# Against “doing your best”

Oct 3 JDN 2459491

It’s an appealing sentiment: Since we all have different skill levels, rather than be held to some constant standard which may be easy for some but hard for others, we should each do our best. This will ensure that we achieve the best possible outcome.

Yet it turns out that this advice is not so easy to follow: What is “your best”?

Is your best the theoretical ideal of what your performance could be if all obstacles were removed and you worked at your greatest possible potential? Then no one in history has ever done their best, and when people get close, they usually end up winning Nobel Prizes.

Is your best the performance you could attain if you pushed yourself to your limit, ignored all pain and fatigue, and forced yourself to work at maximum effort until you literally can’t anymore? Then doing your best doesn’t sound like such a great thing anymore—and you’re certainly not going to be able to do it all the time.

Is your best the performance you would attain by continuing to work at your usual level of effort? Then how is that “your best”? Is it the best you could attain if you work at a level of effort that is considered standard or normative? Is it the best you could do under some constraint limiting the amount of pain or fatigue you are willing to bear? If so, what constraint?

How does “your best” change under different circumstances? Does it become less demanding when you are sick, or when you have a migraine? What if you’re depressed? What if you’re simply not feeling motivated? What if you can’t tell whether this demotivation is a special circumstance, a depression system, a random fluctuation, or a failure to motivate yourself?

There’s another problem: Sometimes you really aren’t good at something.

A certain fraction of performance in most tasks is attributable to something we might call “innate talent”; be it truly genetic or fixed by your early environment, it nevertheless is something that as an adult you are basically powerless to change. Yes, you could always train and practice more, and your performance would thereby improve. But it can only improve so much; you are constrained by your innate talent or lack thereof. No amount of training effort will ever allow me to reach the basketball performance of Michael Jordan, the painting skill of Leonardo Da Vinci, or the mathematical insight of Leonhard Euler. (Of the three, only the third is even visible from my current horizon. As someone with considerable talent and training in mathematics, I can at least imagine what it would be like to be as good as Euler—though I surely never will be. I can do most of the mathematical methods that Euler was famous for; but could I have invented them?)

In fact it’s worse than this; there are levels of performance that would be theoretically possible for someone of your level of talent, yet would be so costly to obtain as to be clearly not worth it. Maybe, after all, there is some way I could become as good a mathematician as Euler—but if it would require me to work 16-hour days doing nothing but studying mathematics for the rest of my life, I am quite unwilling to do so.

With this in mind, what would it mean for me to “do my best” in mathematics? To commit those 16-hour days for the next 30 years and win my Fields Medal—if it doesn’t kill me first? If that’s not what we mean by “my best”, then what do we mean, after all?

Perhaps we should simply abandon the concept, and ask instead what successful people actually do.

This will of course depend on what they were successful at; the behavior of basketball superstars is considerably different from the behavior of Nobel Laureate physicists, which is in turn considerably different from the behavior of billionaire CEOs. But in theory we could each decide for ourselves which kind of success we actually would desire to emulate.

Another pitfall to avoid is looking only at superstars and not comparing them with a suitable control group. Every Nobel Laureate physicist eats food and breathes oxygen, but eating food and breathing oxygen will not automatically give you good odds of winning a Nobel (though I guess your odds are in fact a lot better relative to not doing them!). It is likely that many of the things we observe successful people doing—even less trivial things, like working hard and taking big risks—are in fact the sort of thing that a great many people do with far less success.

Upon making such a comparison, one of the first things that we would notice is that the vast majority of highly-successful people were born with a great deal of privilege. Most of them were born rich or at least upper-middle-class; nearly all of them were born healthy without major disabilities. Yes, there are exceptions to any particular form of privilege, and even particularly exceptional individuals who attained superstar status with more headwinds than tailwinds; but the overwhelming pattern is that people who get home runs in life tend to be people who started the game on third base.

But setting that aside, or recalibrating one’s expectations to try to attain a level of success often achieved by people with roughly the same level of privilege as oneself, we must ask: How often? Should you aspire to the median? The top 20%? The top 10%? The top 1%? And what is your proper comparison group? Should I be comparing against Americans, White male Americans, economists, queer economists, people with depression and chronic migraines, or White/Native American male queer economists with depression and chronic migraines who are American expatriates in Scotland? Make the criteria too narrow, and there won’t be many left in your sample. Make them instead too broad, and you’ll include people with very different circumstances who may not be a fair comparison. Perhaps some sort of weighted average of different groups could work—but with what weighting?

Or maybe it’s right to compare against a very broad group, since this is what ultimately decides our life prospects. What it would take to write the best novel you (or someone “like you” in whatever sense that means) can write may not be the relevant question: What you really needed to know was how likely it is that you could make a living as a novelist.

The depressing truth in such a broad comparison is that you may in fact find yourself faced with so many obstacles that there is no realistic path toward the level of success you were hoping for. If you are reading this, I doubt matters are so dire for you that you’re at serious risk of being homeless and starving—but there definitely are people in this world, millions of people, for whom that is not simply a risk but very likely the best they can hope for.

The question I think we are really trying to ask is this: What is the right standard to hold ourselves against?

Unfortunately, I don’t have a clear answer to this question. I have always been an extremely ambitious individual, and I have inclined toward comparisons with the whole world, or with the superstars of my own fields. It is perhaps not surprising, then, that I have consistently failed to live up to my own expectations for my own achievement—even as I surpass what many others expected for me, and have long-since left behind what most people expect for themselves and each other.

