The radical uncertainty of life

Jul 31 JDN 2459792

It’s a question you get a lot in job interviews, and sometimes from elsewhere as well: “Where do you see yourself in ten years?”

I never quite know how to answer such a question, because the future is so full of uncertainty.

Ten years from now:

I could be a tenured professor, or have left academia entirely. I could be teaching here at Edinburgh, or at an even more prestigious university, or at a tiny, obscure school. I could be working in private industry, or unemployed. I could be working as a full-time freelance writer.

I could have published nothing new, or have published a few things, or have won a Fields Medal. (It’s especially unlikely to have won a Nobel by then, but it’s a bit less unlikely that I might have done work that would one day lead to one.)

I could be still living in the United Kingdom, or back in the United States, or in some other country entirely.

I could be healthier than I am now, or permanently disabled. I could even be dead, from a variety of diseases, or a car accident, or a gunshot wound.

I could have adopted three children, or none. I could be divorced. My spouse could be dead.

It could even all be moot because the Russian war in Ukraine—or some other act of Russian aggression—has escalated into a nuclear Third World War.

These are the relatively likely scenarios.

I’m not saying I’m going to win a Fields Medal—but I am the sort of person who wins Fields Medals, surely far more likely than any randomly selected individual. I’m not saying we’re going to have WW3, but we’re definitely closer to it than we’ve been since the end of the Cold War.

There are plenty of other, unlikely scenarios that still remain possible:

I could be working in finance, or engineering, or medicine. I could be living on a farm. I could be President of the United States. I could have won a multi-million-dollar lottery and retired to a life of luxury and philanthropy. Those seem rather unlikely for me personally—but they are all true of someone, somewhere.

I could be living on a space station, or a Lunar base. I could be cybernetically enhanced. 2032 seems early for such things—but it didn’t to folks writing in the 1980s, so who knows? (Maybe it will even happen so gradually we won’t notice: Is a glucose-monitoring implant a cybernetic enhancement? It doesn’t seem so unlikely I might one day have one of those.)

None of us really knows what the future is going to hold. We could say what we want, or what we expect is the most likely, but more often than not, the world will surprise us.

What does this mean for our lives now? Should we give up trying to make plans, since the future is so unpredictable? Should we “eat, drink, and be merry, for tomorrow we die”?

I think the key is to realize that there is a kind of planning that’s still useful even if you can’t predict what will happen—and that is to plan to be flexible and resilient.

You can keep your eyes open for opportunities, rather than trying too hard to hold onto what you already have. Rather than trying in vain to keep everything the same, you can accept that your life is going to change and try to direct that change in better directions.

Rather than planning on staying in the same career for your whole life—which hardly anyone in our generation does—you should expect to change careers, and be working on building a wide range of transferable skills and a broad network of friends and colleagues. Maybe sooner or later you’ll find the right place to settle down, but it could be awhile.

You may not know where you’ll be living or working in ten years, but odds are pretty good that it’ll still be useful for you to have some money saved up, so you should probably save some money. If we end up in a post-scarcity utopia, you won’t need it, but you also won’t care. If we end up in a post-apocalyptic hellscape, it really won’t matter one way or the other. And those two extremes are about what would need to happen for you not to be able to make use of savings.

And where should you put that saved money? Stocks, bonds, cryptocurrency? Well, crypto would give you a chance at spectacular gains—but a much larger chance of spectacular losses. Bonds are very safe, but also don’t grow very much. So, as I’ve said before, you probably want to buy stocks. Yes, you could end up better off by choosing something else; but you have to play the odds, and stocks give you the best odds.

You will have setbacks at some point, either small or large. Everyone does. You can’t plan for what they will be, but you can plan to have resources available to deal with them.

Hey, maybe you should even buy life insurance, just in case you really do die tomorrow. You probably won’t—but somebody will, and doesn’t know it yet.

On the Overton Window

Jul 24 JDN 2459786

As you are no doubt aware, a lot of people on the Internet like to loudly proclaim support for really crazy, extreme ideas. Some of these people actually believe in those ideas, and if you challenge them, will do their best to defend them. Those people are wrong at the level of substantive policy, but there’s nothing wrong with their general approach: If you really think that anarchism or communism is a good thing, it only makes sense that you’d try to convince other people. You might have a hard time of it (in part because you are clearly wrong), but it makes sense that you’d try.

