Month: January 2018

Why is redistribution of wealth so difficult to achieve in the US?

PNRJ current events, inequality, public policy , , , , , , , , , , , , , ,

Jan 28 JDN 2458147

Income and wealth in equality is much higher in the US than in other First World countries. Within the OECD, only Mexico, Turkey, and Chile have higher income inequality than we do. Over 60% of Americans agree that the distribution of wealth in the US is unfair. Furthermore, the majority of Americans support the use of taxes and transfers to directly redistribute wealth from the rich to the poor.

Why, then, is it so hard to actually get any meaningful wealth redistribution in the United States?

Part of it is surely partisan differences: While about 70% of Democrats favor redistributive taxes, about 70% of Republicans oppose them. So one would not expect a move toward redistribution when Republicans control all three branches of government, and indeed we have seen quite the opposite. (Then again, one would also not expect a government shutdown under one-party rule, and yet that is what we have.)

But even most Republicans say they would like to see a much more equal distribution of wealth than the one we actually have. In fact, when I as an inequality economist look at the distribution of wealth people say they want, it looks a little too equal! Even Denmark and Sweden aren’t that egalitarian! I know more or less how to get from here to Denmark; but from here to “Equalden” looks like an awful long way. So if this is really the distribution of wealth people want, we need to be doing a huge amount of wealth redistribution—but we’re hardly doing any at all.

Indeed, we didn’t actually see all that much redistribution of wealth when Democrats more or less controlled all three branches in the period from 2008-2010. We may have seen a little bit shortly thereafter, and tax policy typically does come with a delay of a year or two. But as you can see in this graph, the Great Recession did more to reduce the top 1% income share than any tax policy changes:

US_top_income_share_1pct

The biggest changes made to our tax code under Obama were actually the handling of capital gains; the increase of the top rate on capital gains from 15% to 20%, plus the 3.8% capital surtax from the Affordable Care Act raised the tax bill for the top 0.1% by tens of billions of dollars. Surprisingly, Trump’s tax cuts don’t actually remove these provisions, though they did dramatically cut the corporate tax rate, which will probably have a similar effect on the income distribution.

To be honest, I’m not as disappointed with Trump’s tax cuts as I thought I would be. Some genuinely good ideas (like the reduction of the mortgage interest deduction, tighter restrictions on carried interest, and increase of the personal standard deduction) and some reasonable but debatable ideas (like cuts to the corporate tax rate, switching to a territorial corporate tax system, limits to deductions on corporate debt payments, removal of the deduction of state taxes, and extensions of 529 savings plans to private primary and secondary schools) were mixed in with the absolutely ludicrous and terrible ideas (like eliminating the Obamacare mandate, doubling the estate tax threshold, cutting the alcohol tax, and allowing offshore drilling in Alaska [One of these things is not like the other ones….]). Some of the terrible ideas, like ending the deduction of student loan interest and tuition waivers, were actually removed in the final version of the bill. Of course, you won’t be surprised when I tell you that the overall US tax system became a lot less progressive as a result of this bill. And even if cutting the corporate tax while raising the capital gains tax is probably a good idea (as I and many economists believe), cutting the corporate tax without raising the capital gains tax probably isn’t.

(An aside: For how much they claim to be “tough on crime”, it’s always kind of baffling to see how often Republicans like to cut alcohol taxes and pollution regulations, which are pretty much the only things that have ever been empirically shown to actually reduce crime. There is some evidence that maybe more policing also helps, but if so, it does so in a far less cost-effective way—indeed, the direct cost of alcohol taxes and pollution taxes is negative. Even if they didn’t work at all, they’d still be worth it just because they raise revenue. I begin to suspect that Republicans don’t actually want to reduce crime, because they know they can use the fear of crime to win votes; they simply want to appear tough on crime, and so they press as hard as they can for more policing and incarceration in the country that already has the highest incarceration rate in the world. This may be a more general phenomenon: While Democrats want to actually solve problems, Republicans want to appear to solve problems while actually exacerbating them, thus insuring their own job security. Compare how Bush kept talking about Osama bin laden while invading Iraq, and Obama actually killed Osama bin Laden. Is this too cynical? Can anything be too cynical in the era of Trump? There were 50,000 Russian bots on Twitter trying to tilt our election! Mueller’s FBI investigation is already implicating several of Trump’s top officials! Everything that seemed like paranoia or cynicism just a few years ago is turning out to be entirely true.)

This is what seems to happen: Year after year, we raise some taxes, then we cut some taxes. Then when raise some taxes, then we cut some taxes. The tax system gets a little more progressive for a few years and inequality begins to fall, and then those changes are removed and inequality begins to rise again. Back and forth and round and round we go.

