweight loss from the sales tax; but at a typical 5% to 10% in the US this is pretty minimal, and even the hefty 20% or 30% VATs in some European countries only have a moderate effect. (Denmark’s 180% sales tax on cars seems a bit excessive to me, but it is Pigovian to disincentivize driving, so it also has very little deadweight loss.)

But what would happen if you implemented a 5% transaction tax on stocks? The entire stock market would immediately collapse.

A typical return on stocks is between 5% and 15% per year. As a rule of thumb, let’s say about 10%.

If you pay 5% sales tax and trade once per year, tax just cut your return in half.

If you pay 5% sales tax and trade twice per year, tax destroyed your return completely.

Even if you only trade once every five years, a 5% sales tax means that instead of your stocks being worth 61% more after those 5 years they are only worth 53% more. Your annual return has been reduced from 10% to 8.9%.

But in fact there are many perfectly legitimate reasons to trade as often as monthly, and a 5% tax would make monthly trading completely unviable.

Even if you could somehow stop everyone from pulling out all their money just before the tax takes effect, you would still completely dry up the stock market as a source of funding for all but the most long-term projects. Corporations would either need to finance their entire operations out of cash or bonds, or collapse and trigger a global depression.

Derivatives are even more extreme. The notional value of derivatives is often ludicrously huge; we currently have over a quadrillion dollars in notional value of outstanding derivatives. Assume that say 10% of those are traded every year, and we’re talking $100 trillion in notional value of transactions. At 0.5% you’re trying to take in a tax of$500 billion. That sounds fantastic—so much money!—but in fact what you should be thinking about is that’s a really strong avoidance incentive. You don’t think banks will find a way to restructure their trading practices—or stop trading altogether—to avoid this tax?

Honestly, maybe a total end to derivatives trading would be tolerable. I certainly think we need to dramatically reduce the amount of derivatives trading, and much of what is being traded—credit default swaps, collateralized debt obligations, synthetic collateralized debt obligations, etc.—really should not exist and serves no real function except to obscure fraud and speculation. (Credit default swaps are basically insurance you can buy on other people’s companies. There’s a reason you’re not allowed to buy insurance on other people’s stuff!) Interest rate swaps aren’t terrible (when they’re not being used to perpetrate the largest white-collar crime in history), but they also aren’t necessary. You might be able to convince me that commodity futures and stock options are genuinely useful, though even these are clearly overrated. (Fun fact: Futures markets have been causing financial crises since at least Classical Rome.) Exchange-traded funds are technically derivatives, and they’re just fine (actually ETFs are very low-risk, because they are inherently diversified—which is why you should probably be buying them); but actually their returns are more like stocks, so the 0.5% might not be insanely high in that case.

But stocks? We kind of need those. Equity financing has been the foundation of capitalism since the very beginning. Maybe we could conceivably go to a fully debt-financed system, but it would be a radical overhaul of our entire financial system and is certainly not something to be done lightly.

Indeed, TruthOut even seems to think we could apply the same sales tax rate to bonds, which means that debt financing would also collapse, and now we’re definitely talking about global depression. How exactly is anyone supposed to finance new investments, if they can’t sell stock or bonds? And a 5% tax on the face value of stock or bonds, for all practical purposes, is saying that you can’t sell stock or bonds. It would make no one want to buy them.

Wealthy investors buying of stocks and bonds is essentially no different than average folks buying food, clothing or other real “goods and services.”

Yes it is. It is fundamentally different.

People buy goods to use them. People buy stocks to make money selling them.

This seems perfectly obvious, but it is a vital distinction that seems to be lost on TruthOut.

When you buy an apple or a shoe or a phone or a car, you care how much it costs relative to how useful it is to you; if we make it a bit more expensive, that will make you a bit less likely to buy it—but probably not even one-to-one so that a 5% tax would reduce purchases by 5%; it would probably be more like a 2% reduction. Demand for goods is inelastic. Taxing them will raise a lot of revenue and not reduce the quantity purchased very much.

But when you buy a stock or a bond or an interest rate swap, you care how much it costs relative to what you will be able to sell it for—you care about not its utility but its return. So a 5% tax will reduce the amount of buying and selling by substantially more than 5%—it could well be 50% or even 100%. Demand for financial assets is elastic. Taxing them will not raise much revenue but will substantially reduce the quantity purchased.

Now, for some financial assets, we want to reduce the quantity purchased—the derivatives market is clearly too big, and high-frequency trading that trades thousands of times per second can do nothing but destabilize the financial system. Joseph Stiglitz supports a small financial transaction tax precisely because it would substantially reduce high-frequency trading, and he’s a Nobel Laureate as you may recall. Naturally, he was excluded from the SEC hearings on the subject, because reasons. But the figures Stiglitz is talking about (and I agree with) are on the order of 0.1% for stocks and 0.01% for derivatives—50 times smaller than what TruthOut is advocating.

At the end, they offer another “compromise”:

Okay, half it again, to a 2.5 percent tax on stocks and bonds and a 0.25 percent on derivative trades. That certainly won’t discourage stock and bond trading by the rich (not that that is an all bad idea either).

Yes it will. By a lot. That’s the whole point.

A financial transaction tax is a great idea whose time has come; let’s not ruin its reputation by setting it at a preposterous value. Just as a $15 minimum wage is probably a good idea but a$250 minimum wage is definitely a terrible idea, a 0.1% financial transaction tax could be very beneficial but a 5% financial transaction tax would clearly be disastrous.

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. 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.

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. 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. 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.) 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. 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 3: Taxation and the value of money

JDN 2457352

Our journey through the world of taxes continues. I’ve already talked about how taxes have upsides and downsides, as well as how taxes directly affect prices and “before-tax” prices are almost meaningless.

Now it’s time to get into something that even a lot of economists don’t quite seem to grasp, yet which turns out to be fundamental to what taxes truly are.

In the usual way of thinking, it works something like this: We have an economy, through which a bunch of money flows, and then the government comes in and takes some of that money in the form of taxes. They do this because they want to spend money on a variety of services, from military defense to public schools, and in order to afford doing that they need money, so they take in taxes.