I would thus not exactly recommend my own standards. Yet I also can’t quite bear to abandon them, out of a deep-seated fear that it is only by holding myself to the patently unreasonable standard of trying to be the next Einstein or Schrodinger or Keynes or Nash that I have even managed what meager achievements I have made thus far.

Of course this could be entirely wrong: Perhaps I’d have achieved just as much if I held myself to a lower standard—or I could even have achieved more, by avoiding the pain and stress of continually failing to achieve such unattainable heights. But I also can’t rule out the possibility that it is true. I have no control group.

In general, what I think I want to say is this: Don’t try to do your best. You have no idea what your best is. Instead, try to find the highest standard you can consistently meet.

# Escaping the wrong side of the Yerkes-Dodson curve

Jul 25 JDN 2459421

I’ve been under a great deal of stress lately. Somehow I ended up needing to finish my dissertation, get married, and move overseas to start a new job all during the same few months—during a global pandemic.

A little bit of stress is useful, but too much can be very harmful. On complicated tasks (basically anything that involves planning or careful thought), increased stress will increase performance up to a point, and then decrease it after that point. This phenomenon is known as the Yerkes-Dodson law.

The Yerkes-Dodson curve very closely resembles the Laffer curve, which shows that since extremely low tax rates raise little revenue (obviously), and extremely high tax rates also raise very little revenue (because they cause so much damage to the economy), the tax rate that maximizes government revenue is actually somewhere in the middle. There is a revenue-maximizing tax rate (usually estimated to be about 70%).

Instead of a revenue-maximizing tax rate, the Yerkes-Dodson law says that there is a performance-maximizing stress level. You don’t want to have zero stress, because that means you don’t care and won’t put in any effort. But if your stress level gets too high, you lose your ability to focus and your performance suffers.

Since stress (like taxes) comes with a cost, you may not even want to be at the maximum point. Performance isn’t everything; you might be happier choosing a lower level of performance in order to reduce your own stress.

But once thing is certain: You do not want to be to the right of that maximum. Then you are paying the cost of not only increased stress, but also reduced performance.

And yet I think many of us spent a great deal of our time on the wrong side of the Yerkes-Dodson curve. I certainly feel like I’ve been there for quite awhile now—most of grad school, really, and definitely this past month when suddenly I found out I’d gotten an offer to work in Edinburgh.

My current circumstances are rather exceptional, but I think the general pattern of being on the wrong side of the Yerkes-Dodson curve is not.

The World Health Organization lists “work-related stress” as one of its top concerns. Over 70% of people in a cross-section of countries report physical symptoms related to stress, a rate which has significantly increased since before the pandemic.

The pandemic is clearly a contributing factor here, but even without it, there seems to be an awful lot of stress in the world. Even back in 2018, over half of Americans were reporting high levels of stress. Why?

For once, I think it’s actually fair to blame capitalism.

One thing capitalism is exceptionally good at is providing strong incentives for work. This is often a good thing: It means we get a lot of work done, so employment is high, productivity is high, GDP is high. But it comes with some important downsides, and an excessive level of stress is one of them.

But this can’t be the whole story, because if markets were incentivizing us to produce as much as possible, that ought to put us near the maximum of the Yerkes-Dodson curve—but it shouldn’t put us beyond it. Maximizing productivity might not be what makes us happiest—but many of us are currently so stressed that we aren’t even maximizing productivity.

I think the problem is that competition itself is stressful. In a capitalist economy, we aren’t simply incentivized to do things well—we are incentivized to do them better than everyone else. Often quite small differences in performance can lead to large differences in outcome, much like how a few seconds can make the difference between an Olympic gold medal and an Olympic “also ran”.

An optimally productive economy would be one that incentivizes you to perform at whatever level maximizes your own long-term capability. It wouldn’t be based on competition, because competition depends too much on what other people are capable of. If you are not especially talented, competition will cause you great stress as you try to compete with people more talented than you. If you happen to be exceptionally talented, competition won’t provide enough incentive!

Here’s a very simple model for you. Your total performance p is a function of two components, your innate ability aand your effort e. In fact let’s just say it’s a sum of the two: p = a + e

People are randomly assigned their level of capability from some probability distribution, and then they choose their effort. For the very simplest case, let’s just say there are two people, and it turns out that person 1 has less innate ability than person 2, so a1 < a2.

There is also a certain amount of inherent luck in any competition. As it says in Ecclesiastes (by far the best book of the Old Testament), “The race is not to the swift or the battle to the strong, nor does food come to the wise or wealth to the brilliant or favor to the learned; but time and chance happen to them all.” So as usual I’ll model this as a contest function, where your probability of winning depends on your total performance, but it’s not a sure thing.

Let’s assume that the value of winning and cost of effort are the same across different people. (It would be simple to remove this assumption, but it wouldn’t change much in the results.) The value of winning I’ll call y, and I will normalize the cost of effort to 1.

Then this is each person’s expected payoff ui:

ui = (ai + ei)/(a1+e1+a2 + e2) V – ei

You choose effort, not ability, so maximize in terms of ei:

(a2 + e2) V = (a1 +e1+a2 + e2)2 = (a1 + e1) V

a1 + e1 = a2 + e2

p1 = p2

In equilibrium, both people will produce exactly the same level of performance—but one of them will be contributing more effort to compensate for their lesser innate ability.

I’ve definitely had this experience in both directions: Effortlessly acing math tests that I knew other people barely passed despite hours of studying, and running until I could barely breathe to keep up with other people who barely seemed winded. Clearly I had too little incentive in math class and too much in gym class—and competition was obviously the culprit.

If you vary the cost of effort between people, or make it not linear, you can make the two not exactly equal; but the overall pattern will remain that the person who has more ability will put in less effort because they can win anyway.