But there is another class of people who argue for crazy, extreme ideas. When pressed, they will admit they don’t really believe in abolishing the police or collectivizing all wealth, but they believe in something else that’s sort of vaguely in that direction, and they think that advocating for the extreme idea will make people more likely to accept what they actually want.

They often refer to this as “shifting the Overton Window”. As Matt Yglesias explained quite well a year ago, this is not actually what Overton was talking about.

But, in principle, it could still be a thing that works. There is a cognitive bias known as anchoring which is often used in marketing: If I only offered a $5 bottle of wine and a $20 bottle of wine, you might think the $20 bottle is too expensive. But if I also include a $50 bottle, that makes you adjust your perceptions of what constitutes a “reasonable” price for wine, and may make you more likely to buy the $20 bottle after all.

It could be, therefore, that an extreme policy demand makes people more willing to accept moderate views, as a sort of compromise. Maybe demanding the abolition of police is a way of making other kinds of police reform seem more reasonable. Maybe showing pictures of Marx and chanting “eat the rich” could make people more willing to accept higher capital gains taxes. Maybe declaring that we are on the verge of apocalyptic climate disaster will make people more willing to accept tighter regulations on carbon emissions and subsidies for solar energy.

Then again—does it actually seem to do that? I see very little evidence that it does. All those demands for police abolition haven’t changed the fact that defunding the police is unpopular. Raising taxes on the rich is popular, but it has been for awhile now (and never was with, well, the rich). And decades of constantly shouting about imminent climate catastrophe is really starting to look like crying wolf.

To see why this strategy seems to be failing, I think it’s helpful to consider how it feels from the other side. Take a look at some issues where someone else is trying to get you to accept a particular view, and consider whether someone advocating a more extreme view would make you more likely to compromise.

Your particular opinions may vary, but here are some examples that would apply to me, and, I suspect, many of you.

If someone says they want tighter border security, I’m skeptical—it’s pretty tight already. But in and of itself, this would not be such a crazy idea. Certainly I agree that it is possible to have too little border security, and so maybe that turns out to be the state we’re in.

But then, suppose that same person, or someone closely allied to them, starts demanding the immediate deportation of everyone who was not born in the United States, even those who immigrated legally and are naturalized or here on green cards. This is a crazy, extreme idea that’s further in the same direction, so on this anchoring theory, it should make me more willing to accept the idea of tighter border security. And yet, I can say with some confidence that it has no such effect.

Indeed, if anything I think it would make me less likely to accept tighter border security, in proportion to how closely aligned those two arguments are. If they are coming from the same person, or the same political party, it would cause me to suspect that the crazy, extreme policy is the true objective, and the milder, compromise policy is just a means toward that end. It also suggests certain beliefs and attitudes about immigration in general—xenophobia, racism, ultranationalism—that I oppose even more strongly. If you’re talking about deporting all immigrants, you make me suspect that your reasons for wanting tighter border security are not good ones.

Let’s try another example. Suppose someone wants to cut taxes on upper income brackets. In our current state, I think that would be a bad idea. But there was a time not so long ago when I would have agreed with it: Even I have to admit that a top bracket of 94% (as we had in 1943) sounds a little ridiculous, and is surely on the wrong side of the Laffer curve. So the basic idea of cutting top tax rates is not inherently crazy or ridiculous.

Now, suppose that same idea came from the same person, or the same party, or the same political movement, as one that was arguing for the total abolition of all taxation. This is a crazy, extreme idea; it would amount to either total anarcho-capitalism with no government at all, or some sort of bizarre system where the government is funded entirely through voluntary contributions. I think it’s pretty obvious that such a system would be terrible, if not outright impossible; and anyone whose understanding of political economy is sufficiently poor that they would fail to see this is someone whose overall judgment on questions of policy I must consider dubious. Once again, the presence of the extreme view does nothing to make me want to consider the moderate view, and may even make me less willing to do so.