This view is not simply wrong—it’s almost literally backwards. Money is not something the economy had that the government comes in and takes. Money is something that the government creates and then adds to the economy to make it function more efficiently. Taxes are not the government taking out money that they need to use; taxes are the government regulating the quantity of money in the system in order to stabilize its value. The government could spend as much money as they wanted without collecting a cent in taxes (not should, but could—it would be a bad idea, but definitely possible); taxes do not exist to fund the government, but to regulate the money supply.

Indeed—and this is the really vital and counter-intuitive point—without taxes, money would have no value.

There is an old myth of how money came into existence that involves bartering: People used to trade goods for other goods, and then people found that gold was particularly good for trading, and started using it for everything, and then eventually people started making paper notes to trade for gold, and voila, money was born.

In fact, such a “barter economy” has never been documented to exist. It probably did once or twice, just given the enormous variety of human cultures; but it was never widespread. Ancient economies were based on family sharing, gifts, and debts of honor.

It is true that gold and silver emerged as the first forms of money, “commodity money”, but they did not emerge endogenously out of trading that was already happening—they were created by the actions of governments. The real value of the gold or silver may have helped things along, but it was not the primary reason why people wanted to hold the money. Money has been based upon government for over 3000 years—the history of money and civilization as we know it. “Fiat money” is basically a redundancy; almost all money, even in a gold standard system, is ultimately fiat money.

The primary reason why people wanted the money was so that they could use it to pay taxes.

It’s really quite simple, actually.

When there is a rule imposed by the government that you will be punished if you don’t turn up on April 15 with at least $4,287 pieces of green paper marked “US Dollar”, you will try to acquire$4,287 pieces of green paper marked “US Dollar”. You will not care whether those notes are exchangeable for gold or silver; you will not care that they were printed by the government originally. Because you will be punished if you don’t come up with those pieces of paper, you will try to get some.

If someone else has some pieces of green paper marked “US Dollar”, and knows that you need them to avoid being punished on April 15, they will offer them to you—provided that you give them something they want in return. Perhaps it’s a favor you could do for them, or something you own that they’d like to have. You will be willing to make this exchange, in order to avoid being punished on April 15.
Thus, taxation gives money value, and allows purchases to occur.

Once you establish a monetary system, it becomes self-sustaining. If you know other people will accept money as payment, you are more willing to accept money as payment because you know that you can go spend it with those people. “Legal tender” also helps this process along—the government threatens to punish people who refuse to accept money as payment. In practice, however, this sort of law is rarely enforced, and doesn’t need to be, because taxation by itself is sufficient to form the basis of the monetary system.

It’s deeply ironic that people who complain about printing money often say we are “debasing” the currency; when you think carefully about what debasement was, it clearly shows that the value of money never really resided in the gold or silver itself. If a government can successfully extract revenue from its monetary system by changing the amount of gold or silver in each coin, then the value of those coins can’t be in the gold and silver—it has to be in the power of the government. You can’t make a profit by dividing a commodity into smaller pieces and then selling the pieces. (Okay, you sort of can, by buying in bulk and selling at retail. But that’s not what we’re talking about. You can’t make money by buying 100 50-gallon barrels of oil and then selling them as 125 40-gallon barrels of oil; it’s the same amount of oil.)

Similarly, the fact that there is such a thing as seignioragethe value of currency in excess of its cost to create—shows that governments impart value to their money. Indeed, one of the reasons for debasement was to realign the value of coins with the value of the metals in the coins, which wouldn’t be necessary if those were simply by definition the same thing.

Taxation serves another important function in the monetary system, which is to regulate the supply of money. The government adds money to the economy by spending, and removes it by taxing; if they add more than they remove—a deficit—the money supply increases, while if they remove more than they add—a surplus—the money supply decreases. In order to maintain stable prices, you want the money supply to increase at approximately the rate of growth; for moderate inflation (which is probably better than actual price stability), you want the money supply to increase slightly faster than the rate of growth. Thus, in general we want the government deficit as a portion of GDP to be slightly larger than the growth rate of the economy. Thus, our current deficit of 2.8% of GDP is actually about where it should be, and we have no particular reason to want to decrease it. (This is somewhat oversimplified, because it ignores the contribution of the Federal Reserve, interest rates, and bank-created money. Most of the money in the world is actually not created by the government, but by banks which are restrained to greater or lesser extent by the government.)

Even a lot of people who try to explain modern monetary theory mistakenly speak as though there was a fundamental shift when we fully abandoned the gold standard in the 1970s. (This is a good explanation overall, but it makes this very error.) But in fact a gold standard really isn’t money “backed” by anything—gold is not what gives the money value, gold is almost worthless by itself. It’s pretty and it doesn’t corrode, but otherwise, what exactly can you do with it? Being tied to money is what made gold valuable, not the other way around. To see this, imagine a world where you have 20,000 tons of gold, but you know that you can never sell it. No one will ever purchase a single ounce. Would you feel particularly rich in that scenario? I think not. Now suppose you have a virtually limitless quantity of pieces of paper that you know people will accept for anything you would ever wish to buy. They are backed by nothing, they are just pieces of paper—but you are now rich, by the standard definition of the word. I can even make the analogy remove the exchange value of money and just use taxation: if you know that in two days you will be imprisoned if you don’t have this particular piece of paper, for the next two days you will guard that piece of paper with your life. It won’t bother you that you can’t exchange that piece of paper for anything else—you wouldn’t even want to. If instead someone else has it, you’ll be willing to do some rather large favors for them in order to get it.

Whenever people try to tell me that our money is “worthless” because it’s based on fiat instead of backed by gold (this happens surprisingly often), I always make them an offer: If you truly believe that our money is worthless, I’ll gladly take any you have off of your hands. I will even provide you with something of real value in return, such as an empty aluminum can or a pair of socks. If they truly believe that fiat money is worthless, they should eagerly accept my offer—yet oddly, nobody ever does.

