# Where is the money going in academia?

Feb 19 JDN 2459995

A quandary for you:

My salary is £41,000.

Annual tuition for a full-time full-fee student in my department is £23,000.

I teach roughly the equivalent of one full-time course (about 1/2 of one and 1/4 of two others; this is typically counted as “teaching 3 courses”, but if I used that figure, it would underestimate the number of faculty needed).

Each student takes about 5 or 6 courses at a time.

Why do I have 200 students?

If you multiply this out, the 200 students I teach, divided by the 6 instructors they have at one time, times the £23,000 they are paying… I should be bringing in over £760,000 for the university. Why am I paid only 5% of that?

Granted, there are other costs a university must bear aside from paying instructors. There are facilities, and administration, and services. And most of my students are not full-fee paying; that £23,000 figure really only applies to international students.

Students from Scotland pay only £1,820, but there aren’t very many of them, and public funding is supposed to make up that difference. Even students from the rest of the UK pay £9,250. And surely the average tuition paid has got to be close to that? Yet if we multiply that out, £9,000 times 200 divided by 6, we’re still looking at £300,000. So I’m still getting only 14%.

Where is the rest going?

This isn’t specific to my university by any means. It seems to be a global phenomenon. The best data on this seems to be from the US.

According to salary.com, the median salary for an adjunct professor in the US is about \$63,000. This actually sounds high, given what I’ve heard from other entry-level faculty. But okay, let’s take that as our figure. (My pay is below this average, though how much depends upon the strength of the pound against the dollar. Currently the pound is weak, so quite a bit.)

This means that an adjunct professor in the US with 200 students takes in \$760,000 but receives \$63,000. Where does that other \$700,000 go?

If you think that it’s just a matter of paying for buildings, service staff, and other costs of running a university, consider this: It wasn’t always this way.

Since 1970, inflation-adjusted salaries for US academic faculty at public universities have risen a paltry 3.1%. In other words, basically not at all.

This is considerably slower than the growth of real median household income, which has risen almost 40% in that same time.

Over the same interval, nominal tuition has risen by over 2000%; adjusted for inflation, this is a still-staggering increase of 250%.

In other words, over the last 50 years, college has gotten three times as expensive, but faculty are still paid basically the same. Where is all this extra money going?

Part of the explanation is that public funding for colleges has fallen over time, and higher tuition partly makes up the difference. But private school tuition has risen just as fast, and their faculty salaries haven’t kept up either.

In their annual budget report, the University of Edinburgh proudly declares that their income increased by 9% last year. Let me assure you, my salary did not. (In fact, inflation-adjusted, my salary went down.) And their EBITDA—earnings before interest, taxes, depreciation, and amortization—was £168 million. Of that, £92 million was lost to interest and depreciation, but they don’t pay taxes at all, so their real net income was about £76 million. In the report, they include price changes of their endowment and pension funds to try to make this number look smaller, ending up with only £37 million, but that’s basically fiction; these are just stock market price drops, and they will bounce back.

Using similar financial alchemy, they’ve been trying to cut our pensions lately, because they say they “are too expensive” (because the stock market went down—nevermind that it’ll bounce back in a year or two). Fortunately, the unions are fighting this pretty hard. I wish they’d also fight harder to make them put people like me on the tenure track.

Had that £76 million been distributed evenly between all 5,000 of us faculty, we’d each get an extra £15,600.

Well, then, that solves part of the mystery in perhaps the most obvious, corrupt way possible: They’re literally just hoarding it.

And Edinburgh is far from the worst offender here. No, that would be Harvard, who are sitting on over \$50 billion in assets. Since they have 21,000 students, that is over \$2 million per student. With even a moderate return on its endowment, Harvard wouldn’t need to charge tuition at all.

But even then, raising my salary to £56,000 wouldn’t explain why I need to teach 200 students. Even that is still only 19% of the £300,000 those students are bringing in. But hey, then at least the primary service for which those students are here for might actually account for one-fifth of what they’re paying!

Since 1970, that same time interval when faculty salaries were rising a pitiful 3% and tuition was rising a staggering 250%, how much did chancellors’ salaries increase? Over 60%.

Of course, the number of administrators is not fixed. You might imagine that with technology allowing us to automate a lot of administrative tasks, the number of administrators could be reduced over time. If that’s what you thought happened, you would be very, very wrong. The number of university administrators in the US has more than doubled since the 1980s. This is far faster growth than the number of students—and quite frankly, why should the number of administrators even grow with the number of students? There is a clear economy of scale here, yet it doesn’t seem to matter.

