Tax plan possibilities

Mar 26, JDN 2457839

Recently President Trump (that phrase may never quite feel right) began presenting his new tax plan. To be honest, it’s not as ridiculous as I had imagined it might be. I mean, it’s still not very good, but it’s probably better than Reagan’s tax plan his last year in office, and it’s not nearly as absurd as the half-baked plan Trump originally proposed during the campaign.

But it got me thinking about the incredible untapped potential of our tax system—the things we could achieve as a nation, if we were willing to really commit to them and raise taxes accordingly.

A few years back I proposed a progressive tax system based upon logarithmic utility. I now have a catchy name for that tax proposal; I call it the logtax. It depends on two parameters—a poverty level, at which the tax rate goes to zero; and what I like to call a metarate—the fundamental rate that sets all the actual tax rates by the formula.

For the poverty level, I suggest we use the highest 2-household poverty level set by the Department of Health and Human Services: Because of Alaska’s high prices, that’s the Alaska poverty level, and the resulting figure is $20,290—let’s round to $20,000.

I would actually prefer to calculate taxes on an individual basis—I see no reason to incentivize particular household arrangements—but as current taxes are calculated on a household basis, I’m going to use that for now.

The metarate can be varied, and in the plans below I will compare different options for the metarate.

I will compare six different tax plans:

  1. Our existing tax plan, set under the Obama administration
  2. Trump’s proposed tax plan
  3. A flat rate of 30% with a basic income of $12,000, replacing welfare programs and Medicaid
  4. A flat rate of 40% with a basic income of $15,000, replacing welfare programs and Medicaid
  5. A logtax with a metarate of 20%, all spending intact
  6. A logtax with a metarate of 25% and a basic income of $12,000, replacing welfare programs and Medicaid
  7. A logtax with a metarate of 35% and a basic income of $15,000, cutting military spending by 50% and expanding Medicare to the entire population while eliminating Medicare payroll taxes

To do a proper comparison, I need estimates of the income distribution in the United States, in order to properly estimate the revenue from each type of tax. For that I used US Census data for most of the income data, supplementing with the World Top Incomes database for the very highest income brackets. The household data is broken up into brackets of $5,000 and only goes up to $250,000, so it’s a rough approximation to use the average household income for each bracket, but it’s all I’ve got.

The current brackets are 10%, 15%, 25%, 28%, 33%, 35%, and 39.6%. These are actually marginal rates, not average rates, which makes the calculation a lot more complicated. I did it properly though; for example, when you start paying the marginal rate of 28%, your average rate is really only 20.4%.

Worst of all, I used static scoring—that is, I ignored the Laffer Effect by which increasing taxes changes incentives and can change pre-tax incomes. To really do this analysis properly, one should use dynamic scoring, taking these effects into account—but proper dynamic scoring is an enormous undertaking, and this is a blog post, not my dissertation.

Still, I was able to get pretty close to the true figures. The actual federal budget shows total revenue net of payroll taxes to be $2.397 trillion, whereas I estimated $2.326 trillion; the true deficit is $608 billion and I estimated $682 billion.

Under Trump’s tax plan, almost all rates are cut. He also plans to remove some deductions, but all reports I could find on the plan were vague as to which ones, and with data this coarse it’s very hard to get any good figures on deduction amounts anyway. I also want to give him credit where it’s due: It was a lot easier to calculate the tax rates under Trump’s plan (but still harder than under mine…). But in general what I found was the following:

Almost everyone pays less income tax under Trump’s plan, by generally about 4-5% of their income. The poor benefit less or are slightly harmed; the rich benefit a bit more.

For example, a household in poverty making $12,300 would pay $1,384 currently, but $1,478 under Trump’s plan, losing $94 or 0.8% of their income. An average household making $52,000 would pay $8,768 currently but only $6,238 under Trump’s plan, saving $2,530 or about 4.8% of their income. A household making $152,000 would pay $35,580 currently but only $28,235 under Trump’s plan, saving $7,345 or again about 4.8%. A top 1% household making $781,000 would pay $265,625 currently, but only $230,158 under Trump’s plan, saving $35,467 or about 4.5%. A top 0.1% household making $2,037,000 would pay $762,656 currently, but only $644,350 under Trump’s plan, saving $118,306 or 5.8% of their income. A top 0.01% household making $9,936,000 would pay $3,890,736 currently, but only $3,251,083 under Trump’s plan, saving $639,653 or 6.4% of their income.