This does actually create a rather interesting argument against progressive taxation: If the goal of taxation is simply to control inflation, shouldn’t we tax people based only on their spending? Well, if that were the only goal, maybe. But we also have other goals, such as maintaining employment and controlling inequality. Progressive taxation may actually take a larger amount of money out of the system than would be necessary simply to control inflation; but it does so in order to ensure that the super-rich do not become even more rich and powerful.

Governments are limited by real constraints of power and resources, but they they have no monetary constraints other than those they impose themselves. There is definitely something strongly coercive about taxation, and therefore about a monetary system which is built upon taxation. Unfortunately, I don’t know of any good alternatives. We might be able to come up with one: Perhaps people could donate to public goods in a mutually-enforced way similar to Kickstarter, but nobody has yet made that practical; or maybe the government could restructure itself to make a profit by selling private goods at the same time as it provides public goods, but then we have all the downsides of nationalized businesses. For the time being, the only system which has been shown to work to provide public goods and maintain long-term monetary stability is a system in which the government taxes and spends.

A gold standard is just a fiat monetary system in which the central bank arbitrarily decides that their money supply will be directly linked to the supply of an arbitrarily chosen commodity. At best, this could be some sort of commitment strategy to ensure that they don’t create vastly too much or too little money; but at worst, it prevents them from actually creating the right amount of money—and the gold standard was basically what caused the Great Depression. A gold standard is no more sensible a means of backing your currency than would be a standard requiring only prime-numbered interest rates, or one which requires you to print exactly as much money per minute as the price of a Ferrari.

No, the real thing that backs our money is the existence of the tax system. Far from taxation being “taking your hard-earned money”, without taxes money itself could not exist.

Tax incidence revisited, part 2: How taxes affect prices

JDN 2457341

One of the most important aspects of taxation is also one of the most counter-intuitive and (relatedly) least-understood: Taxes are not externally applied to pre-existing exchanges of money. Taxes endogenously interact with the system of prices, changing what the prices will be and then taking a portion of the money exchanged.

The price of something “before taxes” is not actually the price you would pay for it if there had been no taxes on it. Your “pre-tax income” is not actually the income you would have had if there were no income or payroll taxes.

The most obvious case to consider is that of government employees: If there were no taxes, public school teachers could not exist, so the “pre-tax income” of a public school teacher is a meaningless quantity. You don’t “take taxes out” of a government salary; you decide how much money the government employee will actually receive, and then at the same time allocate a certain amount into other budgets based on the tax code—a certain amount into the state general fund, a certain amount into the Social Security Trust Fund, and so on. These two actions could in principle be done completely separately; instead of saying that a teacher has a “pre-tax salary” of $50,000 and is taxed 20%, you could simply say that the teacher receives$40,000 and pay $10,000 into the appropriate other budgets. In fact, when there is a conflict of international jurisdiction this is sometimes literally what we do. Employees of the World Bank are given immunity from all income and payroll taxes (effectively, diplomatic immunity, though this is not usually how we use the term) based on international law, except for US citizens, who have their taxes paid for them by the World Bank. As a result, all World Bank salaries are quoted “after-tax”, that is, the actual amount of money employees will receive in their paychecks. As a result, a$120,000 salary at the World Bank is considerably higher than a $120,000 salary at Goldman Sachs; the latter would only (“only”) pay about$96,000 in real terms.

For private-sector salaries, it’s not as obvious, but it’s still true. There is actually someone who pays that “before-tax” salary—namely, the employer. “Pre-tax” salaries are actually a measure of labor expenditure (sometimes erroneously called “labor costs”, even by economists—but a true labor cost is the amount of effort, discomfort, stress, and opportunity cost involved in doing labor; it’s an amount of utility, not an amount of money). The salary “before tax” is the amount of money that the employer has to come up with in order to pay their payroll. It is a real amount of money being exchanged, divided between the employee and the government.

The key thing to realize is that salaries are not set in a vacuum. There are various economic (and political) pressures which drive employers to set different salaries. In the real world, there are all sorts of pressures that affect salaries: labor unions, regulations, racist and sexist biases, nepotism, psychological heuristics, employees with different levels of bargaining skill, employers with different concepts of fairness or levels of generosity, corporate boards concerned about public relations, shareholder activism, and so on.

But even if we abstract away from all that for a moment and just look at the fundamental economics, assuming that salaries are set at the price the market will bear, that price depends upon the tax system.

This is because taxes effectively drive a wedge between supply and demand.

Indeed, on a graph, it actually looks like a wedge, as you’ll see in a moment.

Let’s pretend that we’re in a perfectly competitive market. Everyone is completely rational, we all have perfect information, and nobody has any power to manipulate the market. We’ll even assume that we are dealing with hourly wages and we can freely choose the number of hours worked. (This is silly, of course; but removing this complexity helps to clarify the concept and doesn’t change the basic result that prices depend upon taxes.)

We’ll have a supply curve, which is a graph of the minimum price the worker is willing to accept for each hour in order to work a given number of hours. We generally assume that the supply curve slopes upward, meaning that people are willing to work more hours if you offer them a higher wage for each hour. The idea is that it gets progressively harder to find the time—it eats into more and more important alternative activities. (This is in fact a gross oversimplification, but it’ll do for now. In the real world, labor is the one thing for which the supply curve frequently bends backward.)

We’ll also have a demand curve, which is a graph of the maximum price the employer is willing to pay for each hour, if the employee works that many hours. We generally assume that the demand curve slopes downward, meaning that the employer is willing to pay less for each hour if the employee works more hours. The reason is that most activities have diminishing marginal returns, so each extra hour of work generally produces less output than the previous hour, and is therefore not worth paying as much for. (This too is an oversimplification, as I discussed previously in my post on the Law of Demand.)