Yet presumably the amount of effort we want to incentivize isn’t less for those who are more talented. If anything, it may be more: Since an hour of work produces more when done by the more talented person, if the cost to them is the same, then the net benefit of that hour of work is higher than the same hour of work by someone less talented.

In a large population, there are almost certainly many people whose talents are similar to your own—but there are also almost certainly many below you and many above you as well. Unless you are properly matched with those of similar talent, competition will systematically lead to some people being pressured to work too hard and others not pressured enough.

But if we’re all stressed, where are the people not pressured enough? We see them on TV. They are celebrities and athletes and billionaires—people who got lucky enough, either genetically (actors who were born pretty, athletes who were born with more efficient muscles) or environmentally (inherited wealth and prestige), to not have to work as hard as the rest of us in order to succeed. Indeed, we are constantly bombarded with images of these fantastically lucky people, and by the availability heuristic our brains come to assume that they are far more plentiful than they actually are.

This dramatically exacerbates the harms of competition, because we come to feel that we are competing specifically with the people who were handed the world on a silver platter. Born without the innate advantages of beauty or endurance or inheritance, there’s basically no chance we could ever measure up; and thus we feel utterly inadequate unless we are constantly working as hard as we possibly can, trying to catch up in a race in which we always fall further and further behind.

How can we break out of this terrible cycle? Well, we could try to replace capitalism with something like the automated luxury communism of Star Trek; but this seems like a very difficult and long-term solution. Indeed it might well take us a few hundred years as Roddenberry predicted.

In the shorter term, we may not be able to fix the economic problem, but there is much we can do to fix the psychological problem.

By reflecting on the full breadth of human experience, not only here and now, but throughout history and around the world, you can come to realize that you—yes, you, if you’re reading this—are in fact among the relatively fortunate. If you have a roof over your head, food on your table, clean water from your tap, and ibuprofen in your medicine cabinet, you are far more fortunate than the average person in Senegal today; your television, car, computer, and smartphone are things that would be the envy even of kings just a few centuries ago. (Though ironically enough that person in Senegal likely has a smartphone, or at least a cell phone!)

Likewise, you can reflect upon the fact that while you are likely not among the world’s most very most talented individuals in any particular field, there is probably something you are much better at than most people. (A Fermi estimate suggests I’m probably in the top 250 behavioral economists in the world. That’s probably not enough for a Nobel, but it does seem to be enough to get a job at the University of Edinburgh.) There are certainly many people who are less good at many things than you are, and if you must think of yourself as competing, consider that you’re also competing with them.

Yet perhaps the best psychological solution is to learn not to think of yourself as competing at all. So much as you can afford to do so, try to live your life as if you were already living in a world that rewards you for making the best of your own capabilities. Try to live your life doing what you really think is the best use of your time—not your corporate overlords. Yes, of course, we must do what we need to in order to survive, and not just survive, but indeed remain physically and mentally healthy—but this is far less than most First World people realize. Though many may try to threaten you with homelessness or even starvation in order to exploit you and make you work harder, the truth is that very few people in First World countries actually end up that way (it couldbe brought to zero, if our public policy were better), and you’re not likely to be among them. “Starving artists” are typically a good deal happier than the general population—because they’re not actually starving, they’ve just removed themselves from the soul-crushing treadmill of trying to impress the neighbors with manicured lawns and fancy SUVs.

Jun 20 JDN 2459386

Minimum wage. Environmental regulations. Worker safety. Even bans on child slavery.No matter what the regulation is, it seems that businesses will always oppose it, always warn that these new regulations will destroy their business and leave thousands out of work—and always be utterly, completely wrong.

In fact, the overall impact of US federal government regulations on employment is basically negligible, and the impact on GDP is very clearly positive. This really isn’t surprising if you think about it: Despite what some may have you believe, our government doesn’t go around randomly regulating things for no reason. The regulations we impose are specifically chosen because their benefits outweighed their costs, and the rigorous, nonpartisan analysis of our civil service is one of the best-kept secrets of American success and the envy of the world.

But when businesses are so consistently insistent that new regulations (of whatever kind, however minor or reasonable they may be) will inevitably destroy their industry—when such catastrophic outcomes have basically never occurred, that cries out for an explanation. How can such otherwise competent, experienced, knowledgeable people be always so utterly wrong about something so basic? These people are experts in what they do. Shouldn’t business owners know what would happen if we required them to raise wages a little, or require basic safety standards, or reduce pollution caps, or not allow their suppliers to enslave children?

Well, what do you mean by “them”? Herein lies the problem. There is a fundamental difference between what would happen if we required any specific business to comply with a new regulation (but left their competitors exempt), versus what happens if we require an entire industry to comply with that same regulation.

Business owners are accustomed to thinking in an open system, what economists call partial equilibrium: They think about how things will affect them specifically, and not how they will affect broader industries or the economy as a whole. If wages go up, they’ll lay off workers. If the price of their input goes down, they’ll buy more inputs and produce more outputs. They aren’t thinking about how these effects interact with one another at a systemic level, because they don’t have to.

This works because even a huge multinational corporation is only a small portion of the US economy, and doesn’t have much control over the system as a whole. So in general when a business tries to maximize its profit in partial equilibrium, it tends to get the right answer (at least as far as maximizing GDP goes).

But large-scale regulation is one time where we absolutely cannot do this. If we try to analyze federal regulations purely in partial equilibrium terms, we will be consistently and systematically wrong—as indeed business owners are.