Is there some way to lock in these tax changes for a longer period of time? The only way I can see would be a change in voter behavior: Keep voting in Democrats to all branches of government consistently for 20 years, and then maybe we would see a serious reduction in income and wealth inequality. Or at least stop voting in Republicans; aside from the Democrats, there are some third parties that would also support redistribution, like the Green Party. And yes, it really is about voting behavior: As prevalent as gerrymandering has become, as terrible as the Electoral College is, as widespread as voter suppression has gotten, Trump only won because 63 million Americans voted for him. Even after everything he’s done, Trumps’ approval rating is still about 39%. As long as there are enough people in this country whose partisan loyalty so strongly outweighs any rational assessment of policy, we are going to continue to see such travesties continue.

It would certainly help if our voting system were fairer, so that third parties had a better chance at taking seats. But it’s also difficult to see how that could happen any time soon. For now, the best I can come up with is trying to show people two things:

First, most Americans favor redistribution of wealth. You’re not alone in wanting that. It’s not some fringe opinion.

Second, there is a real difference between Democrats and Republicans on this issue. The canard “The two parties are the same” is the most untrue it has been in at least twenty years.

I would even understand if there are other issues you consider more important than wealth redistribution. Ecological sustainability is the most defensible—you can’t eat GNP—though that would push you even harder toward the left. Among things that might push you right, I can understand being concerned about higher taxes hurting economic growth, and while I think the view that abortion is murder is ludicrous, given that as your belief I can understand why you would want to prioritize fighting abortion. (If I thought we were murdering millions of babies every year, I’d be pretty mad too! Of course, you should be glad, then, that the US abortion rate has been falling. Right? You know about that, right?)

What I don’t get, however, is people who thought that voting for Donald Trump would help working people. I don’t understand how you can see someone who epitomizes everything that is wrong with the billionaire rentier class and think, “Yeah, he seems like he’s definitely a populist. That guy who was born insanely rich and made even more mind-boggling amounts of money by lying and screwing people over is definitely going to look out for folks like me.”

If I understood that, maybe I would know where to go from here. But people’s political beliefs can be astonishingly intransigent to evidence. Politics is the mind-killer.

Did the World Bank modify its ratings to manipulate the outcome of an election in Chile?

PNRJ current events, development economics, ethics, inequality, public policy , , , , , , , , , , , , , , ,

Jan 21 JDN 2458140

(By the way, my birthday is January 19. I can’t believe I’m turning 30.)

This is a fairly obscure news item, so you may have missed it. It should be bigger news than it is.
I can’t fault the New York Times for having its front page focus mainly on the false missile alert that was issued to some people in Hawaii; a false alarm of nuclear attack definitely is the most important thing that could be going on in the world, short of course of actual nuclear war.

CNN, on the other hand, is focused entirely on Trump. When I first wrote this post, they were also focused on Trump, mainly interested in asking whether Trump’s comments about “immigrants from shithole countries” was racist. My answer: Yes, but not because he said the countries were “shitholes”. That was crude, yes, but not altogether inaccurate. Countries like Syria, Afghanistan, and Sudan are, by any objective measure, terrible places. His comments were racist because they attributed that awfulness to the people leaving these countries. But in fact we have a word for immigrants who flee terrible places seeking help and shelter elsewhere: Refugees. We call those people refugees. There are over 10 million refugees in the world today, most of them from Syria.

So anyway, here’s the news item you should have heard about but probably didn’t: The Chief Economist of the World Bank (Paul Romer, who coincidentally I mentioned in my post about DSGE models) has opened an investigation into the possibility that the World Bank’s ratings of economic freedom were intentionally manipulated in order to tilt a Presidential election in Chile.

The worst part is, it may have worked: Chile’s “Doing Business” rating consistently fell under President Michelle Bachelet and rose under President Sebastian Piñera, and Piñera won the most recent election. Was that the reason he won? Who knows? I’m still not entirely clear on how we ended up with President Trump. But it very likely contributed.

The World Bank is supposed to be an impartial institution representing the interests of global economic development. I’m not naive; I recognize that no human institution is perfect, and there will always be competing political and economic interests within any complex institution. Development economists are subject to cognitive biases just like anyone else. If this was the work of a handful of economic analysts (or if Romer turns out to be wrong and the changes in statistical methodology were totally reasonable), so be it; let’s make sure that the bias is corrected and the analysts involved are punished.

But I fear that the rot may run deeper than this. The World Bank is effectively a form of unelected international government. It has been accused of inherent pro-capitalist (or even racist) bias due to the fact that Western governments are overrepresented in its governance, but I actually consider that accusation unfair: There are very good reasons to make sure that your international institutions are managed by liberal democracies, and turns out that most of the world’s liberal democracies are Western. The fact that the US, France, Germany, and the UK make most of the decisions is entirely sensible: Those are in fact the countries we should want making global decisions.