Put these two together, and in a competitive market the price will be set at the point at which supply is equal to demand, so that the very last hour of work was worth exactly what the employer paid for it. That last hour is just barely worth it to the employer, and just barely worth it to the worker; any additional time would either be too expensive for the employer or not lucrative enough for the worker. But for all the previous hours, the value to the employer is higher than the wage, and the cost to the worker is lower than the wage. As a result, both the employer and the worker benefit.

But now, suppose we implement a tax. For concreteness, suppose the previous market-clearing wage was $20 per hour, the worker was working 40 hours, and the tax is 20%. If the employer still offers a wage of$20 for 40 hours of work, the worker is no longer going to accept it, because they will only receive $16 per hour after taxes, and$16 isn’t enough for them to be willing to work 40 hours. The worker could ask for a pre-tax wage of $25 so that the after-tax wage would be$20, but then the employer will balk, because $25 per hour is too expensive for 40 hours of work. In order to restore the balance (and when we say “equilibrium”, that’s really all we mean—balance), the employer will need to offer a higher pre-tax wage, which means they will demand fewer hours of work. The worker will then be willing to accept a lower after-tax wage for those reduced hours. In effect, there are now two prices at work: A supply price, the after-tax wage that the worker receives, which must be at or above the supply curve; and a demand price, the pre-tax wage that the employer pays, which must be at or below the demand curve. The difference between those two prices is the tax. In this case, I’ve set it up so that the pre-tax wage is$22.50, the after-tax wage is $18, and the amount of the tax is$4.50 or 20% of $22.50. In order for both the employer and the worker to accept those prices, the amount of hours worked has been reduced to 35. As a result of the tax, the wage that we’ve been calling “pre-tax” is actually higher than the wage that the worker would have received if the tax had not existed. This is a general phenomenon; it’s almost always true that your “pre-tax” wage or salary overestimates what you would have actually gotten if the tax had not existed. In one extreme case, it might actually be the same; in another extreme case, your after-tax wage is what you would have received and the “pre-tax” wage rises high enough to account for the entirety of the tax revenue. It’s not really “pre-tax” at all; it’s the after-tax demand price. Because of this, it’s fundamentally wrongheaded for people to complain that taxes are “taking your hard-earned money”. In all but the most exceptional cases, that “pre-tax” salary that’s being deducted from would never have existed. It’s more of an accounting construct than anything else, or like I said before a measure of labor expenditure. It is generally true that your after-tax salary is lower than the salary you would have gotten without the tax, but the difference is generally much smaller than the amount of the tax that you see deducted. In this case, the worker would see$4.50 per hour deducted from their wage, but in fact they are only down $2 per hour from where they would have been without the tax. And of course, none of this includes the benefits of the tax, which in many cases actually far exceed the costs; if we extended the example, it wouldn’t be hard to devise a scenario in which the worker who had their wage income reduced received an even larger benefit in the form of some public good such as national defense or infrastructure. 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): 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”.

What you need to know about tax incidence

JDN 2457152 EDT 14:54.

I said in my previous post that I consider tax incidence to be one of the top ten things you should know about economics. If I actually try to make a top ten list, I think it goes something like this:

1. Supply and demand
2. Monopoly and oligopoly
3. Externalities
4. Tax incidence
5. Utility, especially marginal utility of wealth
6. Pareto-efficiency
7. Risk and loss aversion
8. Biases and heuristics, including sunk-cost fallacy, scope neglect, herd behavior, anchoring and representative heuristic
9. Asymmetric information
10. Winner-takes-all effect

So really tax incidence is in my top five things you should know about economics, and yet I still haven’t talked about it very much. Well, today I will. The basic principles of supply and demand I’m basically assuming you know, but I really should spend some more time on monopoly and externalities at some point.

Why is tax incidence so important? Because of one central fact: The person who pays the tax is not the person who writes the check.

It doesn’t matter whether a tax is paid by the buyer or the seller; it matters what the buyer and seller can do to avoid the tax. If you can change your behavior in order to avoid paying the tax—buy less stuff, or buy somewhere else, or deduct something—you will not bear the tax as much as someone else who can’t do anything to avoid the tax, even if you are the one who writes the check. If you can avoid it and they can’t, other parties in the transaction will adjust their prices in order to eat the tax on your behalf.

Thus, if you have a good that you absolutely must buy no matter what—like, say, table saltand then we make everyone who sells that good pay an extra $5 per kilogram, I can guarantee you that you will pay an extra$5 per kilogram, and the suppliers will make just as much money as they did before. (A salt tax would be an excellent way to redistribute wealth from ordinary people to corporations, if you’re into that sort of thing. Not that we have any trouble doing that in America.)

On the other hand, if you have a good that you’ll only buy at a very specific price—like, say, fast food—then we can make you write the check for a tax of an extra $5 per kilogram you use, and in real terms you’ll pay hardly any tax at all, because the sellers will either eat the cost themselves by lowering the prices or stop selling the product entirely. (A fast food tax might actually be a good idea as a public health measure, because it would reduce production and consumption of fast food—remember, heart disease is one of the leading causes of death in the United States, making cheeseburgers a good deal more dangerous than terrorists—but it’s a bad idea as a revenue measure, because rather than pay it, people are just going to buy and sell less.) In the limit in which supply and demand are both completely fixed (perfectly inelastic), you can tax however you want and it’s just free redistribution of wealth however you like. In the limit in which supply and demand are both locked into a single price (perfectly elastic), you literally cannot tax that good—you’ll just eliminate production entirely. There aren’t a lot of perfectly elastic goods in the real world, but the closest I can think of is cash. If you instituted a 2% tax on all cash withdrawn, most people would stop using cash basically overnight. If you want a simple way to make all transactions digital, find a way to enforce a cash tax. When you have a perfect substitute available, taxation eliminates production entirely. To really make sense out of tax incidence, I’m going to need a lot of a neoclassical economists’ favorite thing: Supply and demand curves. These things pop up everywhere in economics; and they’re quite useful. I’m not so sure about their application to things like aggregate demand and the business cycle, for example, but today I’m going to use them for the sort of microeconomic small-market stuff that they were originally designed for; and what I say here is going to be basically completely orthodox, right out of what you’d find in an ECON 301 textbook. Let’s assume that things are linear, just to make the math easier. You’d get basically the same answers with nonlinear demand and supply functions, but it would be a lot more work. Likewise, I’m going to assume a unit tax on goods—like$2890 per hectare—as opposed to a proportional tax on sales—like 6% property tax—again, for mathematical simplicity.