If we went to a specific corporation and told them, “You must pay your workers $2 more per hour.”, what would happen? They would be forced to lay off workers. No doubt about it. If we specifically targeted one particular corporation and required them to raise their wages, they would be unable to compete with other businesses who had not been forced to comply. In fact, they really might go out of business completely. This is the panic that business owners are expressing when they warn that even really basic regulations like “You can’t dump toxic waste in our rivers” or “You must not force children to pick cocoa beans for you” will cause total economic collapse. But when you regulate an entire industry in this way, no such dire outcomes happen. The competitors are also forced to comply, and so no businesses are given special advantages relative to one another. Maybe there’s some small reduction in employment or output as a result, but at least if the regulation is reasonably well-planned—as virtually all US federal regulations are, by extremely competent people—those effects will be much smaller than the benefits of safer workers, or cleaner water, or whatever was the reason for the regulation in the first place. Think of it this way. Businesses are in a constant state of fierce, tight competition. So let’s consider a similarly tight competition such as the Olympics. The gold medal for the 100-meter sprint is typically won by someone who runs the whole distance in less than 10 seconds. Suppose we had told one of the competitors: “You must wait an extra 3 seconds before starting.” If we did this to one specific runner, that runner would lose. With certainty. There has never been an Olympic 100-meter sprint where the first-place runner was more than 3 seconds faster than the second-place runner. So it is basically impossible for that runner to ever win the gold, simply because of that 3-second handicap. And if we imposed that constraint on some runners but not others, we would ensure that only runners without the handicap had any hope of winning the race. But now suppose we had simply started the competition 3 seconds late. We had a minor technical issue with the starting gun, we fixed it in 3 seconds, and then everything went as normal. Basically no one would notice. The winner of the race would be the same as before, all the running times would be effectively the same. Things like this have almost certainly happened, perhaps dozens of times, and no one noticed or cared. It’s the same 3-second delay, but the outcome is completely different. The difference is simple but vital: Are you imposing this constraint on some competitors, or on all competitors? A constraint imposed on some competitors will be utterly catastrophic for those competitors. A constraint imposed on all competitors may be basically unnoticeable to all involved. Now, with regulations it does get a bit more complicated than that: We typically can’t impose regulations on literally everyone, because there is no global federal government with the authority to do that. Even international human rights law, sadly, is not that well enforced. (International intellectual property lawvery nearly is—and that contrast itself says something truly appalling about our entire civilization.) But when regulation is imposed by a large entity like the United States (or even the State of California), it generally affects enough of the competitors—and competitors who already had major advantages to begin with, like the advanced infrastructure, impregnable national security, and educated population of the United States—that the effects on competition are, if not negligible, at least small enough to be outweighed by the benefits of the regulation. So, whenever we propose a new regulation and business owners immediately panic about its catastrophic effects, we can safely ignore them. They do this every time, and they are always wrong. But take heed: Economists are trained to think in terms of closed systems and general equilibrium. So if economists are worried about the outcome of a regulation, then there is legitimate reason to be concerned. It’s not that we know better how to run their businesses—we certainly don’t. Rather, we much better understand the difference between imposing a 3-second delay on a single runner versus simply starting the whole race 3 seconds later. # Hyper-competition Dec13 JDN 2459197 This phenomenon has been particularly salient for me the last few months, but I think it’s a common experience for most people in my generation: Getting a job takes an awful lot of work. Over the past six months, I’ve applied to over 70 different positions and so far gone through 4 interviews (2 by video, 2 by phone). I’ve done about 10 hours of test work. That so far has gotten me no offers, though I have yet to hear from 50 employers. Ahead of me I probably have about another 10 interviews, then perhaps 4 of what would have been flyouts and in-person presentations but instead will be “comprehensive interviews” and presentations conducted online, likely several more hours of test work, and then finally, maybe, if I’m lucky, I’ll get a good offer or two. If I’m unlucky, I won’t, and I’ll have to stick around for another year and do all this over again next year. Aside from the limitations imposed by the pandemic, this is basically standard practice for PhD graduates. And this is only the most extreme end of a continuum of intensive job search efforts, for which even applying to be a cashier at Target requires a formal application, references, and a personality test. This wasn’t how things used to be. Just a couple of generations ago, low-wage employers would more or less hire you on the spot, with perhaps a resume or a cursory interview. More prestigious employers would almost always require a CV with references and an interview, but it more or less stopped there. I discussed in an earlier post how much of the difference actually seems to come from our chronic labor surplus. Is all of this extra effort worthwhile? Are we actually fitting people to better jobs this way? Even if the matches are better, are they enough better to justify all this effort? It is a commonly-held notion among economists that competition in markets is good, that it increases efficiency and improves outcomes. I think that this is often, perhaps usually, the case. But the labor market has become so intensely competitive, particularly for high-paying positions, that the costs of this competitive effort likely outweigh the benefits. How could this happen? Shouldn’t the free market correct for such an imbalance? Not necessarily. Here is a simple formal model of how this sort of intensive competition can result in significant waste. Note that this post is about a formal mathematical model, so it’s going to use a lot of algebra. If you are uninterested in such things, you can read the next two paragraphs and then skip to the conclusions at the end. The overall argument is straightforward: If candidates are similar in skill level, a complicated application process can make sense from a firm’s perspective, but be harmful from society’s perspective, due to the great cost to the applicants. This can happen because the difficult application process imposes an externality on the workers who don’t get the job. All right, here is where the algebra begins. I’ve included each equation as both formatted text and LaTeX. Consider a competition between two applicants, X and Z. They are each asked to complete a series of tasks in an application process. The amount of effort X puts into the application is x, and the amount of effort Z puts into the application is z. Let’s say each additional bit of effort has a fixed cost, normalized to 1. Let’s say that their skills are similar, but not identical; this seems quite realistic. X has skill level hx, and Z has skill level hz. Getting hired has a payoff for each worker of V. This includes all the expected benefits of the salary, benefits, and working conditions. I’ll assume that these are essentially