Perhaps I am an unusually rational person, not so greatly affected by anchoring biases? Perhaps. But whereas I do feel briefly tempted by to buy the $20 wine bottle by the effect of the $50 wine bottle, and must correct myself with knowledge I have about anchoring bias, the presentation of an extreme political view never even makes me feel any temptation to accept some kind of compromise with it. Learning that someone supports something crazy or ridiculous—or is willing to say they do, even if deep down they don’t—makes me automatically lower my assessment of their overall credibility. If anything, I think I am tempted to overreact in that direction, and have to remind myself of the Stopped Clock Principle: reversed stupidity is not intelligence, and someone can have both bad ideas and good ones.

Moreover, the empirical data, while sketchy, doesn’t seem to support this either; where the Overton Window (in the originally intended sense) has shifted, as on LGBT rights, it was because people convincingly argued that the “extreme” position was in fact an entirely reasonable and correct view. There was a time not so long ago that same-sex marriage was deemed unthinkable, and the “moderate” view was merely decriminalizing sodomy; but we demanded, and got, same-sex marriage, not as a strategy to compromise on decriminalizing sodomy, but because we actually wanted same-sex marriage and had good arguments for it. I highly doubt we would have been any more successful if we had demanded something ridiculous and extreme, like banning opposite-sex marriage.

The resulting conclusion seems obvious and banal: Only argue for things you actually believe in.

Yet, somehow, that seems to be a controversial view these days.

Krugman and rockets and feathers

Jul 17 JDN 2459797

Well, this feels like a milestone: Paul Krugman just wrote a column about a topic I’ve published research on. He didn’t actually cite our paper—in fact the literature review he links to is from 2014—but the topic is very much what we were studying: Asymmetric price transmission, ‘rockets and feathers’. He’s even talking about it from the perspective of industrial organization and market power, which is right in line with our results (and a bit different from the mainstream consensus among economic policy pundits).

The phenomenon is a well-documented one: When the price of an input (say, crude oil) rises, the price of outputs made from that input (say, gasoline) rise immediately, and basically one to one, sometimes even more than one to one. But when the price of an input falls, the price of outputs only falls slowly and gradually, taking a long time to converge to the same level as the input prices. Prices go up like a rocket, but down like a feather.

Many different explanations have been proposed to explain this phenomenon, and they aren’t all mutually exclusive. They include various aspects of market structure, substitution of inputs, and use of inventories to smooth the effects of prices.

One that I find particularly unpersuasive is the notion of menu costs: That it requires costly effort to actually change your prices, and this somehow results in the asymmetry. Most gas stations have digital price boards; it requires almost zero effort for them to change prices whenever they want. Moreover, there’s no clear reason this would result in asymmetry between raising and lowering prices. Some models extend the notion of “menu cost” to include expected customer responses, which is a much better explanation; but I think that’s far beyond the original meaning of the concept. If you fear to change your price because of how customers may respond, finding a cheaper way to print price labels won’t do a thing to change that.

But our paper—and Krugman’s article—is about one factor in particular: market power. We don’t see prices behave this way in highly competitive markets. We see it the most in oligopolies: Markets where there are only a small number of sellers, who thus have some control over how they set their prices.

Krugman explains it as follows:

When oil prices shoot up, owners of gas stations feel empowered not just to pass on the cost but also to raise their markups, because consumers can’t easily tell whether they’re being gouged when prices are going up everywhere. And gas stations may hang on to these extra markups for a while even when oil prices fall.

That’s actually a somewhat different mechanism from the one we found in our experiment, which is that asymmetric price transmission can be driven by tacit collusion. Explicit collusion is illegal: You can’t just call up the other gas stations and say, “Let’s all set the price at $5 per gallon.” But you can tacitly collude by responding to how they set their prices, and not trying to undercut them even when you could get a short-run benefit from doing so. It’s actually very similar to an Iterated Prisoner’s Dilemma: Cooperation is better for everyone, but worse for you as an individual; to get everyone to cooperate, it’s vital to severely punish those who don’t.

In our experiment, the participants in our experiment were acting as businesses setting their prices. The customers were fully automated, so there was no opportunity to “fool” them in this way. We also excluded any kind of menu costs or product inventories. But we still saw prices go up like rockets and down like feathers. Moreover, prices were always substantially higher than costs, especially during that phase when they are falling down like feathers.

Our explanation goes something like this: Businesses are trying to use their market power to maintain higher prices and thereby make higher profits, but they have to worry about other businesses undercutting their prices and taking all the business. Moreover, they also have to worry about others thinking that they are trying to undercut prices—they want to be perceived as cooperating, not defecting, in order to preserve the collusion and avoid being punished.