The next concept I’m going to have to talk about is elasticitywhich is the proportional amount that quantity sold changes relative to price. If price increases 2% and you buy 4% less, you have a demand elasticity of -2. If price increases 2% and you buy 1% less, you have a demand elasticity of -1/2. If price increases 3% and you sell 6% more, you have a supply elasticity of 2. If price decreases 5% and you sell 1% less, you have a supply elasticity of 1/5.

Elasticity doesn’t have any units of measurement, it’s just a number—which is part of why we like to use it. It also has some very nice mathematical properties involving logarithms, but we won’t be needing those today.

The price that renters are willing and able to pay, the demand price PD will start at their maximum price, the reserve price PR, and then it will decrease linearly according to the quantity of land rented Q, according to a linear function (simply because we assumed that) which will vary according to a parameter e that represents the elasticity of demand (it isn’t strictly equal to it, but it’s sort of a linearization).

We’re interested in what is called the consumer surplus; it is equal to the total amount of value that buyers get from their purchases, converted into dollars, minus the amount they had to pay for those purchases. This we add to the producer surplus, which is the amount paid for those purchases minus the cost of producing themwhich is basically just the same thing as profit. Togerther the consumer surplus and producer surplus make the total economic surplus, which economists generally try to maximize. Because different people have different marginal utility of wealth, this is actually a really terrible idea for deep and fundamental reasons—taking a house from Mitt Romney and giving it to a homeless person would most definitely reduce economic surplus, even though it would obviously make the world a better place. Indeed, I think that many of the problems in the world, particularly those related to inequality, can be traced to the fact that markets maximize economic surplus rather than actual utility. But for now I’m going to ignore all that, and pretend that maximizing economic surplus is what we want to do.

You can read off the economic surplus straight from the supply and demand curves; it’s the area between the lines. (Mathematically, it’s an integral; but that’s equivalent to the area under a curve, and with straight lines they’re just triangles.) I’m going to call the consumer surplus just “surplus”, and producer surplus I’ll call “profit”.

Below the demand curve and above the price is the surplus, and below the price and above the supply curve is the profit:

I’m going to be bold here and actually use equations! Hopefully this won’t turn off too many readers. I will give each equation in both a simple text format and in proper LaTeX. Remember, you can render LaTeX here.

PD = PR – 1/e * Q

P_D = P_R – \frac{1}{e} Q \\

The marginal cost that landlords have to pay, the supply price PS, is a bit weirder, as I’ll talk about more in a moment. For now let’s say that it is a linear function, starting at zero cost for some quantity Q0 and then increases linearly according to a parameter n that similarly represents the elasticity of supply.

PS = 1/n * (Q – Q0)

P_S = \frac{1}{n} \left( Q – Q_0 \right) \\

Now, if you introduce a tax, there will be a difference between the price that renters pay and the price that landlords receive—namely, the tax, which we’ll call T. I’m going to assume that, on paper, the landlord pays the whole tax. As I said above, this literally does not matter. I could assume that on paper the renter pays the whole tax, and the real effect on the distribution of wealth would be identical. All we’d have to do is set PD = P and PS = P – T; the consumer and producer surplus would end up exactly the same. Or we could do something in between, with P’D = P + rT and P’S = P – (1 – r) T.

Then, if the market is competitive, we just set the prices equal, taking the tax into account:

P = PD – T = PR – 1/e * Q – T = PS = 1/n * (Q – Q0)

P= P_D – T = P_R – \frac{1}{e} Q – T= P_S = \frac{1}{n} \left(Q – Q_0 \right) \\

P_R – 1/e * Q – T = 1/n * (Q – Q0)

P_R – \frac{1}{e} Q – T = \frac{1}{n} \left(Q – Q_0 \right) \\

Notice the equivalency here; if we set P’D = P + rT and P’S = P – (1 – r) T, so that the consumer now pays a fraction of the tax r.

P = P’D – rT = P_r – 1/e*Q = P’S + (1 – r) T + 1/n * (Q – Q0) + (1 – r) T

P^\prime_D – r T = P = P_R – \frac{1}{e} Q = P^\prime_S = \frac{1}{n} \left(Q – Q_0 \right) + (1 – r) T\\

The result is exactly the same:

P_R – 1/e * Q – T = 1/n * (Q – Q0)

P_R – \frac{1}{e} Q – T = \frac{1}{n} \left(Q – Q_0 \right) \\

I’ll spare you the algebra, but this comes out to:

Q = (PR – T)/(1/n + 1/e) + (Q0)/(1 + n/e)

Q = \frac{P_R – T}{\frac{1}{n} + \frac{1}{e}} + \frac{Q_0}{1 + \frac{n}{e}}

P = (PR – T)/(1+ n/e) – (Q0)/(e + n)

P = \frac{P_R – T}}{1 + \frac{n}{e}} – \frac{Q_0}{e+n} \\

That’s if the market is competitive.

If the market is a monopoly, instead of setting the prices equal, we set the price the landlord receives equal to the marginal revenue—which takes into account the fact that increasing the amount they sell forces them to reduce the price they charge everyone else. Thus, the marginal revenue drops faster than the price as the quantity sold increases.