the same for both workers, which also seems realistic. The benefit to the employer is proportional to the worker’s skill, so letting h be the skill level of the actually hired worker, the benefit of hiring that worker is hY. The reason they are requiring this application process is precisely because they want to get the worker with the highest h. Let’s say that this application process has a cost to implement, c. Who will get hired? Well, presumably whoever does better on the application. The skill level will amplify the quality of their output, let’s say proportionally to the effort they put in; so X’s expected quality will be hxx and Z’s expected output will be hzz. Let’s also say there’s a certain amount of error in the process; maybe the more-qualified candidate will sleep badly the day of the interview, or make a glaring and embarrassing typo on their CV. And quite likely the quality of application output isn’t perfectly correlated with the quality of actual output once hired. To capture all this, let’s say that having more skill and putting in more effort only increases your probability of getting the job, rather than actually guaranteeing it. In particular, let’s say that the probability of X getting hired is P[X] = hxx/(hxx + hzz). $P[X] = \frac{h_x}{h_x x + h_z z}$ This results in a contest function, a type of model that I’ve discussed in some earlier posts in a rather different context. The expected payoff for worker X is: E[Ux] = hxx/(hxx + hzz) V – x $E[U_x] = \frac{h_x x}{h_x x + h_z z} V – x$ Maximizing this with respect to the choice of effort x (which is all that X can control at this point) yields: hxhzz V = (hxx + hzz)2 $h_x h_z x V = (h_x x + h_z z)^2$ A similar maximization for worker Z yields: hxhzx V = (hxx + hzz)2 $h_x h_z z V = (h_x x + h_z z)^2$ It follows that x=z, i.e. X and Z will exert equal efforts in Nash equilibrium. Their probability of success will then be contingent entirely on their skill levels: P[X] = hx/(hx + hz). $P[X] = \frac{h_x}{h_x + h_y}$ Substituting that back in, we can solve for the actual amount of effort: hxhzx V = (hx + hz)2x2 $h_x h_z x V = (h_x + h_z)^2 x^2$ x = hxhzV/(hx + hz)2 $x = \frac{h_x h_z}{h_x + h_z} V$ Now let’s see what that gives for the expected payoffs of the firm and the workers. This is worker X’s expected payoff: E[Ux] = hx/(hx + hz) V – hxhzV/(hx + hz)2 = (hx/(hx + hz))2 V $E[U_x] = \frac{h_x}{h_x + h_z} V – \frac{h_x h_z}{(h_x + h_z)^2} V = \left( \frac{h_x}{h_x + h_z}\right)^2 V$ Worker Z’s expected payoff is the same, with hx and hz exchanged: E[Uz] = (hz/(hx + hz))2 V $E[U_z] = \left( \frac{h_z}{h_x + h_z}\right)^2 V$ What about the firm? Their expected payoff is the the probability of hiring X, times the value of hiring X, plus the probability of hiring Z, times the value of hiring Z, all minus the cost c: E[Uf] = hx/(hx + hz) hx Y + hz/(hx + hz) hz Y – c= (hx2 + hz2)/(hx + hz) Y – c $E[U_f] = \frac{h_x}{h_x + h_z} h_x Y + \frac{h_z}{h_x + h_z} h_z Y – c = \frac{h_x^2 + h_z^2}{h_x + h_z} Y – c$ To see whether the application process was worthwhile, let’s compare against the alternative of simply flipping a coin and hiring X or Z at random. The probability of getting hired is then 1/2 for each candidate. Expected payoffs for X and Z are now equal: E[Ux] = E[Uz] = V/2 $E[U_x] = E[U_z] = \frac{V}{2}$ The expected payoff for the firm can be computed the same as before, but now without the cost c: E[Uf] = 1/2 hx Y + 1/2 hz Y = (hx + hz)/2 Y $E[U_f] = \frac{1}{2} h_x Y + \frac{1}{2} h_z Y = \frac{h_x + h_z}{2} Y$ This has a very simple interpretation: The expected value to the firm is just the average quality of the two workers, times the overall value of the job. Which of these two outcomes is better? Well, that depends on the parameters, of course. But in particular, it depends on the difference between hx and hz. Consider two extremes: In one case, the two workers are indistinguishable, and hx = hz = h. In that case, the payoffs for the hiring process reduce to the following: E[Ux] = E[Uz] = V/4 $E[U_x] = E[U_z] = \frac{V}{4}$ E[Uf] = h Y – c $E[U_f] = h Y – c$ Compare this against the payoffs for hiring randomly: E[Ux] = E[Uz] = V/2 $E[U_x] = E[U_z] = \frac{V}{2}$ E[Uf] = h Y $E[U_f] = h Y$ Both the workers and the firm are strictly better off if the firm just hires at random. This makes sense, since the workers have identical skill levels. Now consider the other extreme, where one worker is far better than the other; in fact, one is nearly worthless, so hz ~ 0. (I can’t do exactly zero because I’d be dividing by zero, but let’s say one is 100 times better or something.) In that case, the payoffs for the hiring process reduce to the following: E[Ux] = V E[Uz] = 0 $E[U_x] = V$ $E[U_z] = 0$ X will definitely get the job, so X is much better off. E[Uf] = hx Y – c $E[U_f] = h_x Y – c$ If the firm had hired randomly, this would have happened instead: E[Ux] = E[Uz] = V/2 $E[U_x] = E[U_z] = \frac{V}{2}$ E[Uf] = hY/2 $E[U_f] = \frac{h}{2} Y$ As long as c < hY/2, both the firm and the higher-skill worker are better off in this scenario. (The lower-skill worker is worse off, but that’s not surprising.) The total expected benefit for everyone is also higher in this scenario. Thus, the difference in skill level between the applicants is vital. If candidates are very different in skill level, in a way that the application process can accurately measure, then a long and costly application process can be beneficial, not only for the firm but also for society as a whole. In these extreme examples, it was either not worth it for the firm, or worth it for everyone. But there is an intermediate case worth looking at, where the long and costly process can be worth it for the firm, but not for society as a whole. I will call this case hyper-competition—a system that is so competitive it makes society overall worse off. This inefficient result occurs precisely when: c < (hx2 + hz2)/(hx + hz) Y – (hx + hz)/2 Y < c + (hx/(hx + hz))2 V + (hz/(hx + hz))2 V $c < \frac{h_x^2 + h_z^2}{h_x + h_z} Y – \frac{h_x + h_z}{2} Y < c + \left( \frac{h_x}{h_x + h_z}\right)^2 V + \left( \frac{h_z}{h_x + h_z}\right)^2 V$ This simplifies to: c < (hx – hz)2/(2hx + 2hz) Y < c + (hx2 + hz2)/(hx + hz)2 V $c < \frac{(h_x – h_z)^2}{2 (h_x + h_z)} Y < c + \frac{(h_x^2 + h_z^2)}{(h_x+h_z)^2} V$ If c is small, then we are interested in the case where: (hx – hz)2 Y/2 < (hx2 + hz2)/(hx + hz) V $\frac{(h_x – h_z)^2}{2} Y < \frac{h_x^2 + h_z^2}{h_x + h_z} V$ This is true precisely when the difference hx – hz is small compared to the overall size of hx or hz—that is, precisely when candidates are highly skilled but similar. This is pretty clearly the typical case in the real world. If the candidates were obviously different, you wouldn’t need a competitive process. For instance, suppose that hx = 10 and hz = 8, while V = 180, Y = 20 and c = 1. Then, if we hire randomly, these are the expected payoffs: E[Uf] = (hx + hz)/2 Y = 180 E[Ux] = E[Uz] = V/2 = 90 If we use the complicated hiring process, these are the expected payoffs: E[Ux] = (hx/(hx + hz))2 V = 55.5 E[Uz] = (hz/(hx + hz))2 V = 35.5 E[Uf] = (hx2 + hz2)/(hx + hz) Y – c = 181 The firm gets a net benefit of 1, quite small; while the workers face a far larger total expected loss of 90. And these candidates aren’t that similar: One is 25% better than the other. Yet because the effort expended in applying was so large, even this improvement in quality wasn’t worth it from society’s perspective. This conclude’s the algebra for today, if you’ve been skipping it. In this model I’ve only considered the case of exactly two applicants, but this can be generalized to more applicants, and the effect only gets stronger: Seemingly-large differences in each worker’s skill level can be outweighed by the massive cost of making so many people work so hard to apply and get nothing to show for it. Thus, hyper-competition can exist despite apparently large differences in skill. Indeed, it is precisely the typical real-world scenario with many applicants who are similar that we