Combine those two facts: 60% higher pay times twice as many administrators means that universities now spend at least 3 times as much on administration as they did 50 years ago. (Why, that’s just about the proportional increase in tuition! Coincidence? I think not.)

Edinburgh isn’t even so bad in this regard. They have 6,000 administrative staff versus 5,000 faculty. If that already sounds crazy—more admins than instructors?—consider that the University of Michigan has 7,000 faculty but 19,000 administrators.

Michigan is hardly exceptional in this regard: Illinois UC has 2,500 faculty but nearly 8,000 administrators, while Ohio State has 7,300 faculty and 27,000 administrators. UCLA is even worse, with only 4,000 faculty but 26,000 administrators—a ratio of 6 to 1. It’s not the UC system in general, though: My (other?) alma mater of UC Irvine somehow supports 5,600 faculty with only 6,400 administrators. Yes, that’s right; compared to UCLA, UCI has 40% more faculty but 76% fewer administrators. (As far as students? UCLA has 47,000 while UCI has 36,000.)

At last, I think we’ve solved the mystery! Where is all the money in academia going? Administrators.

They keep hiring more and more of them, and paying them higher and higher salaries. Meanwhile, they stop hiring tenure-track faculty and replace them with adjuncts that they can get away with paying less. And then, whatever they manage to save that way, they just squirrel away into the endowment.

A common right-wing talking point is that more institutions should be “run like a business”. Well, universities seem to have taken that to heart. Overpay your managers, underpay your actual workers, and pocket the savings.

# Why do we need “publish or perish”?

June 23 JDN 2458658

This question may seem a bit self-serving, coming from a grad student who is struggling to get his first paper published in a peer-reviewed journal. But given the deep structural flaws in the academic publishing system, I think it’s worth taking a step back to ask just what peer-reviewed journals are supposed to be accomplishing.

The argument is often made that research journals are a way of sharing knowledge. If this is their goal, they have utterly and totally failed. Most papers are read by only a handful of people. When scientists want to learn about the research their colleagues are doing, they don’t read papers; they go to conferences to listen to presentations and look at posters. The way papers are written, they are often all but incomprehensible to anyone outside a very narrow subfield. When published by proprietary journals, papers are often hidden behind paywalls and accessible only through universities. As a knowledge-sharing mechanism, the peer-reviewed journal is a complete failure.

But academic publishing serves another function, which in practice is its only real function: Peer-reviewed publications are a method of evaluation. They are a way of deciding which researchers are good enough to be hired, get tenure, and receive grants. Having peer-reviewed publications—particularly in “top journals”, however that is defined within a given field—is a key metric that universities and grant agencies use to decide which researchers are worth spending on. Indeed, in some cases it seems to be utterly decisive.

We should be honest about this: This is an absolutely necessary function. It is uncomfortable to think about the fact that we must exclude a large proportion of competent, qualified people from being hired or getting tenure in academia, but given the large number of candidates and the small amounts of funding available, this is inevitable. We can’t hire everyone who would probably be good enough. We can only hire a few, and it makes sense to want those few to be the best. (Also, don’t fret too much: Even if you don’t make it into academia, getting a PhD is still a profitable investment. Economists and natural scientists do the best, unsurprisingly; but even humanities PhDs are still generally worth it. Median annual earnings of \$77,000 is nothing to sneeze at: US median household income is only about \$60,000. Humanities graduates only seem poor in relation to STEM or professional graduates; they’re still rich compared to everyone else.)

But I think it’s worth asking whether the peer review system is actually selecting the best researchers, or even the best research. Note that these are not the same question: The best research done in graduate school might not necessarily reflect the best long-run career trajectory for a researcher. A lot of very important, very difficult questions in science are just not the sort of thing you can get a convincing answer to in a couple of years, and so someone who wants to work on the really big problems may actually have a harder time getting published in graduate school or as a junior faculty member, even though ultimately work on the big problems is what’s most important for society. But I’m sure there’s a positive correlation overall: The kind of person who is going to do better research later is probably, other things equal, going to do better research right now.

Yet even accepting the fact that all we have to go on in assessing what you’ll eventually do is what you have already done, it’s not clear that the process of publishing in a peer-reviewed journal is a particularly good method of assessing the quality of research. Some really terrible research has gotten published in journals—I’m gonna pick on Daryl Bem, because he’s the worst—and a lot of really good research never made it into journals and is languishing on old computer hard drives. (The term “file drawer problem” is about 40 years obsolete; though to be fair, it was in fact coined about 40 years ago.)

That by itself doesn’t actually prove that journals are a bad mechanism. Even a good mechanism, applied to a difficult problem, is going to make some errors. But there are a lot of things about academic publishing, at least as currently constituted, that obviously don’t seem like a good mechanism, such as for-profit publishers, unpaid reviewiers, lack of double-blinded review, and above all, the obsession with “statistical significance” that leads to p-hacking.