Because taxes are cut across the board, Trump’s plan would raise less revenue. My static scoring will exaggerate this effect, but only moderately; my estimate says we would lose over $470 billion in annual revenue, while the true figure might be $300 billion. In any case, Trump will definitely increase the deficit substantially unless he finds a way to cut an awful lot of spending elsewhere—and his pet $54 billion increase to the military isn’t helping in that regard. My estimate of the new deficit under Trump’s plan is $1.155 trillion—definitely not the sort of deficit you should be running during a peacetime economic expansion.

Let’s see what we might have done instead.

If we value simplicity and ease of calculation, it’s hard to beat a flat tax plus basic income. With a flat tax of 30% and a basic income of $12,000 per household, the poor do much better off because of the basic income, while the rich do a little better because of the flat tax, and the middle class feels about the same because the two effects largely cancel. Calculating your tax liability now couldn’t be easier; multiply your income by 3, remove a zero—that’s what you owe in taxes. And how much do you get in basic income? The same as everyone else, $12,000.

Using the same comparison households: The poor household making $12,300 would now receive $8,305—increasing their income by $9,689 or 78.8% relative to the current system. The middle-class household making $52,000 would pay $3,596, saving $5,172 or 10% of their income. The upper-middle-class household making $152,000 would now pay $33,582, saving only $1998 or 1.3% of their income. The top 1% household making $782,000 would pay $234,461, saving $31,164 or 4.0%. The top 0.1% household making $2,037,000 would pay $611,000, saving $151,656 or 7.4%. Finally, the top 0.01% household making $9,936,000 would pay $2,980,757, saving $910,000 or 9.1%.

Thus, like Trump’s plan, the tax cut almost across the board results in less revenue. However, because of the basic income, we can now justify cutting a lot of spending on social welfare programs. I estimated we could reasonably save about $630 billion by cutting Medicaid and other social welfare programs, while still not making poor people worse off because of the basic income. The resulting estimated deficit comes in at $1.085 trillion, which is still too large—but less than what Trump is proposing.

If I raise the flat rate to 40%—just as easy to calculate—I can bring that deficit down, even if I raise the basic income to $15,000 to compensate. The poverty household now receives $10,073, and the other representative households pay $5,974; $45,776; $297,615; $799,666; and $3,959,343 respectively. This means that the poor are again much better off, the middle class are about the same, and the rich are now substantially worse off. But what’s our deficit now? $180 billion—that’s about 1% of GDP, the sort of thing you can maintain indefinitely with a strong currency.

Can we do better than this? I think we can, with my logtax.

I confess that the logtax is not quite as easy to calculate as the flat tax. It does require taking exponents, and you can’t do it in your head. But it’s actually still easier than the current system, because there are no brackets to keep track of, no discontinuous shifts in the marginal rate. It is continuously progressive for all incomes, and the same formula can be used for all incomes from zero to infinity.
The simplest plan just replaces the income tax with a logtax of 20%. The poor household now receives $1,254, just from the automatic calculation of the tax—no basic income was added. The middle-class household pays $9,041, slightly more than what they are currently paying. Above that, people start paying more for sure: $50,655; $406,076; $1,228,795; and $7,065,274 respectively.

This system is obviously more progressive, but does it raise sufficient revenue? Why, as a matter of fact it removes the deficit entirely. The model estimates that the budget would now be at surplus of $110 billion. This is probably too optimistic; under dynamic scoring the distortions are probably going to cut the revenue a little. But it would almost certainly reduce the deficit, and very likely eliminate it altogether—without any changes in spending.