expect to see the greatest inefficiencies. In the absence of intervention, we should expect markets to get this wrong. Of course, we don’t actually want employers to hire randomly, right? We want people who are actually qualified for their jobs. Yes, of course; but you can probably assess that with nothing more than a resume and maybe a short interview. Most employers are not actually trying to find qualified candidates; they are trying to sift through a long list of qualified candidates to find the one that they think is best qualified. And my suspicion is that most of them honestly don’t have good methods of determining that. This means that it could be an improvement for society to simply ban long hiring processes like these—indeed, perhaps ban job interviews altogether, as I can hardly think of a more efficient mechanism for allowing employers to discriminate based on race, gender, age, or disability than a job interview. Just collect a resume from each applicant, remove the ones that are unqualified, and then roll a die to decide which one you hire. This would probably make the fit of workers to their jobs somewhat worse than the current system. But most jobs are learned primarily through experience anyway, so once someone has been in a job for a few years it may not matter much who was hired originally. And whatever cost we might pay in less efficient job matches could be made up several times over by the much faster, cheaper, easier, and less stressful process of applying for jobs. Indeed, think for a moment of how much worse it feels being turned down for a job after a lengthy and costly application process that is designed to assess your merit (but may or may not actually do so particularly well), as opposed to simply finding out that you lost a high-stakes die roll. Employers could even send out letters saying one of two things: “You were rejected as unqualifed for this position.” versus “You were qualified, but you did not have the highest die roll.” Applying for jobs already feels like a crapshoot; maybe it should literally be one. People would still have to apply for a lot of jobs—actually, they’d probably end up applying for more, because the lower cost of applying would attract more applicants. But since the cost is so much lower, it would still almost certainly be easier to do a job search than it is in the current system. In fact, it could largely be automated: simply post your resume on a central server and the system matches you with employers’ requirements and then randomly generates offers. Employers and prospective employees could fill out a series of forms just once indicating what they were looking for, and then the system could do the rest. What I find most interesting about this policy idea is that it is in an important sense anti-meritocratic. We are in fact reducing the rewards for high levels of skill—at least a little bit—in order to improve society overall and especially for those with less skill. This is exactly the kind of policy proposal that I had hoped to see from a book like The Meritocracy Trap, but never found there. Perhaps it’s too radical? But the book was all about how we need fundamental, radical change—and then its actual suggestions were simple, obvious, and almost uncontroversial. Note that this simplified process would not eliminate the incentives to get major, verifiable qualifications like college degrees or years of work experience. In fact, it would focus the incentives so that only those things matter, instead of whatever idiosyncratic or even capricious preferences HR agents might have. There would be no more talk of “culture fit” or “feeling right for the job”, just: “What is their highest degree? How many years have they worked in this industry?” I suppose this is credentialism, but in a world of asymmetric information, I think credentialism may be our only viable alternative to nepotism. Of course, it’s too late for me. But perhaps future generations may benefit from this wisdom. # The Race to the Bottom is not inevitable Jul 19 JDN 2459050 The race to the bottom is a common result of competition, between firms, between states, or even between countries. One firm finds a way to cut corners and reduce costs, then lowers their price to undercut others; then soon every firm is cutting those same corners. Or one country decides to weaken their regulations in order to attraction more business; then soon every other country has to weaken their regulations as well. Let’s first consider individual firms. Suppose that you run a business, and you are an upstanding, ethical person. You want to treat your employees, your customers, and your community well. You have high labor standards, you exceed the requirements of environmental regulations, and you make a high-quality product at a reasonable price for a moderate profit. Then, a competitor appears. The owner of this company is not so ethical. They exploit their workers, perhaps even stealing their wages. They flaunt environmental regulations. They make shoddy products. All of this allows them to make their products for a lower price than yours. Suppose that most customers can’t tell the difference between your product and theirs. What will happen? They will stop buying yours, because it’s more expensive. What do you do then? You could simply go out of business. But that doesn’t really solve anything. Probably you’ll be forced to lower your standards. You’ll treat your workers worse, pollute more, reduce product quality. You may not do so as much as the other company, but you’ll have to do it some in order to get the price down low enough to still compete. And your profits will be lower than theirs as a result. Far better would be for the government to step in and punish that other business for breaking the rules—or if what they’re doing is technically legal, change the rules so that it’s not anymore. Then you could continue to produce high-quality products with fair labor standards and good environmental sustainability. But there are some problems with this. First, consider this from the point of view of a regulator, who is being lobbied by both companies. Your company asks for higher standards to improve product quality while protecting workers and the environment. But theirs claims that these higher standards will push them out of business. Who will they believe? In fact, it may be worse than that: Suppose we’ve already settled into an equilibrium where all the firms have low standards. In that case, all the lobbyists will be saying that regulations need to be kept weak, lest the whole industry fail. But in fact there’s no reason to think that stricter regulations would actually destroy the whole industry. Firm owners are used to thinking in terms of fixed competitors: They act in response to what competitors do. And in many cases it’s actually true that if just one firm tried to raise their standards, they would be outcompeted and go out of business. This does not mean that if all firms were forced to raise their standards, the industry would collapse. In fact, it’s much more likely that stricter regulations would only moderately reduce output and profits, if imposed consistently across the whole industry. To see why, let’s consider a very simple model, a Bertrand competition game. There are two firms, A and B. Each can either use process H, producing a product of high quality with high labor standards and good sustainability, or use process L, producing a product of low quality with low labor standards and poor sustainability. Process H costs$100 per unit, process L costs $50 per unit. Customers can’t tell the difference, so they will buy whichever product is offered at the lowest price. Let’s say you are in charge of firm A. You choose which process to use, and set your price. At the same time, firm B chooses a process and sets their price. Suppose choose to use process H. The lowest possible price you could charge to still make a profit would be a price of$101 (ignoring cents; let’s say customers also ignore them, which might be true!).

