Rethinking progressive taxation

Apr 17 JDN 2459687

There is an extremely common and quite bizarre result in the standard theory of taxation, which is that the optimal marginal tax rate for the highest incomes should be zero. Ever since that result came out, economists have basically divided into two camps.

The more left-leaning have said, “This is obviously wrong; so why is it wrong? What are we missing?”; the more right-leaning have said, “The model says so, so it must be right! Cut taxes on the rich!”

I probably don’t need to tell you that I’m very much in the first camp. But more recently I’ve come to realize that even the answers left-leaning economists have been giving for why this result is wrong are also missing something vital.

There have been papers explaining that “the zero top rate only applies at extreme incomes” (uh, $50 billion sounds pretty extreme to me!) or “the optimal tax system can be U-shaped” (I don’t want U-shaped—we’re not supposed to be taxing the poor!)


And many economists still seem to find it reasonable to say that marginal tax rates should decline over some significant part of the distribution.

In my view, there are really two reasons why taxes should be progressive, and they are sufficiently general reasons that they should almost always override other considerations.

The first is diminishing marginal utility of wealth. The real value of a dollar is much less to someone who already has $1 million than to someone who has only $100. Thus, if we want to raise the most revenue while causing the least pain, we typically want to tax people who have a lot of money rather than people who have very little.

But the right-wing economists have an answer to this one, based on these fancy models: Yes, taking a given amount from the rich would be better (a lump-sum tax), but you can’t do that; you can only tax their income at a certain rate. (So far, that seems right. Lump-sum taxes are silly and economists talk about them too much.) But the rich are rich because they are more productive! If you tax them more, they will work less, and that will harm society as a whole due to their lost productivity.

This is the fundamental intuition behind the “top rate should be zero” result: The rich are so fantastically productive that it isn’t worth it to tax them. We simply can’t risk them working less.

But are the rich actually so fantastically productive? Are they really that smart? Do they really work that hard?

If Tony Stark were real, okay, don’t tax him. He is a one-man Singularity: He invented the perfect power source on his own, “in a cave, with a box of scraps!”; he created a true AI basically by himself; he single-handedly discovered a new stable island element and used it to make his already perfect power source even better.

But despite what his fanboys may tell you, Elon Musk is not Tony Stark. Tesla and SpaceX have done a lot of very good things, but in order to do they really didn’t need Elon Musk for much. Mainly, they needed his money. Give me $270 billion and I could make companies that build electric cars and launch rockets into space too. (Indeed, I probably would—though I’d also set up some charitable foundations as well, more like what Bill Gates did with his similarly mind-boggling wealth.)

Don’t get me wrong; Elon Musk is a very intelligent man, and he works, if anything, obsessively. (He makes his employees work excessively too—and that’s a problem.) But if he were to suddenly die, as long as a reasonably competent CEO replaced him, Tesla and SpaceX would go on working more or less as they already do. The spectacular productivity of these companies is not due to Musk alone, but thousands of highly-skilled employees. These people would be productive if Musk had not existed, and they will continue to be productive once Musk is gone.

And they aren’t particularly rich. They aren’t poor either, mind you—a typical engineer at Tesla or SpaceX is quite well-paid, and rightly so. (Median salary at SpaceX is over $115,000.) These people are brilliant, tremendously hard-working, and highly productive; and they get quite well-paid. But very few of these people are in the top 1%, and basically none of them will ever be billionaires—let alone the truly staggering wealth of a hectobillionaire like Musk himself.

How, then, does one become a billionaire? Not by being brilliant, hard-working, or productive—at least that is not sufficient, and the existence of, say, Donald Trump suggests that it is not necessary either. No, the really quintessential feature every billionaire has is remarkably simple and consistent across the board: They own a monopoly.

You can pretty much go down the list, finding what monopoly each billionaire owned: Bill Gates owned software patents on (what is still) the most widely-used OS and office suite in the world. J.K. Rowling owns copyrights on the most successful novels in history. Elon Musk owns technology patents on various innovations in energy storage and spaceflight technology—very few of which he himself invented, I might add. Andrew Carnegie owned the steel industry. John D. Rockefeller owned the oil industry. And so on.