The next logtax plan adds a basic income of $12,000. To cover this, I raised the metarate to 25%. Now the poor household is receiving $11,413, the middle-class household is paying a mere $1,115, and the other households are paying $50,144; $458,140; $1,384,475; and $7,819,932 respectively. That top 0.01% household isn’t going to be happy, as they are now paying 78% of their income where in our current system they would pay only 39%. But their after-tax income is still over $2 million.

How does the budget look now? As with the flat tax plan, we can save about $630 billion by cutting redundant social welfare programs. So we are once again looking at a surplus, this time of about $63 billion. Again, the dynamic scoring might show some deficit, but definitely not a large one.

Finally, what if I raise the basic income to $15,000 and raise the metarate to 35%? The poor household now receives $14,186, while the median household pays $2,383. The richer households of course foot the bill, paying $64,180; $551,031; $1,618,703; and $8,790,124 respectively. Oh no, the top 0.01% household will have to make do with only $1.2 million; how will they survive!?

This raises enough revenue that it allows me to do some even more exciting things. With a $15,000 basic income, I can eliminate social welfare programs for sure. But then I can also cut military spending, say in half—still leaving us the largest military in the world. I can move funds around to give Medicare to every single American, an additional cost of about twice what we currently pay for Medicare. Then Medicaid doesn’t just get cut; it can be eliminated entirely, folded into Medicare. Assuming that the net effect on total spending is zero, the resulting deficit is estimated at only $168 billion, well within the range of what can be sustained indefinitely.

And really, that’s only the start. Once you consider all the savings on healthcare spending—an average of $4000 per person per year, if switching to single-payer brings us down to the average of other highly-developed countries. This is more than what the majority of the population would be paying in taxes under this plan—meaning that once you include the healthcare benefits, the majority of Americans would net receive money from the government. Compared to our current system, everyone making under about $80,000 would be better off. That is what we could be doing right now—free healthcare for everyone, a balanced budget (or close enough), and the majority of Americans receiving more from the government than they pay in taxes.

These results are summarized in the table below. (I also added several more rows of representative households—though still not all the brackets I used!) I’ve color-coded who would be paying less in tax in green and who would be more in tax in red under each plan, compared to our current system. This color-coding is overly generous to Trump’s plan and the 30% flat tax plan, because it doesn’t account for the increased government deficit (though I did color-code those as well, again relative to the current system). And yet, over 50% of households make less than $51,986, putting the poorest half of Americans in the green zone for every plan except Trump’s. For the last plan, I also color-coded those between $52,000 and $82,000 who would pay additional taxes, but less than they save on healthcare, thus net saving money in blue. Including those folks, we’re benefiting over 69% of Americans.

Household

pre-tax income

Current tax system Trump’s tax plan Flat 30% tax with $12k basic income Flat 40% tax with $15k basic income Logtax 20% Logtax 25% with $12k basic income Logtax 35% with $15k basic income, single-payer healthcare
$1,080 $108 $130 -$11,676 -$14,568 -$856 -$12,121 -$15,173
$12,317 $1,384 $1,478 -$8,305 -$10,073 -$1,254 -$11,413 -$14,186
$22,162 $2,861 $2,659 -$5,351 -$6,135 $450 -$9,224 -$11,213
$32,058 $4,345 $3,847 -$2,383 -$2,177 $2,887 -$6,256 -$7,258
$51,986 $8,768 $6,238 $3,596 $5,794 $9,041 $1,115 $2,383
$77,023 $15,027 $9,506 $11,107 $15,809 $18,206 $11,995 $16,350
$81,966 $16,263 $10,742 $12,590 $17,786 $20,148 $14,292 $17,786
$97,161 $20,242 $14,540 $17,148 $23,864 $26,334 $21,594 $28,516
$101,921 $21,575 $15,730 $18,576 $27,875 $30,571 $23,947 $31,482
$151,940 $35,580 $28,235 $33,582 $45,776 $50,655 $50,144 $64,180
$781,538 $265,625 $230,158 $222,461 $297,615 $406,076 $458,140 $551,031
$2,036,666 $762,656 $644,350 $599,000 $799,666 $1,228,795 $1,384,475 $1,618,703
$9,935,858 $3,890,736 $3,251,083 $2,968,757 $3,959,343 $7,065,274 $7,819,932 $8,790,124
Change in federal spending $0 $0 -$630 billion -$630 billion $0 -$630 billion $0
Estimated federal surplus -$682 billion -$1,155 billion -$822 billion -$180 billion $110 billion $63 billion -$168 billion

Whose tax plan makes the most sense?