Each of these problems I’ve listed has a simple fix (though whether the powers that be actually are willing to implement it is a different question: Questions of policy are often much easier to solve than problems of politics). But maybe we should ask whether the system is even worth fixing, or if it should simply be replaced entirely.

While we’re at it, let’s talk about the academic tenure system, because the peer-review system is largely an evaluation mechanism for the academic tenure system. Publishing in top journals is what decides whether you get tenure. The problem with “Publish or perish” isn’t the “publish”; it’s the perish”. Do we even need an academic tenure system?

The usual argument for academic tenure concerns academic freedom: Tenured professors have job security, so they can afford to say things that may be controversial or embarrassing to the university. But the way the tenure system works is that you only have this job security after going through a long and painful gauntlet of job insecurity. You have to spend several years prostrating yourself to the elders of your field before you can get inducted into their ranks and finally be secure.

Of course, job insecurity is the norm, particularly in the United States: Most employment in the US is “at-will”, meaning essentially that your employer can fire you for any reason at any time. There are specifically illegal reasons for firing (like gender, race, and religion); but it’s extremely hard to prove wrongful termination when all the employer needs to say is, “They didn’t do a good job” or “They weren’t a team player”. So I can understand how it must feel strange for a private-sector worker who could be fired at any time to see academics complain about the rigors of the tenure system.

But there are some important differences here: The academic job market is not nearly as competitive as the private sector job market. There simply aren’t that many prestigious universities, and within each university there are only a small number of positions to fill. As a result, universities have an enormous amount of power over their faculty, which is why they can get away with paying adjuncts salaries that amount to less than minimum wage. (People with graduate degrees! Making less than minimum wage!) At least in most private-sector labor markets in the US, the market is competitive enough that if you get fired, you can probably get hired again somewhere else. In academia that’s not so clear.

I think what bothers me the most about the tenure system is the hierarchical structure: There is a very sharp divide between those who have tenure, those who don’t have it but can get it (“tenure-track”), and those who can’t get it. The lines between professor, associate professor, assistant professor, lecturer, and adjunct are quite sharp. The higher up you are, the more job security you have, the more money you make, and generally the better your working conditions are overall. Much like what makes graduate school so stressful, there are a series of high-stakes checkpoints you need to get through in order to rise in the ranks. And several of those checkpoints are based largely, if not entirely, on publication in peer-reviewed journals.

In fact, we are probably stressing ourselves out more than we need to. I certainly did for my advancement to candidacy; I spent two weeks at such a high stress level I was getting migraines every single day (clearly on the wrong side of the Yerkes-Dodson curve), only to completely breeze through the exam.

I think I might need to put this up on a wall somewhere to remind myself:

Most grad students complete their degrees, and most assistant professors get tenure.

The real filters are admissions and hiring: Most applications to grad school are rejected (though probably most graduate students are ultimately accepted somewhere—I couldn’t find any good data on that in a quick search), and most PhD graduates do not get hired on the tenure track. But if you can make it through those two gauntlets, you can probably make it through the rest.

In our current system, publications are a way to filter people, because the number of people who want to become professors is much higher than the number of professor positions available. But as an economist, this raises a very big question: Why aren’t salaries falling?

You see, that’s how markets are supposed to work: When supply exceeds demand, the price is supposed to fall until the market clears. Lower salaries would both open up more slots at universities (you can hire more faculty with the same level of funding) and shift some candidates into other careers (if you can get paid a lot better elsewhere, academia may not seem so attractive). Eventually there should be a salary point at which demand equals supply. So why aren’t we reaching it?

Well, it comes back to that tenure system. We can’t lower the salaries of tenured faculty, not without a total upheaval of the current system. So instead what actually happens is that universities switch to using adjuncts, who have very low salaries indeed. If there were no tenure, would all faculty get paid like adjuncts? No, they wouldn’tbecause universities would have all that money they’re currently paying to tenured faculty, and all the talent currently locked up in tenured positions would be on the market, driving up the prevailing salary. What would happen if we eliminated tenure is not that all salaries would fall to adjunct level; rather, salaries would all adjust to some intermediate level between what adjuncts currently make and what tenured professors currently make.

What would the new salary be, exactly? That would require a detailed model of the supply and demand elasticities, so I can’t tell you without starting a whole new research paper. But a back-of-the-envelope calculation would suggest something like the overall current median faculty salary. This suggests a median salary somewhere around \$75,000. This is a lot less than some professors make, but it’s also a lot more than what adjuncts make, and it’s a pretty good living overall.