I honestly can’t find any real exceptions: Basically every billionaire either owned a monopoly or inherited from ancestors who did. The closest things to exceptions are billionaire who did something even worse, like defrauding thousands of people, enslaving an indigenous population or running a nation with an iron fist. (And even then, Leopold II and Vladimir Putin both exerted a lot of monopoly power as part of their murderous tyranny.)

In other words, billionaire wealth is almost entirely rent. You don’t earn a billion dollars. You don’t get it by working. You get it by owning—and by using that ownership to exert monopoly power.

This means that taxing billionaire wealth wouldn’t incentivize them to work less; they already don’t work for their money. It would just incentivize them to fight less hard at extracting wealth from everyone else using their monopoly power—which hardly seems like a downside.

Since virtually all of the wealth at the top is simply rent, we have no reason not to tax it away. It isn’t genuine productivity at all; it’s just extracting wealth that other people produced.

Thus, my second, and ultimately most decisive reason for wanting strongly progressive taxes: rent-seeking. The very rich don’t actually deserve the vast majority of what they have, and we should take it back so that we can give it to people who really need and deserve it.

Now, there is a somewhat more charitable version of the view that high taxes even on the top 0.01% would hurt productivity, and it is worth addressing. That is based on the idea that entrepreneurship is valuable, and part of the incentive for becoming and entrepreneur is the chance at one day striking it fabulously rich, so taxing the fabulously rich might result in a world of fewer entrepreneurs.

This isn’t nearly as ridiculous as the idea that Elon Musk somehow works a million times as hard as the rest of us, but it’s still pretty easy to find flaws in it.

Suppose you were considering starting a business. Indeed, perhaps you already have considered it. What are your main deciding factors in whether or not you will?

Surely they do not include the difference between a 0.0001% chance of making $200 billion and a 0.0001% chance of making $50 billion. Indeed, that probably doesn’t factor in at all; you know you’ll almost certainly never get there, and even if you did, there’s basically no real difference in your way of life between $50 billion and $200 billion.

No, more likely they include things like this: (1) How likely are you to turn a profit at all? Even a profit of $50,000 per year would probably be enough to be worth it, but how sure are you that you can manage that? (2) How much funding can you get to start it in the first place? Depending on what sort of business you’re hoping to found, it could be as little as thousands or as much as millions of dollars to get it set up, well before it starts taking in any revenue. And even a few thousand is a lot for most middle-class people to come up with in one chunk and be willing to risk losing.

This means that there is a very simple policy we could implement which would dramatically increase entrepreneurship while taxing only billionaires more, and it goes like this: Add an extra 1% marginal tax to capital gains for billionaires, and plow it into a fund that gives grants of $10,000 to $100,000 to promising new startups.

That 1% tax could raise several billion dollars a year—yes, really; US billionaires gained some $2 trillion in capital gains last year, so we’d raise $20 billion—and thereby fund many, many startups. Say the average grant is $20,000 and the total revenue is $20 billion; that’s one million new startups funded every single year. Every single year! Currently, about 4 million new businesses are founded each year in the US (leading the world by a wide margin); this could raise that to 5 million.

So don’t tell me this is about incentivizing entrepreneurship. We could do that far better than we currently do, with some very simple policy changes.

Meanwhile, the economics literature on optimal taxation seems to be completely missing the point. Most of it is still mired in the assumption that the rich are rich because they are productive, and thus terribly concerned about the “trade-off” between efficiency and equity involved in higher taxes. But when you realize that the vast, vast majority—easily 99.9%—of billionaire wealth is unearned rents, then it becomes obvious that this trade-off is an illusion. We can improve efficiency and equity simultaneously, by taking some of this ludicrous hoard of unearned wealth and putting it back into productive activities, or giving it to the people who need it most. The only people who will be harmed by this are billionaires themselves, and by diminishing marginal utility of wealth, they won’t be harmed very much.

Fortunately, the tide is turning, and more economists are starting to see the light. One of the best examples comes from Piketty, Saez, and Stantcheva in their paper on how CEO “pay for luck” (e.g. stock options) respond to top tax rates. There are a few other papers that touch on similar issues, such as Lockwood, Nathanson, and Weyl and Rothschild and Scheuer. But there’s clearly a lot of space left for new work to be done. The old results that told us not to raise taxes were wrong on a deep, fundamental level, and we need to replace them with something better.