After a bunch of algebra (and just a dash of calculus), that comes out to these very similar, but not quite identical, equations:

Q = (PR – T)/(1/n + 2/e) + (Q0)/(1+ 2n/e)

Q = \frac{P_R – T}{\frac{1}{n} + \frac{2}{e}} + \frac{Q_0}{1 + \frac{2n}{e}} \\

P = (PR – T)*((1/n + 1/e)/(1/n + 2/e) – (Q0)/(e + 2n)

P = \left( P_R – T\right)\frac{\frac{1}{n} + \frac{1}{e}}{\frac{1}{n} + \frac{2}{e}} – \frac{Q_0}{e+2n} \\

Yes, it changes some 1s into 2s. That by itself accounts for the full effect of monopoly. That’s why I think it’s worthwhile to use the equations; they are deeply elegant and express in a compact form all of the different cases. They look really intimidating right now, but for most of the cases we’ll consider these general equations simplify quite dramatically.

There are several cases to consider.

Land has an extremely high cost to create—for practical purposes, we can consider its supply fixed, that is, perfectly inelastic. If the market is competitive, so that landlords have no market power, then they will simply rent out all the land they have at whatever price the market will bear:

This is like setting n = 0 and T = 0 in the above equations, the competitive ones.

Q = Q0

Q = Q_0 \\

P = PR – Q0/e

P = P_R – \frac{Q_0}{e} \\

If we now introduce a tax, it will fall completely on the landlords, because they have little choice but to rent out all the land they have, and they can only rent it at a price—including tax—that the market will bear.

Now we still have n = 0 but not T = 0.

Q = Q0

Q = Q_0 \\

P = PR – T – Q0/e

P = P_R – T – \frac{Q_0}{e} \\

The consumer surplus will be:

½ (Q)(PR – P – T) = 1/(2e)* Q02

\frac{1}{2}Q(P_R – P – T) = \frac{1}{2e}Q_0^2 \\

Notice how T isn’t in the result. The consumer surplus is unaffected by the tax.

The producer surplus, on the other hand, will be reduced by the tax:

(Q)(P) = (PR – T – Q0/e) Q0 = PR Q0 – 1/e Q02 – TQ0

(Q)(P) = (P_R – T – \frac{Q_0}{e})Q_0 = P_R Q_0 – \frac{1}{e} Q_0^2 – T Q_0 \\

T appears linearly as TQ0, which is the same as the tax revenue. All the money goes directly from the landlord to the government, as we want if our goal is to redistribute wealth without raising rent.

But now suppose that the market is not competitive, and by tacit collusion or regulatory capture the landlords can exert some market power; this is quite likely the case in reality. Actually in reality we’re probably somewhere in between monopoly and competition, either oligopoly or monopolistic competitionwhich I will talk about a good deal more in a later post, I promise.

It could be that demand is still sufficiently high that even with their market power, landlords have an incentive to rent out all their available land, in which case the result will be the same as in the competitive market.

A tax will then fall completely on the landlords as before:

Indeed, in this case it doesn’t really matter that the market is monopolistic; everything is the same as it would be under a competitive market. Notice how if you set n = 0, the monopolistic equations and the competitive equations come out exactly the same. The good news is, this is quite likely our actual situation! So even in the presence of significant market power the land tax can redistribute wealth in just the way we want.

But there are a few other possibilities. One is that demand is not sufficiently high, so that the landlords’ market power causes them to actually hold back some land in order to raise the price:

This will create some of what we call deadweight loss, in which some economic value is wasted. By restricting the land they rent out, the landlords make more profit, but the harm they cause to tenant is created than the profit they gain, so there is value wasted.

Now instead of setting n = 0, we actually set n = infinity. Why? Because the reason that the landlords restrict the land they sell is that their marginal revenue is actually negative beyond that point—they would actually get less money in total if they sold more land. Instead of being bounded by their cost of production (because they have none, the land is there whether they sell it or not), they are bounded by zero. (Once again we’ve hit upon a fundamental concept in economics, particularly macroeconomics, that I don’t have time to talk about today: the zero lower bound.) Thus, they can change quantity all they want (within a certain range) without changing the price, which is equivalent to a supply elasticity of infinity.

Introducing a tax will then exacerbate this deadweight loss (adding DWL2 to the original DWL1), because it provides even more incentive for the landlords to restrict the supply of land:

Q = e/2*(PR – T)

Q = \frac{e}{2} \left(P_R – T\right)\\

P = 1/2*(PR – T)

P = \frac{1}{2} \left(P_R – T\right) \\

The quantity Q0 completely drops out, because it doesn’t matter how much land is available (as long as it’s enough); it only matters how much land it is profitable to rent out.

We can then find the consumer and producer surplus, and see that they are both reduced by the tax. The consumer surplus is as follows:

½ (Q)(PR – 1/2(PR – T)) = e/4*(PR2 – T2)

\frac{1}{2}Q \left( P_R – \frac{1}{2}left( P – T \right) \right) = \frac{e}{4}\left( P_R^2 – T^2 \right) \\

This time, the tax does have an effect on reducing the consumer surplus.

The producer surplus, on the other hand, will be:

(Q)(P) = 1/2*(PR – T)*e/2*(PR – T) = e/4*(PR – T)2

(Q)(P) = \frac{1}{2}\left(P_R – T \right) \frac{e}{2} \left(P_R – T\right) = \frac{e}{4} \left(P_R – T)^2 \\

Notice how it is also reduced by the tax—and no longer in a simple linear way.

The tax revenue is now a function of the demand:

TQ = e/2*T(PR – T)

T Q = \frac{e}{2} T (P_R – T) \\

If you add all these up, you’ll find that the sum is this:

e/2 * (PR^2 – T^2)

\frac{e}{2} \left(P_R^2 – T^2 \right) \\

The sum is actually reduced by an amount equal to e/2*T^2, which is the deadweight loss.

Finally there is an even worse scenario, in which the tax is so large that it actually creates an incentive to restrict land where none previously existed:

Notice, however, that because the supply of land is inelastic the deadweight loss is still relatively small compared to the huge amount of tax revenue.

But actually this isn’t the whole story, because a land tax provides an incentive to get rid of land that you’re not profiting from. If this incentive is strong enough, the monopolistic power of landlords will disappear, as the unused land gets sold to more landholders or to the government. This is a way of avoiding the tax, but it’s one that actually benefits society, so we don’t mind incentivizing it.