China is not underrepresented, because China is not a democracy and doesn’t deserve to be represented. They are already more represented in the World Bank than they should be, because representing the PRC is not actually representing the interests of the people of China. Russia and Saudi Arabia are undeniably overrepresented. India is underrepresented; they should be complaining. Some African democracies, such as Namibia and Botswana, would also have a legitimate claim to underrepresentation. But I don’t lose any sleep over the fact that Zimbabwe and Iran aren’t getting votes in the World Bank. If and when those countries actually start representing their people, then we can talk about giving them representation in world government. I don’t see how refusing to give international authority to dictators and theocrats constitutes racism or pro-capitalist bias.

That said, there are other reasons to think that the World Bank might actually have some sort of pro-capitalist bias. The World Bank was instrumental in forming the Washington Consensus, which opened free trade and increase economic growth worldwide, but also exposed many poor countries to risk from deregulated financial markets and undermined social safety nets through fiscal austerity programs. They weren’t wrong to want more free trade, and many of their reforms did make sense; but they were at best wildly overconfident in their policy prescriptions, and at worst willing to sacrifice people in poor countries at the altar of bank profits. World poverty has in fact fallen by about half since 1990, and the World Bank has a lot to do with that. But things may have gone faster and smoother if they hadn’t insisted on removing so many financial regulations so quickly without clear forecasts of what would happen. I don’t share Jason Hickel’s pessimistic view that the World Bank’s failures were intentional acts toward an ulterior agenda, but I can see how it begins to look that way when they keep failing the same ways over and over again. (I instead invoke Hanlon’s razor: “Never attribute to malice that which is adequately explained by stupidity.”)

There are also reports of people facing retaliation for criticizing World Bank projects, including those within the World Bank who raise ethical concerns. If this was politically-motivated data manipulation, there may have been people who saw it happening, but were afraid to say anything for fear of being fired or worse.

And Chile in particular has reason to be suspicious. The World Bank suddenly started giving loans to Chile when Augusto Pinochet took power (the CIA denies supporting the coup, by the way—though, given the source, I can understand why one would take that with a grain of salt), and did so under the explicit reasoning that an authoritarian capitalist regime was somehow “more trustworthy” than a democratic socialist regime. Even in the narrow sense of financial creditworthiness that seems difficult to defend; the World Bank knew almost nothing about what kind of government Pinochet was going to create, and in fact despite the so-called “Miracle of Chile”, rapid economic growth in Chile didn’t really happen until the 1990s, after Chile became a democratic capitalist regime.

What I’m really getting at here is that the World Bank has a lot to answer for. I am prepared to believe that most of these actions were honest mistakes or ideological blinders, rather than corruption or cruelty; but even so, when millions of lives are at stake, even honest mistakes aren’t so forgivable. They should be looking for ways to improve their internal governance to make sure that mistakes are caught and corrected quickly. They should be constantly vigilant for biases—either intentional or otherwise—that might seep into their research. Error should be met with immediate correction and public apology; malfeasance should be met with severe punishment.

Perhaps Romer’s investigation actually signals a shift toward such a policy. If so, this is a very good thing. If only we had done this, say, thirty years ago.

What about a tax on political contributions?

PNRJ ethics, market failure, public policy, Uncategorized , , , , , ,

Jan 7, JDN 2458126

In my previous post, I argued that an advertising tax could reduce advertising, raise revenue, and produce almost no real economic distortion. Now I’m going to generalize this idea to an even bolder proposal: What if we tax political contributions?

Donations to political campaigns are very similar to advertising. A contest function framework also makes a lot of sense: Increased spending improves your odds of winning, but it doesn’t actually produce any real goods.

Suppose there’s some benefit B that I get if a given politician wins an election. That benefit could include direct benefits to me, as well as altruistic benefits to other citizens I care about, or even my concern for the world as a whole. But presumably, I do benefit in some fashion from my favored politician winning—otherwise, why are they my favored politician?

In this very simple model, let’s assume that there are only two parties and two donors (obviously in the real world there are more parties and vastly more donors; but it doesn’t fundamentally change the argument). Say I will donate x and the other side will donate y.

Assuming that donations are all that matter, the probability my party will win the election is x/(x+y).

Fortunately that isn’t the case. A lot of things matter, some that should (policy platforms, experience, qualifications, character) and some that shouldn’t (race, gender, age, height—part of why Trump won may in fact be that he is tall; he’s about 6’1”.). So let’s put all the other factors that affect elections into a package and call that F.

The probability that my candidate wins is then x/(x+y) + F, where F can be positive or negative. If F is positive, it means that my candidate is more likely to win, while if it’s negative, it means my candidate is less likely to win. (If you want to be pedantic, the probability of winning has to be capped at 0 and 1, but this doesn’t fundamentally change the argument, and only matters for candidates that are obvious winners or obvious losers regardless of how much anyone donates.)