JDN 2457496

The election for the President of the United States has now come down to four candidates; the most likely winner is Hillary Clinton, but despite claims to the contrary Bernie Sanders could still win the Democratic nomination. On the Republican side Donald Trump holds a small lead over Ted Cruz, and then there’s a small chance that Kasich could win or a new candidate could emerge if neither can win a majority and they go to a brokered convention (I’ve heard Romney and Ryan suggested, and either of them would be far better).

There are a lot of differences between the various candidates, and while it feels partisan to say so I really think it’s pretty obvious that Clinton and Sanders are superior candidates to Trump and Cruz. Trump is a plutocratic crypto-fascist blowhard with no actual qualifications, and Cruz seems to extrude sleaze from his every pore—such that basically nobody who knows him well actually likes him.

In general I’ve preferred Sanders, though when he started talking about trade policy the other day it actually got me pretty worried that he doesn’t appreciate the benefits of free trade. So while I think a lot of Clinton’s plans are kind of lukewarm, I wouldn’t mind if she won, if only because her trade policy is clearly better.

But today I’m going to compare all four candidates in a somewhat wonkier way: Let’s talk about taxes.

Specifically, federal income tax. There are a lot of other types of taxes of course, but federal income tax is the chief source of revenue for the US federal government, as well as the chief mechanism by which the United States engages in redistribution of wealth. I’ll also briefly discuss payroll taxes, which are the second-largest source of federal revenue.
So, I’ve looked up the income tax plans of Hillary Clinton, Bernie Sanders, Donald Trump, and Ted Cruz respectively, and they are summarized below. The first column gives the minimum income threshold for that marginal tax rate (since they vary slightly I’ll be rounding to the nearest thousand). For comparison I’ve included the current income tax system as well. I’m using the rates for an individual filing singly with no deductions for simplicity.

Current system Hillary Clinton Bernie Sanders Donald Trump Ted Cruz
0 10% 10% 10% 0% 0%
9,000 15% 15% 15% 0% 0%
25,000 15% 15% 15% 10% 0%
36,000 25% 25% 25% 10% 10%
37,000 25% 25% 25% 10% 10%
50,000 25% 25% 25% 20% 10%
91,000 28% 28% 28% 20% 10%
150,000 28% 28% 28% 25% 10%
190,000 33% 33% 33% 25% 10%
250,000 33% 33% 37% 25% 10%
412,000 35% 35% 37% 25% 10%
413,000 39.6% 35% 37% 25% 10%
415,000 39.6% 39.6% 37% 25% 10%
500,000 39.6% 39.6% 43% 25% 10%
2,000,000 39.6% 39.6% 48% 25% 10%
5,000,000 39.6% 43.6% 48% 25% 10%
10,000,000 39.6% 43.6% 52% 25% 10%

As you can see, Hillary Clinton’s plan is basically our current system, with some minor adjustments and a slight increase in progressivity.In addition to these slight changes in the income tax code, she also proposes to close some loopholes in corporate taxes, but she basically doesn’t change the payroll tax system at all. Her plan would not change a whole lot, but we know it would work, because our current tax system does work.

Despite calling himself a social democrat and being accused of being a far more extreme sort of socialist, Bernie Sanders offers a tax plan that isn’t very radical either; he makes our income tax system a bit more progressive, especially at very high incomes; but it’s nothing out of the ordinary by historical standards. Sanders’ top rate of 52% is about what Reagan set in his first tax cut plan in 1982, and substantially lower than the about 90% top rates we had from 1942 to 1964 and the about 70% top rates we had from 1965 to 1981. Sanders would also lift the income cap on payroll taxes (which it makes no sense not to do—why would we want payroll taxes to be regressive?) and eliminate the payroll tax deduction for fringe benefits (which is something a lot of economists have been clamoring for).