If the salary for professors fell, the pool of candidates would decrease, and we wouldn’t need such harsh filtering mechanisms. We might decide we don’t need a strict evaluation system at all, and since the knowledge-sharing function of journals is much better served by other means, we could probably get rid of them altogether.

Of course, who am I kidding? That’s not going to happen. The people who make these rules succeeded in the current system. They are the ones who stand to lose high salaries and job security under a reform policy. They like things just the way they are.

# Why “marginal productivity” is no excuse for inequality

May 28, JDN 2457902

In most neoclassical models, workers are paid according to their marginal productivity—the additional (market) value of goods that a firm is able to produce by hiring that worker. This is often used as an excuse for inequality: If someone can produce more, why shouldn’t they be paid more?

The most extreme example of this is people like Maura Pennington writing for Forbes about how poor people just need to get off their butts and “do something”; but there is a whole literature in mainstream economics, particularly “optimal tax theory”, arguing based on marginal productivity that we should tax the very richest people the least and never tax capital income. The Chamley-Judd Theorem famously “shows” (by making heroic assumptions) that taxing capital just makes everyone worse off because it reduces everyone’s productivity.

The biggest reason this is wrong is that there are many, many reasons why someone would have a higher income without being any more productive. They could inherit wealth from their ancestors and get a return on that wealth; they could have a monopoly or some other form of market power; they could use bribery and corruption to tilt government policy in their favor. Indeed, most of the top 0.01% do literally all of these things.

But even if you assume that pay is related to productivity in competitive markets, the argument is not nearly as strong as it may at first appear. Here I have a simple little model to illustrate this.

Suppose there are 10 firms and 10 workers. Suppose that firm 1 has 1 unit of effective capital (capital adjusted for productivity), firm 2 has 2 units, and so on up to firm 10 which has 10 units. And suppose that worker 1 has 1 unit of so-called “human capital”, representing their overall level of skills and education, worker 2 has 2 units, and so on up to worker 10 with 10 units. Suppose each firm only needs one worker, so this is a matching problem.

Furthermore, suppose that productivity is equal to capital times human capital: That is, if firm 2 hired worker 7, they would make 2*7 = \$14 of output.

What will happen in this market if it converges to equilibrium?

Well, first of all, the most productive firm is going to hire the most productive worker—so firm 10 will hire worker 10 and produce \$100 of output. What wage will they pay? Well, they need a wage that is high enough to keep worker 10 from trying to go elsewhere. They should therefore pay a wage of \$90—the next-highest firm productivity times the worker’s productivity. That’s the highest wage any other firm could credibly offer; so if they pay this wage, worker 10 will not have any reason to leave.

Now the problem has been reduced to matching 9 firms to 9 workers. Firm 9 will hire worker 9, making \$81 of output, and paying \$72 in wages.

And so on, until worker 1 at firm 1 produces \$1 and receives… \$0. Because there is no way for worker 1 to threaten to leave, in this model they actually get nothing. If I assume there’s some sort of social welfare system providing say \$0.50, then at least worker 1 can get that \$0.50 by threatening to leave and go on welfare. (This, by the way, is probably the real reason firms hate social welfare spending; it gives their workers more bargaining power and raises wages.) Or maybe they have to pay that \$0.50 just to keep the worker from starving to death.

What does inequality look like in this society?
Well, the most-productive firm only has 10 times as much capital as the least-productive firm, and the most-educated worker only has 10 times as much skill as the least-educated worker, so we might think that incomes would vary only by a factor of 10.

But in fact they vary by a factor of over 100.

The richest worker makes \$90, while the poorest worker makes \$0.50. That’s a ratio of 180. (Still lower than the ratio of the average CEO to their average employee in the US, by the way.) The worker is 10 times as productive, but they receive 180 times as much income.

The firm profits vary along a more reasonable scale in this case; firm 1 makes a profit of \$0.50 while firm 10 makes a profit of \$10. Indeed, except for firm 1, firm n always makes a profit of \$n. So that’s very nearly a linear scaling in productivity.

Where did this result come from? Why is it so different from the usual assumptions? All I did was change one thing: I allowed for increasing returns to scale.

If you make the usual assumption of constant returns to scale, this result can’t happen. Multiplying all the inputs by 10 should just multiply the output by 10, by assumption—since that is the definition of constant returns to scale.

But if you look at the structure of real-world incomes, it’s pretty obvious that we don’t have constant returns to scale.

If we had constant returns to scale, we should expect that wages for the same person should only vary slightly if that person were to work in different places. In particular, to have a 2-fold increase in wage for the same worker you’d need more than a 2-fold increase in capital.