Consider how this affects their decisions when input prices change. If the price of oil goes up, then there’s no reason not to raise the price of gasoline immediately, because that isn’t violating the collusion. If anything, it’s being nice to your fellow colluders; they want prices as high as possible. You’ll want to raise the prices as high and fast as you can get away with, and you know they’ll do the same. But if the price of oil goes down, now gas stations are faced with a dilemma: You could lower prices to get more customers and make more profits, but the other gas stations might consider that a violation of your tacit collusion and could punish you by cutting their prices even more. Your best option is to lower prices very slowly, so that you can take advantage of the change in the input market, but also maintain the collusion with other gas stations. By slowly cutting prices, you can ensure that you are doing it together, and not trying to undercut other businesses.

Krugman’s explanation and ours are not mutually exclusive; in fact I think both are probably happening. They have one important feature in common, which fits the empirical data: Markets with less competition show greater degrees of asymmetric price transmission. The more concentrated the oligopoly, the more we see rockets and feathers.

They also share an important policy implication: Market power can make inflation worse. Contrary to what a lot of economic policy pundits have been saying, it isn’t ridiculous to think that breaking up monopolies or putting pressure on oligopolies to lower their prices could help reduce inflation. It probably won’t be as reliably effective as the Fed’s buying and selling of bonds to adjust interest rates—but we’re also doing that, and the two are not mutually exclusive. Besides, breaking up monopolies is a generally good thing to do anyway.

It’s not that unusual that I find myself agreeing with Krugman. I think what makes this one feel weird is that I have more expertise on the subject than he does.

How to pack the court

Jul 10 JDN 2459790

By now you have no doubt heard the news that Roe v. Wade was overturned. The New York Times has an annotated version of the full opinion.

My own views on abortion are like those of about 2/3 of Americans: More nuanced than can be neatly expressed by ‘pro-choice’ or ‘pro-life’, much more comfortable with first-trimester abortion (which is what 90% of abortions are, by the way) than later, and opposed to overturning Roe v. Wade in its entirety. I also find great appeal in Clinton’s motto on the issue: “safe, legal, and rare”.Several years ago I moderated an online discussion group that reached what we called the Twelve Week Compromise: Abortion would be legal for any reason up to 12 weeks of pregnancy, after which it would only be legal for extenuating circumstances including rape, incest, fetal nonviability, and severe health risk to the mother. This would render the vast majority of abortions legal without simply saying that it should be permitted without question. Roe v. Wade was actually slightly more permissive than this, but it was itself a very sound compromise.

But even if you didn’t like Roe v. Wade, you should be outraged at the manner in which it was overturned. If the Supreme Court can simply change its mind on rights that have been established for nearly 50 years, then none of our rights are safe. And in chilling comments, Clarence Thomas has declared that this is his precise intention: “In future cases, we should reconsider all of this Court’s substantive due process precedents, including Griswold, Lawrence, and Obergefell.” That is to say, Thomas wants to remove our rights to use contraception and have same-sex relationships. (If Lawrence were overturned, sodomy could be criminalized in several states!)

The good news here is that even the other conservative justices seem much less inclined to overturn these other precedents. Kavanaugh’s concurrent opinion explicitly states he has no intention of overturning “Griswold v. Connecticut, 381 U. S. 479 (1965); Eisenstadt v. Baird, 405 U. S. 438 (1972); Loving v. Virginia, 388 U. S. 1 (1967); and Obergefell v. Hodges, 576 U. S. 644 (2015)”. It seems quite notable that Thomas did not mention Loving v. Virginia, seeing as it was made around the same time as Roe v. Wade, based on very similar principles—and it affects him personally. And even if these precedents are unlikely to be overturned immediately, this ruling shows that the security of all of our rights can depend on the particular inclinations of individual justices.

The Supreme Court is honestly a terrible institution. Courts should not be more powerful than legislatures, lifetime appointments reek of monarchism, and the claim of being ‘apolitical’ that was dubious from the start is now obviously ludicrous. But precisely because it is so powerful, reforming it will be extremely difficult.

The first step is to pack the court. The question is no longer whether we should pack the court, but how, and why we didn’t do it sooner.