No, it’s the Republicans who have really radical tax plans. Donald Trump’s plan involves a substantial cut across the board, to rates close to the lowest they’ve ever been in US history, which was during the Roaring Twenties—the top tax rate was 25% from 1925 to 1931. Trump also proposes to cut the corporate tax in half (which I actually like), and eliminate the payroll tax completely—which would only make sense if you absorbed it into income taxes, which he does not.

Ted Cruz’s plan is even more extreme, removing essentially all progressivity from the US tax code and going to a completely flat tax at the nonsensically low rate of 10%. We haven’t had a rate that low since 1915—so these would be literally the lowest income tax rates we’ve had in a century. Ted Cruz also wants to cut the corporate tax rate in half and eliminate payroll taxes, which is even crazier in his case because of how much he would be cutting income tax rates.

To see why this is so bonkers, take a look at federal spending as a portion of GDP over the last century. We spent only about 10% of GDP in 1915; We currently take in $3.25 trillion per year, 17.4% of GDP, and spend $3.70 trillion per year, 19.8% of GDP. So Ted Cruz’s plan was designed for an era in which the federal government spent about half what it does right now. I don’t even see how we could cut spending that far that fast; it would require essentially eliminating Social Security and Medicare, or else huge cuts in just about everything else. Either that, or we’d have to run the largest budget deficit we have since WW2, and not just for the war spending but indefinitely.

Donald Trump’s plan is not quite as ridiculous, but fact-checkers have skewered him for claiming it will be revenue-neutral. No, it would cut revenue by about $1 trillion per year, which would mean either large deficits (and concomitant risk of inflation and interest rate spikes—this kind of deficit would have been good in 2009, but it’s not so great indefinitely) or very large reductions in spending.

To be fair, both Republicans do claim they intend to cut a lot of spending. But they never quite get around to explaining what spending they’ll be cutting. Are you gutting Social Security? Ending Medicare? Cutting the military in half? These are the kinds of things you’d need to do in order to save this much money.

It’s kind of a shame that Cruz set the rate so low, because if he’d proposed a flat tax of say 25% or 30% that might actually make sense. Applied to consumption instead of income, this would be the Fair Tax, which is 23% if calculated like an income tax or 30% if calculated like a sales tax—either way it’s 26 log points. The Fair Tax could actually provide sufficient revenue to support most existing federal spending,

I still oppose it because I want taxes to be progressive (for reasons I’ve explained previously), and the Fair Tax, by applying only to consumption it would be very regressive (poor people often spend more than 100% of their incomes on consumption—financing it on debt—while rich people generally spend about 50%, and the very rich spend even less). It would exacerbate inequality quite dramatically, especially in capital income, which would be completely untaxed. Even a flat income tax like Cruz’s would still hit the poor harder than the rich in real terms.

But I really do like the idea of a very simple, straightforward tax code that has very few deductions so that everyone knows how much they are going to pay and doesn’t have to deal with hours of paperwork to do it. If this lack of deductions is enshrined in law, it would also remove most of the incentives to lobby for loopholes and tax expenditures, making our tax system much fairer and more efficient.

No doubt about it, flat taxes absolutely are hands-down the easiest to compute. Most people would probably have trouble figuring out a formula like r = I^{-p}, though computers have no such problem (my logarithmic tax plan is easier on computers than the present system); but even fifth-graders can multiply something by 25%. There is something very appealing about everyone knowing at all times that they pay in taxes one-fourth of what they get in income. Adding a simple standard deduction for low incomes makes it slightly more complicated, but also makes it a little bit progressive and is totally worth the tradeoff.

His notion of “eliminating the IRS” is ridiculous (we still need the IRS to audit people to make sure they are honest about their incomes!), and I think the downsides of having no power to redistribute wealth via taxes outweigh the benefits of a flat tax, but the benefits are very real. The biggest problem is that Cruz chose a rate that simply makes no sense; there’s no way to make the numbers work out if the rate is only 10%, especially since you’re excluding half the population from being taxed at all.