The potential of an advertising tax

Jan 7, JDN 2458126

Advertising is everywhere in our society. You may see some on this very page (though if I hit my next Patreon target I’m going to pay to get rid of those). Ad-blockers can help when you’re on the Web, and premium channels like HBO will save you from ads when watching TV, but what are you supposed to do about ads on billboards as you drive down the highway, ads on buses as you walk down the street, ads on the walls of the subway train?

And Banksy isn’t entirely wrong; this stuff can be quite damaging. Based on decades of research, the American Psychological Association has issued official statements condemning the use of advertising to children for its harmful psychological effects. Medical research has shown that advertisements for food can cause overeating—and thus, the correlated rise of advertising and obesity may be no coincidence.

Worst of all, political advertising distorts our view of the world. Though we may not be able to blame advertising per se for Trump; most of his publicity was gained for free by irresponsible media coverage.

And yet, advertising is almost pure rent-seeking. It costs resources, but it doesn’t produce anything. In most cases it doesn’t even raise awareness about something or find new customers. The primary goal of most advertising is to get you to choose that brand instead of a different brand. A secondary goal (especially for food ads) is to increase your overall consumption of that good, but since the means employed typically involve psychological manipulation, this increase in consumption is probably harmful to social welfare.

A general principle of economics that has almost universal consensus is the Pigou Principle: If you want less of something, you should put a tax on it. So, what would happen if we put a tax on advertising?

The amazing thing is that in this case, we would probably not actually reduce advertising spending, but we would reduce advertising, which is what we actually care about. Moreover, we would be able to raise an enormous amount of revenue with zero social cost. Like the other big Pigovian tax (the carbon tax), this a rare example of a tax that will give you a huge amount of revenue while actually yielding a benefit to society.

This is far from obvious, so I think it is worth explaining where it comes from.

The key point is that advertising doesn’t typically increase the overall size of the market (though in some cases it does; I’ll get back to that in a moment). Rather that a conventional production function like we would have for most types of expenditure, advertising is better modeled by what is called a contest function (something that our own Stergios Skaperdas at UCI is actually a world-class expert in). In a production function, inputs increase the total amount of output. But in a contest function, inputs only redistribute output from one place to another. Contest functions thus provide a good model of rent-seeking, which is what most advertising is.

Suppose there’s a total market M for some good, where M is the total profits that can be gained from capturing that entire market.
Then, to keep it simple, let’s suppose there are only two major firms in the market, a duopoly like Coke and Pepsi or Boeing and Airbus.

Let’s say Coke decides to spend an amount x on advertising, and Pepsi decides to spend an amount y.

For now, let’s assume that total beverage consumption won’t change; so the total profits to be had from the market are always M.

What advertising does is it changes the share of that market which each firm will get. Specifically, let’s use the simplest model, where the share of the market is equal to the share of advertising spending.

Then the net profit for Coke is the following:

The share they get, x/(x+y), times the size of the whole market, M, minus the advertising spending x.

max M*x/(x+y) – x

We can maximize this with the usual first-order condition:

y/(x+y)^2 M – 1 = 0

(x+y)^2 = My

Since the game is symmetric, in a Nash equilibrium, Pepsi will use the same reasoning:

(x+y)^2 = Mx

Thus we have:

x = y

(2x)^2 = Mx

x = M/4

In this very simple model, each firm will spend one-fourth of the market’s value, and the total advertising spending will be equal to half the size of the market. Then, each company’s net income will be equal to its advertising spending. This is a pretty good estimate for Coca-Cola in real life, which spends about $3.3 billion on advertising and receives about $2.8 billion in net income each year.

What would happen if we introduce a tax? Let’s say we introduce a proportional tax r on all advertising spending. That is, for every dollar you spend on advertising, you must pay the government $r in tax. The really remarkable thing is that companies who advertise shouldn’t care what we make the tax; the only ones who will care are the advertising companies themselves.

If Coke pays x, the actual amount of advertising they receive is x – r x = x(1-r).

Likewise, Pepsi’s actual advertising received is y(1-r).

But notice that the share of total advertising spending is completely unchanged!

