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.

Is there hope for stopping climate change?

JDN 2457523

This topic was decided by vote of my Patreons (there are still few enough that the vote usually has only two or three people, but hey, what else can I do?).

When it comes to climate change, I have good news and bad news.

First, the bad news:

We are not going to be able to stop climate change, or even stop making it worse, any time soon. Because of this, millions of people are going to die and there’s nothing we can do about it.

Now, the good news:

We can do a great deal to slow down our contribution to climate change, reduce its impact on human society, and save most of the people who would otherwise have been killed by it. It is currently forecasted that climate change will cause somewhere between 10 million and 100 million deaths over the next century; if we can hold to the lower end of that error bar instead of the upper end, that’s half a dozen Holocausts prevented.

There are three basic approaches to take, and we will need all of them:

1. Emission reduction: Put less carbon in

2. Geoengineering: Take more carbon out

3. Adaptation: Protect more humans from the damage

Strategies 1 and 2 are classified as mitigation, while strategy 3 is classified as adaptation. Mitigation is reducing climate change; adaptation is reducing the effect of climate change on people.

Let’s start with strategy 1, emission reduction. It’s probably the most important; without it the others are clearly doomed to fail.

So, what are our major sources of emissions, and what can we do to reduce them?

While within the US and most other First World countries the primary sources of emissions are electricity and transportation, worldwide transportation is less important and agriculture is about as large a source of emissions as electricity. 25% of global emissions are due to electricity, 24% are due to agriculture, 21% are due to industry, 14% are due to transportation, only 6% are due to buildings, and everything else adds up to 10%.


1A. Both within the First World and worldwide, the leading source of emissions is electricity. Our first priority is therefore electrical grid reform.

Energy efficiency can help—and it already is helping, as global electricity consumption has stopped growing despite growth in population and GDP. Energy intensity of GDP is declining. But the main thing we need to do is reform the way that electricity is produced.

Let’s take a look at how the world currently produces electricity. Currently, the leading source of electricity is “liquids”, an odd euphemism for oil; currently about 175 quadrillion BTU per year, 30% of all production. This is closely followed by coal, at about 160 quadrillion BTU per year, 28%. Then we have natural gas, about 130 quadrillion BTU per year (23%), wind, solar, hydroelectric, and geothermal altogether about 60 quadrillion BTU per year (11%), and nuclear fission only about 40 quadrillion BTU per year (7%).

This list basically needs to be reversed. We will probably not be able to completely stop using oil for transportation, but we have no excuse for using for electricity production. We also need to stop using coal for, well, just about anything. There are a few industrial processes that basically have to use coal; fine, use it for that. But just as something to burn, coal is one of the most heavily-polluting technologies in existence—the only things we burn that are worse are wood and animal dung. Simply ending the burning of coal, wood, and dung would by itself save 4 million lives a year just from reduced pollution.

Natural gas burns cleaner than coal or oil, but it still produces a lot of carbon emissions. Even worse, natural gas is itself one of the worst greenhouse gases—and so natural gas leaks are a major source of greenhouse emissions. Last year a single massive leak accounted for 25% of California’s methane emissions. Like oil, natural gas is also something we’ll want to use quite sparingly.

The best power source is solar power, hands-down. In the long run, the goal should be to convert as much as possible of the grid to solar. Wind, hydroelectric, and geothermal are also very useful, though wind power peaks at the wrong time of day for high energy demand and hydro and geothermal require specific geography to work. Solar is also the most scalable; as long as you have the raw materials and the technology, you can keep expanding solar production all the way up to a Dyson Sphere.

But solar is intermittent, and we don’t have good enough energy storage methods right now to ensure a steady grid on solar alone. The bulk of our grid is therefore going to have to be made of the one energy source we have with negligible carbon emissions, mature technology, and virtually unlimited and fully controllable output: Nuclear fission. At least until fusion matures or we solve the solar energy storage problem, nuclear fission is our best option for minimizing carbon emissions immediatelynot waiting for some new technology to come save us, but building efficient reactors now. Why does France only emit 6 tonnes of carbon per person per year while the UK emits 9, Germany emits 10, and the US emits a whopping 17? Because France’s electricity grid is almost entirely nuclear.

But nuclear power is dangerous!” people will say. France has indeed had several nuclear accidents in the last 40 years; guess how many deaths those accidents have caused? Zero. Deepwater Horizon killed more people than the sum total of all nuclear accidents in all First World countries. Worldwide, there was one Black Swan horrible nuclear event—Chernobyl (which still only killed about as many people as die in the US each year of car accidents or lung cancer), and other than that, nuclear power is safer that every form of fossil fuel.