What does it mean to pack the court? Increase the number of justices, appointing new ones who are better than the current ones. (Since almost any randomly-selected American would be better than Clarence Thomas, Samuel Alito, or Brent Kavanaugh, this wouldn’t be hard.) This is 100% Constitutional, as the Constitution does not in any way restrict the number of justices. It can simply be done by an act of Congress.

But of course we can’t stop there. President Biden could appoint four more justices, and then whoever comes after him could appoint another three, and before we know it the Supreme Court has twenty-seven justices and each new President is expected to add a few more.

No, we need to fix the number of justices so that it can’t be increased any further. Ideally this would be done by Constitutional Amendment, though the odds of getting such a thing passed seem rather slim. But there is in fact a sensible way to add new justices now and then justify not adding any more later, and that is to tie justices to federal circuits.

There are currently 13 US federal circuit courts. If we added 4 more Supreme Court justices, there would be 13 Supreme Court justices. Each could even be assigned to be the nominal head of that federal circuit, and responsible for being the first to read appeals coming from that circuit.

Which justice goes where? Well, what if we let the circuits themselves choose? The selection could be made by a popular vote among the people who live there. Make the federal circuit a federal popular vote. The justice responsible for the federal circuit can also be the Chief Justice.

That would also require a Constitutional Amendment, but it would, at a stroke, fundamentally reform what the Supreme Court is and how its justices are chosen. For now, we could simply add three new justices, making the current number 13. Then they could decide amongst themselves who will get what circuit until we implement the full system to let circuits choose their justices.

I’m well aware that electing judges is problematic—but at this point I don’t think we have a choice. (I would also prefer to re-arrange the circuits: it’s weird that DC gets its own circuit instead of being part of circuit 4, and circuit 9 has way more people than circuit 1.) We can’t simply trust each new President to appoint a new justice whenever one happens to retire or die and then leave that justice in place for decades to come. Not in a world where someone like Donald Trump can be elected President.

A lot of centrist people are uncomfortable with such a move, seeing it as ‘playing dirty’. But it’s not. It’s playing hardball—taking seriously the threat that the current Republican Party poses to the future of American government and society, and taking substantive steps to fight that threat. (After its authoritarian shift that started in the mid 2000s but really took off under Trump, the Republican Party now has more in common with far-right extremist parties like Fidesz in Hungary than with mainstream center-right parties like the Tories.) But there is absolutely nothing un-Constitutional about this plan. It’s doing everything possible within the law.

We should have done this before they started overturning landmark precedents. But it’s not too late to do it before they overturn any more.

Why copyrights should be shorter

Jul 3 JDN 2459783

The copyright protection for Mickey Mouse is set to expire in 2024, though a recently-proposed bill that specifically targets large corporations would cause it to end immediately. Steamboat Willie was released in 1928.

This means that Mickey Mouse has been under copyright protection for 94 years, and is scheduled to last 96. Let me remind you that Walt Disney has been dead since 1966. This is, quite frankly, ridiculous. Mickey Mouse should have been released into the public domain decades ago.

Copyright in general has quite a shaky justification, and there are those who argue that it should be eliminated entirely. There’s something profoundly weird—and fundamentally monopolistic—about banning people from copying things.

But clearly we do need some way of ensuring that creators of artistic works can be fairly compensated for their efforts. Copyright is not the only way to do that: A few alternatives that I think are worth considering are expanded crowdfunding (Patreon and Kickstart already support quite a few artists, though most not very much), a large basic income (artists would still create even if they weren’t paid; they really just need money to live on), government grants directly to artists (we have the National Endowment for the Arts, but it doesn’t support very many artists), and some kind of central clearinghouse that surveys consumers about the art they enjoy and then compensates artists according to how much their work is appreciated. But all of these would require substantial changes, and suffer from their own flaws, so for the time being, let’s say we stick with copyright.

Even so, it’s utterly ludicrous that Disney has managed to hold onto the copyright on Mickey Mouse for this long. It makes absolutely no sense from the perspective of supporting artists—indeed, in this case the artist has been dead for over 50 years.

In fact, it wouldn’t even make sense if Walt Disney were still alive. (Not many people live 96 years past their first highly-successful creative work, but it’s at least possible, if you say published as a child and then lived to be a centenarian.) If the goal is to incentivize new creative art, the first few decades—indeed, the first few years—are clearly the most important for doing so.