But firm B could choose process L, and then set a price of $100. They can charge just one dollar less than you charge for their product, but their cost is only$50, so now they are making a large profit—and you get nothing.

So you are forced to lower your standards, in order to match their price. You could try to undercut them at a price of $100, but in the long run that’s a bad idea, since eventually you’ll both be driven to charging a price of 51 and making only a very small profit. And there’s a way to stop them from undercutting you, which is to offer a price-matching guarantee; you can tell your customers that if they see a lower price from firm B than what you’re offering, you’ll match it for them. Then firm B has no incentive to try to undercut you, and you can maintain a stable equilibrium at a price of$100. You have been forced to used process L even though you know it is worse, because any attempt to unilaterally deviate from that industry norm would result in your company going bankrupt.

But now suppose the government comes in and mandates that all firms use process H, and they really enforce this rule so that no firm wants to try to break it. Then you’d want to raise the price, but you wouldn’t necessarily have to raise it all that much. Even $101 would be enough to ensure some profit, and you could even maintain your current profits by raising the price up to$150. In reality the result would probably be somewhere in between those two, depending on the elasticity of demand; so perhaps you end up charging $125 and make half the profit you did before. Even though the new regulation raised costs all the way up to the current price, they did not result in collapsing the industry; because the rule was enforced uniformly, all firms were able to raise their standards and also raise their prices. This is what we should typically expect to happen; so any time someone claims that a new regulation will “destroy the industry” we should be very skeptical of that claim. (It’s not impossible; for instance, a regulation mandating that all fast food workers be paid$200 per hour would surely collapse the fast food industry. But it’s very unlikely that anyone would seriously propose a regulation like that.)

So as long as you have a strong government in place, you can escape the race to the bottom. But then we must consider international competition: What if other countries have weaker regulations, and so firms want to move their production to those other countries?

Well, a small country may actually be forced to lower their standards in order to compete. I’m not sure there’s much that Taiwan or Singapore could do to enforce higher labor standards. If Taiwan decided to tighten all their labor regulations, firms might just move their production to Indonesia or Vietnam. Then again, monthly incomes in Taiwan, once adjusted for currency exchange rates, are considerably higher than those in Vietnam. Indeed, wages in Taiwan aren’t much lower than wages in the US. So apparently Taiwan has some power to control their own labor standards—perhaps due to their highly educated population and strong industrial infrastructure.