Now, let’s compare this to our current system of property taxes, which include the value of buildings. Buildings are expensive to create, but we build them all the time; the supply of buildings is strongly dependent upon the price at which those buildings will sell. This makes for a supply curve that is somewhat elastic.

If the market were competitive and we had no taxes, it would be optimally efficient:

Property taxes create an incentive to produce fewer buildings, and this creates deadweight loss. Notice that this happens even if the market is perfectly competitive:

Since both n and e are finite and nonzero, we’d need to use the whole equations: Since the algebra is such a mess, I don’t see any reason to subject you to it; but suffice it to say, the T does not drop out. Tenants do see their consumer surplus reduced, and the larger the tax the more this is so.

Now, suppose that the market for buildings is monopolistic, as it most likely is. This would create deadweight loss even in the absence of a tax:

Once again, we’d need the full equations, and once again it’s a mess; but the result is, as before, that the tax gets passed on to the tenants in the form of more restricted sales and therefore higher rents.

Because of the finite supply elasticity, there’s no way that the tax can avoid raising the rent. As long as landlords have to pay more taxes when they build more or better buildings, they are going to raise the rent in those buildings accordingly—whether the market is competitive or not.

If the market is indeed monopolistic, there may be ways to bring the rent down: suppose we know what the competitive market price of rent should be, and we can establish rent control to that effect. If we are truly correct about the price to set, this rent control can not only reduce rent, it can actually reduce the deadweight loss:

But if we set the rent control too low, or don’t properly account for the varying cost of different buildings, we can instead introduce a new kind of deadweight loss, by making it too expensive to make new buildings.

In fact, what actually seems to happen is more complicated than that—because otherwise the number of buildings is obviously far too small, rent control is usually set to affect some buildings and not others. So what seems to happen is that the rent market fragments into two markets: One, which is too small, but very good for those few who get the chance to use it; and the other, which is unaffected by the rent control but is more monopolistic and therefore raises prices even further. This is why almost all economists are opposed to rent control (PDF); it doesn’t solve the problem of high rent and simply causes a whole new set of problems.

A land tax with a basic income, on the other hand, would help poor people at least as much as rent control presently does—probably a good deal more—without discouraging the production and maintenance of new apartment buildings.

But now we come to a key point: The land tax must be uniform per hectare.

If it is instead based on the value of the land, then this acts like a finite elasticity of supply; it provides an incentive to reduce the value of your own land in order to avoid the tax. As I showed above, this is particularly pernicious if the market is monopolistic, but even if it is competitive the effect is still there.