To show why this is, I need to take a brief detour into finance, and the concept of a net present value.

As the saying goes: Time is money. $1 today is worth more than $1 a year from now. (And if you doubt this, let me remind you of the old joke: “I’ll give you $1 million dollars if you give me $100! Such a deal! Give me the $100 today, and I’ll give you $1 per year for the next million years.”)

The idea of a net present value is to precisely quantify the monetary value of time (or the time value of money), so that we can compare cashflows over time in a directly comparable way.

To compute a net present value, you need a discount rate. At a discount rate of r, an amount of money X that you get 1 year from now is worth X/(1+r). The discount rate should be positive, because money later is worth less than money now; this means that we want X/(1+r) < X, and therefore r > 0.

This is surprisingly hard to get precisely, but relatively easy to ballpark. A good guess is that it’s somewhere close to the prevailing interest rate, or maybe the average return on the stock market. It should definitely be at least the inflation rate. Right now inflation is running a little high (around 8%), so we’d want to use a relatively high discount rate currently, maybe 10% or 12%. But I think in a more typical scenario, something more like 5-6% would be a reasonable guess.

Once you have a discount rate, it’s pretty simple to figure out the net present value: Just add up all the future cashflows, each discounted by that discount rate for the time you have to wait for it.

So for instance if you get $100 per year for the next 5 years, this would be your net present value:

100/(1+r) + 100/(1+r)^2 + 100/(1+r)^3 + 100/(1+r)^4 + 100/(1+r)^5

If you get $50 this year, $60 next year, $70 the year after that, this would be your next present value:

50 + 60/(1+r) + 70/(1+r)^2

If the cashflow is the same X over time for some fixed amount of time T this can be collapsed into a single formula using a geometric series:

X (1 – (1+r)^(-T)) – 1)/r

This is really just a more compact way of adding up, X + X/(1+r) + X/(1+r)^2 + …; here, let’s do that example of $100 per year for 5 years, with r = 10%.

100/1.1 + 100/1.1^2 + 100/1.1^3 + 100/1.1^4 + 100/1.1^5 = $379

100 (1 – 1.1^(-5))/0.1 = $379

See, we get the same answer either way. Notice that this is less than $100 * 5 = $500, which is what we’d get if we had assumed that $1 a year from now is worth the same as $1 today. But it’s not too much less, because it’s only 5 years.

This formula allows us to consider what happens when the time interval becomes extremely long—even infinite. It gives us the power to ask the question, “What is the value of this perpetual cashflow?”

This feels a bit weird for individuals, since of course we die. We can have heirs, but rare indeed is the thousand-year dynasty. (The Imperial House of Japan does appear to have an unbroken hereditary line for the last 2000 years, but they’re basically alone in that.) But governments and corporations don’t have a lifespan, so it makes more sense for them. The US government was here 200 years ago, and may still be here 200 years from now. Oxford was here 900 years ago, and I see no particular reason to think it won’t still be here 900 years from now.

Since r > 0, (1+r)^(-T) gets smaller as T increases. As T approaches infinity, (1+r)^(-T) approaches zero. So for a perpetual cashflow, we can just make this term zero.

Thus, we can actually assess the value of $1 per year for the next million years! It is this:

1 (1-(1+r)^(10^6))/r

which is basically the same as this:


So if your discount rate is 10%, then $1 per year for 1 million years is worth about as much to you as $1/0.1 = $10 today. If your discount rate is 5%, it would be worth about $1/0.05 = $20 today. And suddenly it makes sense that you’re not willing to pay $100 for this deal.

What if the cashflow is changing? Then this formula won’t work. But if it’s simply a constant rate of growth, we can adjust for that. If the growth rate of the cashflow is g, so that you get X, then X (1+g), then x (1+g)^2, and so on, the formula becomes just a bit more complicated:

X (1-(1+r-g)^(-T))/(r-g)

So for instance if your cashflow grows at 6% per year and your discount rate is 10%, then it’s basically the same as if it didn’t grow at all but your discount rate is 4%. [This is actually an approximation, but it’s a pretty good one.] Let’s call this the effective discount rate.

For a perpetual cashflow, as long as r > g, this becomes:


With this in mind, let’s return to the question of copyright. How long should copyright protection last?