Hopefully you see how this supports my contention that Clinton and Sanders are the serious candidates while Trump and Cruz are awful; Clinton wants to keep our current tax system, and Sanders wants to make it a bit more progressive, while Trump and Cruz prize cutting taxes and making taxes simple so highly that they forgot to make sure the numbers actually make any sense—or worse, didn’t care.

How Reagan ruined America

JDN 2457408

Or maybe it’s Ford?

The title is intentionally hyperbolic; despite the best efforts of Reagan and his ilk, America does yet survive. Indeed, as Obama aptly pointed out in his recent State of the Union, we appear to be on an upward trajectory once more. And as you’ll see in a moment, many of the turning points actually seem to be Gerald Ford, though it was under Reagan that the trends really gained steam.

But I think it’s quite remarkable just how much damage Reaganomics did to the economy and society of the United States. It’s actually a turning point in all sorts of different economic policy measures; things were going well from the 1940s to the 1970s, and then suddenly in the 1980s they take a turn for the worse.

The clearest example is inequality. From the World Top Incomes Database, here’s the graph I featured on my Patreon page of income shares in the United States:

top_income_shares_pretty.png

Inequality was really bad during the Roaring Twenties (no surprise to anyone who has read The Great Gatsby), then after the turmoil of the Great Depression, the New Deal, and World War 2, inequality was reduced to a much lower level.

During this period, what I like to call the Golden Age of American Capitalism:

Instead of almost 50% in the 1920s, the top 10% now received about 33%.

Instead of over 20% in the 1920s, the top 1% now received about 10%.

Instead of almost 5% in the 1920s, the top 0.01% now received about 1%.

This pattern continued to hold, remarkably stable, until 1980. Then, it completely unraveled. Income shares of the top brackets rose, and continued to rise, ever since (fluctuating with the stock market of course). Now, we’re basically back right where we were in the 1920s; the top 10% gets 50%, the top 1% gets 20%, and the top 0.01% gets 4%.

Not coincidentally, we see the same pattern if we look at the ratio of CEO pay to average worker pay, as shown here in a graph from the Economic Policy Institute:

Snapshot_CEO_pay_main

Up until 1980, the ratio in pay between CEOs and their average workers was steady around 20 to 1. From that point forward, it began to rise—and rise, and rise. It continued to rise under every Presidential administration, and actually hit its peak in 2000, under Bill Clinton, at an astonishing 411 to 1 ratio. In the 2000s it fell to about 250 to 1 (hurray?), and has slightly declined since then to about 230 to 1.

By either measure, we can see a clear turning point in US inequality—it was low and stable, until Reagan came along, when it began to explode.

Part of this no doubt is the sudden shift in tax rates. The top marginal tax rates on income were over 90% from WW2 to the 1960s; then JFK reduced them to 70%, which is probably close to the revenue-maximizing rate. There they stayed, until—you know the refrain—along came Reagan, and by the end of his administration he had dropped the top marginal rate to 28%. It then was brought back up to about 35%, where it has basically remained, sometimes getting as high as 40%.

US_income_tax_rates

Another striking example is the ratio between worker productivity and wages. The Economic Policy Institute has a very detailed analysis of this, but I think their graph by itself is quite striking:

productivity_wages

Starting around the 1970s, and then rapidly accelerating from the 1980s onward, we see a decoupling of productivity from wages. Productivity has continued to rise at more or less the same rate, but wages flatten out completely, even falling for part of the period.

For those who still somehow think Republicans are fiscally conservative, take a look at this graph of the US national debt:

US_federal_debt

We were at a comfortable 30-40% of GDP range, actually slowly decreasing—until Reagan. We got back on track to reduce the debt during the mid-1990s—under Bill Clinton—and then went back to raising it again once George W. Bush got in office. It ballooned as a result of the Great Recession, and for the past few years Obama has been trying to bring it back under control.

Of course, national debt is not nearly as bad as most people imagine it to be. If Reagan had only raised the national debt in order to stop unemployment, that would have been fine—but he did not.