The donation costs me money, x. The cost in utility of that money depends on my utility function, so for now I’ll just call it a cost function C(x).
Then my net benefit is:
B*[x/(x+y)+F] – C(x)

I can maximize this by a first-order condition. Notice how the F just drops out. I like F to be large, but it doesn’t affect my choice of x.

B*y/(x+y)^2 = C'(x)

Turning that into an exact value requires knowing my cost function and my opponent’s cost function (which need not be the same, in general; unlike the advertising case, it’s not a matter of splitting fungible profits between us), but it’s actually possible to stop here. We can already tell that there is a well-defined solution: There’s a certain amount of donation x that maximizes my expected utility, given the amount y that the other side has donated. Moreover, with a little bit of calculus you can show that the optimal amount of x is strictly increasing in y, which makes intuitive sense: The more they give, the more you need to give in order to keep up. Since x is increasing in y and y is increasing in x, there is a Nash equilibrium: At some amount x and y we each are giving the optimal amount from our perspective.

We can get a precise answer if we assume that the amount of the donations is small compared to my overall wealth, so I will be approximately risk-neutral; then we can just say C(x) = x, and C'(x) = 1:

B*y/(x+y)^2 = 1
Then we get essentially the same result we did for the advertising:

x = y = B/4

According to this, I should be willing to donate up to one-fourth the benefit I’d get from my candidate winning in donations. This actually sounds quite high; I think once you take into account the fact that lots of other people are donating and political contributions aren’t that effective at winning elections, the optimal donation is actually quite a bit smaller—though perhaps still larger than most people give.

If we impose a tax rate r on political contributions, nothing changes. The cost to me of donating is still the same, and as long as the tax is proportional, the ratio x/(x+y) and the probability x/(x+y) + F will remain exactly the same as before. Therefore, I will continue to donate the same amount, as will my opponent, and each candidate will have the same probability of winning as before. The only difference is that some of the money (r of the money, to be precise) will go to the government instead of the politicians.

The total amount of donations will not change. The probability of each candidate winning will not change. All that will happen is money will be transferred from politicians to the government. If this tax revenue is earmarked for some socially beneficial function, this will obviously be an improvement in welfare.

The revenue gained is not nearly as large an amount of money as is spent on advertising (which tells you something about American society), but it’s still quite a bit: Since we currently spend about $5 billion per year on federal elections, a tax rate of 50% could raise about $2.5 billion.

But in fact this seriously under-estimates the benefits of such a tax. This simple model assumes that political contributions only change which candidate wins; but that’s actually not the main concern. (If F is large enough, it can offset any possible donations.)
The real concern is how political contributions affect the choices politicians make once they get into office. While outright quid-pro-quo bribery is illegal, it’s well-known that many corporations and wealthy individuals will give campaign donations with the reasonable expectation of influencing what sort of policies will be made.

You don’t think Goldman Sachs gives millions of dollars each election out of the goodness of their hearts, do you? And they give to both major parties, which really only makes sense if their goal is not to make a particular candidate win, but to make sure that whoever wins feels indebted to Goldman Sachs. (I guess it could also be to prevent third parties from winning—but they hardly ever win anyway, so that wouldn’t be a smart investment from the bank’s perspective.)

Lynda Powell at the University of Rochester has documented the many subtle but significant ways that these donations have influenced policy. Campaign donations aren’t as important as party platforms, but a lot of subtle changes across a wide variety of policies add up to large differences in outcomes.

A political contribution tax would reduce these influences. If politicians’ sole goal were to win, the tax would have no effect. But it seems quite likely that politicians enjoy various personal benefits from lobbying and campaign contributions: Fine dinners, luxurious vacations, and so on. And insofar as that is influencing politicians’ behavior, it is both obviously corrupt and clearly reduced by a political contribution tax. How large an effect this would be is difficult to say; but the direction of the effect is clearly the one we want.

Taxing donations would also allow us to protect the right to give to campaigns (which does seem to be a limited kind of civil liberty, even though the precise interpretation “money is speech” is Orwellian), while reducing corruption and allowing us to keep close track on donations that are made. Taxing a money stream, even a small amount, is often one of the best ways to incentivize close monitoring of that money stream.

With a subtle change, the tax could even be made to bias in favor of populism: All you need to do is exempt small donations from the tax. If say the first $1000 per person per year is exempt from taxation, then the imposition of the tax will reduce the effectiveness of million-dollar contributions from Goldman Sachs and the Koch brothers without having any effect on $50 donations from people like you and me. That would technically be “distorting” elections—but it seems like it might be a distortion worth making.

Of course, this is probably even less likely to happen than the advertising tax.

The potential of an advertising tax

PNRJ market failure, public policy , , , , , , , , ,

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.