(x(1-r))/(x(1-r) + y(1-r)) = x/(x+y)

Since the payoff for Coke only depends on how much Coke spends and what market share they get, it is also unchanged. Since the same is true for Pepsi, nothing will change in how the two companies behave. They will spend the same amount on advertising, and they will receive the same amount of net income when all is said and done.

The total quantity of advertising will be reduced, from x+y to (x+y)(1-r). That means fewer billboards, fewer posters in subway stations, fewer TV commercials. That will hurt advertising companies, but benefit everyone else.

How much revenue will we get for the government? r x + r y = r(x+y).

Since the goal is to substantially reduce advertising output, and it won’t distort other industries in any way, we should set this tax quite high. A reasonable value for r would be 50%. We might even want to consider something as high as 90%; but for now let’s look at what 50% would do.

Total advertising spending in the US is over $200 billion per year. Since an advertising tax would not change total advertising spending, we can expect that a tax rate of 50% would simply capture 50% of this spending as revenue, which is to say $100 billion per year. That would be enough to pay for the entire Federal education budget, or the foreign aid and environment budgets combined.
Another great aspect of how an advertising tax is actually better than a carbon tax is that countries will want to compete to have the highest advertising taxes. If say Canada imposes a carbon tax but the US doesn’t, industries will move production to the US where it is cheaper, which hurts Canada. Yet the total amount of pollution will remain about the same, and Canada will be just as affected by climate change as they would have been anyway. So we need to coordinate across countries so that the carbon taxes are all the same (or at least close), to prevent industries from moving around; and each country has an incentive to cheat by imposing a lower carbon tax.

But advertising taxes aren’t like that. If Canada imposes an advertising tax and the US doesn’t, companies won’t shift production to the US; they will shift advertising to the US. And having your country suddenly flooded with advertisements is bad. That provides a strong incentive for you to impose your own equal or even higher advertising tax to stem the tide. And pretty soon, everyone will have imposed an advertising tax at the same rate.

Of course, in all the above I’ve assumed a pure contest function, meaning that advertisements are completely unproductive. What if they are at least a little bit productive? Then we wouldn’t want to set the tax too high, but the basic conclusions would be unchanged.

Suppose, for instance, that the advertising spending adds half its value to the value of the market. This is a pretty high estimate of the benefits of advertising.

Under this assumption, in place of M we have M+(x+y)/2. Everything else is unchanged.

We can maximize as before:

max (M+(x+y)/2)*x/(x+y) – x

The math is a bit trickier, but we can still solve by a first-order condition, which simplifies to:

(x+y)^2 = 2My

By the same symmetry reasoning as before:

(2x)^2 = 2Mx

x = M/2

Now, total advertising spending would equal the size of the market without advertising, and net income for each firm after advertising would be:

2M(1/2) – M/2 = M/2

That is, advertising spending would equal net income, as before. (A surprisingly robust result!)

What if we imposed a tax? Now the algebra gets even nastier:

max (M+(x+y)(1-r)/2)*x/(x+y) – x

But the ultimate outcome is still quite similar:

(1+r)(x+y)^2 = 2My

(1+r)(2x)^2 = 2Mx

x = M/2*1/(1+r)

Advertising spending will be reduced by a factor of 1/(1+r). Even if r is 50%, that still means we’ll have 2/3 of the advertising spending we had before.

Total tax revenue will then be M*r/(1+r), which for r of 50% would be M/3.

Total advertising will be M(1-r)/(1+r), which would be M/3. So we managed to reduce advertising by 2/3, while reducing advertising spending by only 1/3. Then we would receive half of that spending as revenue. Thus, instead of getting $100 billion per year, we would get $67 billion, which is still just about enough to pay for food stamps.

What’s the downside of this tax? Unlike most taxes, there really isn’t one. Yes, it would hurt advertising companies, which I suppose counts as a downside. But that was mostly waste anyway; anyone employed in advertising would be better employed almost anywhere else. Millions of minds are being wasted coming up with better ways to sell Viagra instead of better treatments for cancer. Any unemployment introduced by an advertising tax would be temporary and easily rectified by monetary policy, and most of it would hit highly educated white-collar professionals who have high incomes to begin with and can more easily find jobs when displaced.

The real question is why we aren’t doing this already. And that, I suppose, has to come down to politics.