One exception I can see is if there are different tiers based on broad classes of land that it’s difficult to switch between, such as “land in Manhattan” versus “land in Brooklyn” or “desert land” versus “forest land”. But even this policy would have to be done very carefully, because any opportunity to substitute can create an opportunity to pass on the tax to someone else—for instance if land taxes are lower in Brooklyn developers are going to move to Brooklyn. Maybe we want that, in which case that is a good policy; but we should be aware of these sorts of additional consequences. The simplest way to avoid all these problems is to simply make the land tax uniform. And given the quantities we’re talking about—less than $3000 per hectare per year—it should be affordable for anyone except the very large landholders we’re trying to distribute wealth from in the first place. The good news is, most economists would probably be on board with this proposal. After all, the neoclassical models themselves say it would be more efficient than our current system of rent control and property taxes—and the idea is at least as old as Adam Smith. Perhaps we can finally change the fact that the rent is too damn high. What if you couldn’t own land? JDN 2457145 EDT 20:49. Today’s post we’re on the socialism scale somewhere near the The Guess Who, but not quite all the way to John Lennon. I’d like to questions one of the fundamental tenets of modern capitalism, but not the basic concept of private ownership itself: What if you couldn’t own land? Many things that you can own were more-or-less straightforwardly created by someone. A car, a computer, a television, a pair of shoes; for today let’s even take for granted intellectual property like books, movies, and songs; at least those things (“things”) were actually made by someone. But land? We’re talking about chunks of the Earth here. They were here billions of years before us, and in all probability will be here billions of years after we’re gone. There’s no need to incentivize its creation; the vast majority of land was already here and did not need to be created. (I do have to say “the vast majority”, because in places like Japan, Hong Kong, and the Netherlands real estate has become so scarce that people do literally build land out into the sea. But this is something like 0.0001% of the world’s land.) What we want to incentivize is land development; we want it to be profitable to build buildings and irrigate deserts, and yes, even cut down forests sometimes (though then there should be a carbon tax with credits for forested land to ensure that there isn’t too much incentive). Yet our current property tax system doesn’t do this very well; if you build bigger buildings, you end up paying more property taxes. Yes, you may also make some profit on the buildings—but it’s risky, and you may not get enough benefit to justify the added property taxes. Moreover, we want to allocate land—we want some way of deciding who is allowed to use what land where and when (and perhaps why). Allowing land to be bought and sold is one way to do that, but it is not the only way. Indeed, land ownership suffers from a couple of truly glaring flaws as an allocation system: 1. It creates self-perpetuating inequality. Because land grows in value over time (due to population growth and urbanization, among other things), those who currently own land end up getting an ever-growing quantity of wealth while those who do not own land do not, and very likely end up having to pay ever-growing rents to the landlords. (I like calling them “landlords”; it really drives home the fact that our landholding system is still basically the same as it was under feudalism.) In fact, the recent rise in the share of income that goes to owners of capital rather than workers is almost entirely attributable to the rise in the price of real estate. As that post rightly recognizes, this does nothing to undermine Piketty’s central message of rising inequality due to capital income (pace The Washington Post); it merely tells us to focus on real estate instead of other forms of capital. 2. It has no non-arbitrary allocation. If we want to decide who owns a car, we can ask questions like, “Who built it? Did someone buy it from them? Did they pay a fair price?”; if we want to decide who owns a book, we can ask questions like, “Who wrote it? Did they sell it to a publisher? What was the royalty rate?” That is, there is a clear original owner, and there is a sense of whether the transfer of ownership can be considered fair. But if we want to decide who owns a chunk of land, basically all we can ask is, “What does the deed say?” The owner is the owner because they are the owner; there’s no sense in which that ownership is fair. We certainly can’t go back to the original creation of the land, because that was due to natural forces gigayears ago. If we keep tracing the ownership backward, we will eventually end up with some guy (almost certainly a man, a White man in fact) with a gun who pointed that gun at other people and said, “This is mine.” This is true of basically all the land in the world (aside from those little bits of Japan and such); it was already there, and the only reason someone got to own it was because they said so and had a bigger gun. And a flag, perhaps: “Do you have a flag?” I suppose, in theory at least, there are a few ways of allocating land which seem less arbitrary: One would be to give everyone an equal amount. But this is practically very difficult: What do you do when the population changes? If you have 2% annual population growth, do you carve off 2% of everybody’s lot each year? Another would be to let people squat land, and automatically own the land that they live on—but again practical difficulties quickly become enormous. In any case, these two methods bear about as much resemblance to our actual allocation of land as a squirrel does to a Tyrannosaurus. So, what else might we use? The system that makes the most sense to me is that we would own all land as a society. In practical terms this would mean that all land is Federal land, and if you want to use it for something, you need to pay rent to the government. There are many different ways the government could set the rent, but the most sensible might be to charge a flat rate per hectare regardless of where the land is or what it’s being used for, because that would maximize the incentive to develop the land. It would also make the rent fall entirely on the landowner, because the rent would be perfectly inelasticmeaning that you can’t change the quantity you make based on the price, because you aren’t making it; it’s just already sitting there. Of course, this idea is obviously politically impossible in our current environment—or indeed any foreseeable political environment. I’m just fantasizing here, right? Well, not quite. There is one thing we could do that would be economically quite similar to government-only land ownership; it’s called a land tax. The idea is incredibly simple: you just collect a flat tax per hectare of land. Economists have known that a land tax is efficient at providing revenue and reducing inequality since at least Adam Smith. So maybe ownership of land isn’t actually foundational to capitalism, after all; maybe we’ve just never fully gotten over feudalism. (I basically agree with Adam Smith, and for doing so I am often called a socialist.) The beautiful thing about a land tax is that it has a tax incidence in which the owners of the land end up bearing the full brunt of the tax. Tax incidence is something it’s very important to understand; it would be on my list of the top ten economic principles that people should learn. We often have fierce political debates over who will actually write the check: Should employers pay the health insurance premium, or should employees? Will buyers pay sales tax, or sellers? Should we tax corporate profits or personal capital gains? Please understand that I am not exaggerating when I say that these sorts of questions are totally irrelevant. It simply does not matter who actually writes the check; what matters is who bears the cost. Making the employer pay the health insurance premium doesn’t make the slightest difference if all they’re going to do is cut wages by the exact same amount. You can see the irrelevance of the fact that sellers pay sales tax every time you walk into a store—you always end up paying the price plus the tax, don’t you? (I found that the base price of most items was the same between Long Beach and Ann Arbor, but my total expenditure was always 3% more because of the 9% sales tax versus the 6%.) How do we determine who actually pays the tax? It depends on the elasticity—how easily can you change your behavior in order to avoid the tax? Can you find a different job because the health insurance premiums are too high? No? Then you’re probably paying that premium, even if your employer writes the check. If you can find a new job whenever you want, your employer might have to pay it for you even if you write the check. The incidence of corporate taxes and taxes on capital gains are even more complicated, because it could affect the behavior of corporations in many different ways; indeed, many economists argue that the corporate tax simply results in higher unemployment or lower wages for workers. I don’t think that’s actually true, but I honestly can’t rule it out completely, precisely because corporate taxes are so complicated. You need to know all sorts of things about the structure of stock markets, and the freedom of trade, and the mobility of immigration… it’s a complete and total mess. It’s because of tax incidence that a land tax makes so much sense; there’s no way for the landowner to escape it, other than giving up the land entirely. In particular, they can’t charge more for rent without being out-competed (unless landowners are really good at colluding—which might be true for large developers, but not individual landlords). Their elasticity is so low that they’re forced to bear the full cost of the tax. If the land tax were high enough, it could eliminate the automatic growth in wealth that comes from holding land, and thereby reducing long-run inequality dramatically. The revenue could be used for my other favorite fiscal policy, the basic income—and real estate is a big enough part of our nation’s wealth that it’s actually entirely realistic to fund an$8,000 per person per year basic income entirely on land tax revenue. The total value of US land is about $14 trillion, and an$8,000 basic income for 320 million people would cost about $2.6 trillion; that’s only 19%. You’d actually want to make it a flat tax per hectare, so how much would that be? Well, 60% of US land is privately owned at present (no sense taxing the land the government already owns), and total US land area is about 9 million square kilometers, so to raise$2.5 trillion you’d need a tax of $289,000 per square kilometer, or$2,890 per hectare. If you own a hectare—which is bigger than most single-family lots—you’d only pay $2,890 per year in land tax, well within what most middle-class families could handle. But if you own 290,000 acres like Jeff Bezos, (that’s 117,000 hectares) you’re paying$338 million per year. Since Jeff Bezos has about $38 billion in net wealth, he can actually afford to pay that ($338 million per year is about one-tenth of what Jeff Bezos makes automatically on dividends), though he might consider selling off some of the land to avoid the taxes, which is exactly the sort of incentive we wanted to create.

Indeed, when I contemplate this policy I’m struck by the fact that it has basically no downside—usually in public policy you’re forced to make hard compromises and tradeoffs, but a land tax plus basic income is a system that carries almost no downsides at all. It won’t disincentivize investment, it won’t disincentivize working, it will dramatically reduce inequality, it will save the government a great deal of money on social welfare spending, and best of all it will eliminate poverty immediately and forever. The only people it would hurt at all are extremely rich, and they wouldn’t even be hurt very much, while it would benefit millions of people including some of the most needy.

Why aren’t we doing this already!?