We want it to last long enough for artists to be fairly compensated for their work; but what does “fairly compensated” mean? Well, with the concept of a perpetual net present value in mind, we could quantify this as the majority of all revenue that would be expected to be earned by a perpetual copyright.

I think this is actually quite generous: We’re saying that you should get to keep the copyright long enough to get most of what you’d probably get if we allowed you to own it forever. In some cases this might actually result in a copyright that’s too long; but I don’t see how it could result in it being too short.

Mickey Mouse today earns about $3 million per year. That’s honestly amazing, to continue to rake in that much money after such a long period. But, adjusted for inflation, that’s actually quite a bit less than what he took in just a few years after his first films were released, nominally $1 million per year which comes to more like $19 million per year in today’s money.

This means that our discount rate is larger than our growth rate (r > g) even if r is just inflation; but in fact we should use a discount rate higher than inflation. Let’s use a plausible but slightly conservative discount rate of 5%.

To grow from nominally $1 million to nominally $3 million per year in 94 years means a growth rate of about 1% per year.

So, our effective discount rate is 4%.

Then, a perpetual copyright for Mickey Mouse should be worth approximately:

X/(r-g) = 10^6/(0.04) = $25 million

Yes, that’s right; an unending stream of over $1 million per year ends up being worth about the same as a single payment of $25 million way back in 1928.

But isn’t Mickey Mouse a “fictional billionare”, meaning his total income over his existence has been more than $1 billion? Sure. And indeed, at a discount rate of 5%, $1 billion today is worth about $10 million in 1928. So Mickey is indeed well above that. Even if I use Forbes’ higher estimate that Mickey Mouse has taken in $5.8 billion, that would still only be a net present value of $59 million in 1928.

Remember, time is money. When it takes this long to get a cashflow, it ends up worth substantially less.

So, if we were aiming to let Mickey earn half of his perpetual earnings in net present value, when should we have ended his copyright? By my estimate, when the net present value of earnings exceeded $12.5 million. If we use Forbes’s more generous estimate, when it exceeded $30 million.

So now let’s go back to the formula for a finite time horizon, and try to solve it for T, the time horizon. We want the net present value of the finite horizon to be half that of the infinite horizon:

X (1-(1+r-g)^(-T))/(r-g) = (X/2)/(r-g)

(1+r-g)^(-T) = 1/2

To solve this for T, I’ll need to use a logarithm, the inverse of an exponent.

T = ln(2)/ln(1+r – g)

This is a doubling time, very analogous to a half-life in physics. Since logarithms are very difficult to do by hand, if you don’t have a scientific calculator handy, you can also approximate it by dividing the percentage into 69:

T = 69/(r-g)%

This is because ln(2) = 0.69…, and when r-g is a small percentage, ln(1+r-g) is about the same as r-g.

For an effective discount rate of 4%, this becomes:

T = ln(2)/ln(1.04) = 69/4 = 17

That is, only seventeen years. Even for a hugely successful long-running property like Mickey Mouse (in fact, is there really anything on a par with Mickey Mouse?), the majority of the net present value was earned in less than 20 years.

Indeed, it seems especially sensible in this case, because back then, Walt Disney was still alive! He could actually enjoy the fruits of his labors for that period. Now it’s all going to some faceless shareholders of a massive megacorporation, only a few of which are even Walt Disney’s heirs. Only about 3% of Disney shares are owned by anyone actually in the Disney family.

This gives us an answer to the question, “How long should copyrights last?”: About 20 years.

If we’d used a higher discount rate, it would be even shorter: at 10%, you get only 10 years.

And a lower discount rate simply isn’t plausible; inflation and stock market growth are both too fast for net present value to be discounted much less than 4% or 5%. Maybe you could go as low as 3%, which would be 23 years.

Does this accomplish the goal of copyrights—which, remember, was to fairly compensate artists and incentivize the creation of artistic works? I’d say so. They get half of what they would have gotten if we never released their work into the public domain, and I don’t think I’ve ever met an artist who could honestly say that they’d create something if they could hold onto the rights for 96 years, but not if they could for only 20 years. (Maybe they exist, but if so, they are rare.) Most artists really just want to be credited—not paid, credited—for their work and to make a decent living. 20 years is enough for that.

This means that our current copyright system keeps works out of public domain nearly five times as long as there is any real economic justification for.