This is a bit counter-intuitive, so let me explain a bit further. If a 2-fold increase in capital results in a 2-fold increase in wage for a given worker, that’s increasing returns to scale—indeed, it’s precisely the production function I assumed above.
If you had constant returns to scale, a 2-fold increase in wage would require something like an 8-fold increase in capital. This is because you should get a 2-fold increase in total production by doubling everything—capital, labor, human capital, whatever else. So doubling capital by itself should produce a much weaker effect. For technical reasons I’d rather not get into at the moment, usually it’s assumed that production is approximately proportional to capital to the one-third power—so to double production you need to multiply capital by 2^3 = 8.

I wasn’t able to quickly find really good data on wages for the same workers across different countries, but this should at least give a rough idea. In Mumbai, the minimum monthly wage for a full-time worker is about \$80. In Shanghai, it is about \$250. If you multiply out the US federal minimum wage of \$7.25 per hour by 40 hours by 4 weeks, that comes to \$1160 per month.

Of course, these are not the same workers. Even an “unskilled” worker in the US has a lot more education and training than a minimum-wage worker in India or China. But it’s not that much more. Maybe if we normalize India to 1, China is 3 and the US is 10.

Likewise, these are not the same jobs. Even a minimum wage job in the US is much more capital-intensive and uses much higher technology than most jobs in India or China. But it’s not that much more. Again let’s say India is 1, China is 3 and the US is 10.

If we had constant returns to scale, what should the wages be? Well, for India at productivity 1, the wage is \$80. So for China at productivity 3, the wage should be \$240—it’s actually \$250, close enough for this rough approximation. But the US wage should be \$800—and it is in fact \$1160, 45% larger than we would expect by constant returns to scale.

Let’s try comparing within a particular industry, where the differences in skill and technology should be far smaller. The median salary for a software engineer in India is about 430,000 INR, which comes to about \$6,700. If that sounds rather low for a software engineer, you’re probably more accustomed to the figure for US software engineers, which is \$74,000. That is a factor of 11 to 1. For the same job. Maybe US software engineers are better than Indian software engineers—but are they that much better? Yes, you can adjust for purchasing power and shrink the gap: Prices in the US are about 4 times as high as those in India, so the real gap might be 3 to 1. But these huge price differences themselves need to be explained somehow, and even 3 to 1 for the same job in the same industry is still probably too large to explain by differences in either capital or education, unless you allow for increasing returns to scale.

In most industries, we probably don’t have quite as much increasing returns to scale as I assumed in my simple model. Workers in the US don’t make 100 times as much as workers in India, despite plausibly having both 10 times as much physical capital and 10 times as much human capital.

But in some industries, this model might not even be enough! The most successful authors and filmmakers, for example, make literally thousands of times as much money as the average author or filmmaker in their own country. J.K. Rowling has almost \$1 billion from writing the Harry Potter series; this is despite having literally the same amount of physical capital and probably not much more human capital than the average author in the UK who makes only about 11,000 GBP—which is about \$14,000. Harry Potter and the Philosopher’s Stone is now almost exactly 20 years old, which means that Rowling made an average of \$50 million per year, some 3500 times as much as the average British author. Is she better than the average British author? Sure. Is she three thousand times better? I don’t think so. And we can’t even make the argument that she has more capital and technology to work with, because she doesn’t! They’re typing on the same laptops and using the same printing presses. Either the return on human capital for British authors is astronomical, or something other than marginal productivity is at work here—and either way, we don’t have anything close to constant returns to scale.

What can we take away from this? Well, if we don’t have constant returns to scale, then even if wage rates are proportional to marginal productivity, they aren’t proportional to the component of marginal productivity that you yourself bring. The same software developer makes more at Microsoft than at some Indian software company, the same doctor makes more at a US hospital than a hospital in China, the same college professor makes more at Harvard than at a community college, and J.K. Rowling makes three thousand times as much as the average British author—therefore we can’t speak of marginal productivity as inhering in you as an individual. It is an emergent property of a production process that includes you as a part. So even if you’re entirely being paid according to “your” productivity, it’s not really your productivity—it’s the productivity of the production process you’re involved in. A myriad of other factors had to snap into place to make your productivity what it is, most of which you had no control over. So in what sense, then, can we say you earned your higher pay?

Moreover, this problem becomes most acute precisely when incomes diverge the most. The differential in wages between two welders at the same auto plant may well be largely due to their relative skill at welding. But there’s absolutely no way that the top athletes, authors, filmmakers, CEOs, or hedge fund managers could possibly make the incomes they do by being individually that much more productive.

# 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.