“Where will we store the nuclear waste?” Well, that’s a more legitimate question, but you know what? It can wait. Nuclear waste doesn’t accumulate very fast, precisely because fission is thousands of times more efficient than combustion; so we’ll have plenty of room in existing facilities or easily-built expansions for the next century. By that point, we should have fusion or a good way of converting the whole grid to solar. We should of course invest in R&D in the meantime. But right now, we need fission.

So, after we’ve converted the electricity grid to nuclear, what next?
1B. To reduce the effect of agriculture, we need to eat less meat; among agricultural sources, livestock is the leading contributor of greenhouse emissions, followed by land use “emissions” (i.e. deforestation), which could also be reduced by converting more crop production to vegetables instead of meat because vegetables are much more land-efficient (and just-about-everything-else-efficient).

1C. To reduce the effect of transportation, we need huge investments in public transit, as well as more fuel-efficient vehicles like hybrids and electric cars. Switching to public transit could cut private transportation-related emissions in half. 100% electric cars are too much to hope for, but by implementing a high carbon tax, we might at least raise the cost of gasoline enough to incentivize makers and buyers of cars to choose more fuel-efficient models.
The biggest gains in fuel efficiency happen on the most gas-guzzling vehicles—indeed, so much so that our usual measure “miles per gallon” is highly misleading.

Quick: Which of the following changes would reduce emissions more, assuming all the vehicles drive the same amount? Switching from a hybrid of 50 MPG to a zero-emission electric (infinity MPG!), switching from a normal sedan of 20 MPG to a hybrid of 50 MPG, or switching from an inefficient diesel truck of 3 MPG to a modern diesel truck of 7 MPG?

The diesel truck, by far.

If each vehicle drives 10,000 miles per year: The first switch will take us from consuming 200 gallons to consuming 0 gallons—saving 200 gallons. The second switch will take us from consuming 500 gallons to consuming 200 gallons—saving 300 gallons. But the third switch will take us from consuming 3,334 gallons to consuming only 1,429 gallons—saving a whopping 1,905 gallons. Even slight increases in the fuel efficiency of highly inefficient vehicles have a huge impact, while you can raise an already-efficient vehicle to perfect efficiency and barely notice a difference.

We really should measure in gallons per mile—or better yet, liters per megameter. (Most of the world uses liters per 100 km; almost!)

All right, let’s assume we’ve done that: The whole grid is nuclear, and everyone is a vegetarian driving an electric car. That’s a good start. But we can’t stop there. Because of the feedback loops involved, we only reduce our emissions—even to near zero—the amount of carbon dioxide will continue to increase for decades. We need to somehow take the carbon out that is already there, which brings me to strategy 2, geoengineering.

2A. There are some exotic proposals out there for geoengineering (putting sulfur into the air to block out the Sun; what could possibly go wrong?), and maybe we’ll end up using some of them. I think iron fertilization of the oceans is one of the more promising options. But we need to be careful to make sure we actually know what these projects will do; we got into this mess by doing things without appreciating their long-run environmental impact, so let’s not make the same mistake again.

2B. But really, the most effective form of geoengineering is simply reforestation. Trees are very good at capturing carbon from the atmosphere; it’s what they evolved to do. So let’s plant trees—lots of trees. Many countries already have net positive forestation (such as the US as a matter of fact), but the world still has net deforestation, and that needs to be reversed.

But even if we do all that, at this point we probably can’t do enough fast enough to actually stop climate change from causing damage. After we’ve done our best to slow it down, we’re still going to need to respond to its effects and find ways to minimize the harm. That’s strategy 3, adaptation.

3A. Coastal regions around the world are going to have to turn into the Netherlands, surrounded by dikes and polders. First World countries already have the resources to do this, and will most likely do it on our own (many cities already have plans to); but other countries need to be given the resources to do it. We’re responsible for most of the emissions, and we have the most wealth, so we should pick up the tab for most of the adaptation.

3B. Some places aren’t going to be worth saving—so that means saving the people, by moving them somewhere else. We’re going to have global refugee crises, and we need to prepare for them, not in the usual way of “How can I clear my conscience while xenophobically excluding these people?” but by welcoming them with open arms. We are going to need to resettle tens of millions—possibly hundreds of millions—of people, and we need a process for doing that efficiently and integrating these people into the societies they end up living in. We must stop presuming that closed borders are the default and realize that the burden of proof was always on anyone who says that people should have different rights based on whether they were born on the proper side of an imaginary line. If open borders are utopian, then it is utopian we must be.

The bad news is that even if we do all these things, millions of people are still going to die from climate change—but a lot fewer millions than would if we didn’t.

And the really good news is that people are finally starting to do these things. It took a lot longer than it should, and there are still a lot of holdouts; but significant progress is already being made. There are a lot of reasons to be hopeful.