Unemployment had never been above 10% since World War 2 (and in fact reached below 4% in the 1960s!) and yet all the sudden hit almost 11%, shortly after Reagan:
US_unemployment
Let’s look at that graph a little closer. Right now the Federal Reserve uses 5% as their target unemployment rate, the supposed “natural rate of unemployment” (a lot of economists use this notion, despite there being almost no empirical support for it whatsoever). If I draw red lines at 5% unemployment and at 1981, the year Reagan took office, look at what happens.

US_unemployment_annotated

For most of the period before 1981, we spent most of our time below the 5% line, jumping above it during recessions and then coming back down; for most of the period after 1981, we spent most of our time above the 5% line, even during economic booms.

I’ve drawn another line (green) where the most natural break appears, and it actually seems to be the Ford administration; so maybe I can’t just blame Reagan. But something happened in the last quarter of the 20th century that dramatically changed the shape of unemployment in America.

Inflation is at least ambiguous; it was pretty bad in the 1940s and 1950s, and then settled down in the 1960s for awhile before picking up in the 1970s, and actually hit its worst just before Reagan took office:

US_inflation

Then there’s GDP growth.

US_GDP_growth

After World War 2, our growth rate was quite volatile, rising as high as 8% (!) in some years, but sometimes falling to zero or slightly negative. Rates over 6% were common during booms. On average GDP growth was quite good, around 4% per year.

In 1981—the year Reagan took office—we had the worst growth rate in postwar history, an awful -1.9%. Coming out of that recession we had very high growth of about 7%, but then settled into the new normal: More stable growth rates, yes, but also much lower. Never again did our growth rate exceed 4%, and on average it was more like 2%. In 2009, Reagan’s record recession was broken with the Great Recession, a drop of almost 3% in a single year.

GDP per capita tells a similar story, of volatile but fast growth before Reagan followed by stable but slow growth thereafter:

US_GDP_per_capita

Of course, it wouldn’t be fair to blame Reagan for all of this. A lot of things have happened in the late 20th century, after all. In particular, the OPEC oil crisis is probably responsible for many of these 1970s shocks, and when Nixon moved us at last off the Bretton Woods gold standard, it was probably the right decision, but done at a moment of crisis instead of as the result of careful planning.

Also, while the classical gold standard was terrible, the Bretton Woods system actually had some things to recommend it. It required strict capital controls and currency exchange regulations, but the period of highest economic growth and lowest inequality in the United States—the period I’m calling the Golden Age of American Capitalism—was in fact the same period as the Bretton Woods system.

Some of these trends started before Reagan, and all of them continued in his absence—many of them worsening as much or more under Clinton. Reagan took office during a terrible recession, and either contributed to the recovery or at least did not prevent it.

The President only has very limited control over the economy in any case; he can set a policy agenda, but Congress must actually implement it, and policy can take years to show its true effects. Yet given Reagan’s agenda of cutting top tax rates, crushing unions, and generally giving large corporations whatever they want, I think he bears at least some responsibility for turning our economy in this very bad direction.

Tax incidence revisited, part 5: Who really pays the tax?

JDN 2457359

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

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

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

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

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

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

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

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

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

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

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

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

incidence_infinite_notax_surplus

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

incidence_infinite_tax_surplus

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

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

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

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

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

incidence_supply_notax_surplus

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

Total surplus is $780.

incidence_supply_tax_surplus

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

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

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

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

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

incidence_infinite2_notax_surplus

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

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

incidence_infinite2_tax_surplus

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

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

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

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

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

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

Tax incidence revisited, part 4: Surplus and deadweight loss

JDN 2457355

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

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

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

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

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

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

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

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

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

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

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

equilibrium_notax

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

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

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

surplus

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

equilibrium_notax_surplus

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

equilibrium_tax_surplus

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

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

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

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

equilibrium_elastic_tax_surplus

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

equilibrium_inelastic_tax_surplus

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

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

But that’s not all that elasticity does!

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

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.)

supply_curve

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.)

demand_curve

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.

equilibrium_notax

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.

equilibrium_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.