However, a large country like the US or China absolutely has more power than that. If the US wants to enforce stricter labor standards, they can simply impose tariffs on countries that don’t. Actually there are many free-trade rules in place precisely to reduce that power, because it can be easily abused in the service of protectionism.

Perhaps these rules go too far; while I agree with the concern about protectionism, I definitely think we should be doing more to enforce penalties for forced labor, for instance. But this is not the result of too little international governance—if anything it is the result of too much. Our free trade agreements are astonishingly binding, even on the most powerful countries (China has successfully sued the United States under WTO rules!). I wish only that our human rights charters were anywhere near as well enforced.

This means that the race to the bottom is not the inevitable result of competition between firms or even between countries. When it occurs, it is the result of particular policy regimes nationally or internationally. We can make better rules.

The first step may be to stop listening to the people who say that any change will “destroy the industry” because they are unable (or unwilling?) to understand how uniformly-imposed rules differ from unilateral deviations from industry norms.

# The TPP sounds… okay, I guess?

JDN 2457308 EDT 12:56

So, the Trans-Pacific Partnership (TPP) agreement has been signed. This upsets a lot of people, from the far-left who say it gives corporations power over democracy to the far-right who say it makes Obama into a dictator. But more mainstream organizations have also come out against it, particularly from the center-left or “radical center”, such as the Electronic Frontier Foundation and Medecins Sans Frontieres.

Bernie Sanders was opposed to it from the beginning, and now Hillary Clinton is opposed as well—though given her long track record of support for trade agreements it’s unclear whether this opposition is sincere, or simply reflects the way that Sanders has shifted our Overton Window to the left. Many Republicans also opposed the deal, and they’re already calling it “Obamatrade”. (Apparently they didn’t learn their lesson from Obamacare, because it’s been wildly successful, and in about a generation people are going to say “Obamacare” in the same breath as “Medicare” and “the New Deal”, and sticking Obama’s name onto it is going to lionize him.)

In my previous post I explained why I am, like the vast majority of economists, strongly in favor of free trade. So you might think that I would support the TPP, and would want to criticize all these people who are coming out against it as naive protectionists.

But in fact, I feel deeply ambivalent about the TPP, and I’m not alone in that among economists. Indeed I feel a bit proud to say that my view on the agreement is almost exactly aligned with that of Nobel Laureate Paul Krugman. (Krugman is always one of the world’s best economists, but I’d say he should be especially trusted on issues of international trade—because that was the subject of his Nobel-winning research.) The original leaked version looked pretty awful, and not knowing exactly what’s in it worried me, but the more I hear tobacco and pharmaceutical companies complain about it, the more I like the sound of it.

First of all, let me say that I’m still very angry they haven’t released the full text. We have a right to know what our laws are, as a basic principle of democracy. If we are going to be bound by this agreement, we have a right to know what it says. This is non-negotiable. To be bound by laws you haven’t been told about is literally—and let me be clear on the full force I intend by that word, literally—Kafkaesque. Kafka’s The Trial is all about what happens when the government can punish you for disobeying a law they never told you exists.

In the leaked draft version, the TPP would have been the largest handout of corporate welfare in world history. By placing the so-called “intellectual property” of corporations above basic human rights, it amounted to throwing several entire Third World countries under the bus in order to increase the profits of a handful of megacorporations. It would have expanded “investor-state dispute resolution authority” into an unprecedented level of power for multinational corporations to influence the decisions of national governments—what the President of the Capital Institute called “trading away our sovereignty”.

My fear was that the TPP would just be a redone and expanded version of the TRIPS accord, the “Agreement on Trade-Related Aspects of Intellectual Property Rights” (somehow that’s “TRIPS”), which expanded the monopoly power of “intellectual property” corporations, including the music industry, the film industry, and worst of all the pharmaceutical industry. The expansion of patent powers reduced the availability of drugs, including life-saving drugs, to some of the world’s poorest and most vulnerable people. There is supposed to be a system of flexibility provisions that allow exceptions to intellectual property laws in the service of public health, but in practice these are difficult to implement and many Third World governments don’t know how to use them. Based on UNCTAD estimates, Thomas Pogge found that TRIPS and related trade agreements amount to a transfer of wealth from the Third World to the First World on the order of $700 billion per year. (I’m also a bit confused by the WTO’s assertion that “For patents, [TRIPS] allows governments to make exceptions to patent holders’ rights such as in national emergencies, anti-competitive practices, […]”; aren’t patents by definition anti-competitive practices? We’ll protect your monopoly, as long as you don’t try to have a monopoly?) If TPP makes these already too-strong provisions stronger, millions of people could be denied medicines they need—which is why Medecins San Frontieres is among the organizations opposing the agreement. Yet, in principle free trade is a good idea, and it’s definitely a good thing to remove the ridiculous tariffs we still have on Japanese cars. Of course, Ford Motor Company is complaining about the additional competition, but that’s a good sign—corporations complaining about extra competition is exactly the sort of response a good trade agreement would provoke. (Also, “razor-thin profit margins”? I think not; car manufacturing is near the very top of capital-intensive industries with high barriers to entry, and Ford Motor Company has a gross profit margin of 16% and net income margin of 5%. So, that 2.5% you might have to cut prices because you no longer get the tariff support… well, you could just take it out of your profits, and I don’t see why we should feel bad if you have to do that.) It still angers me that they won’t tell us exactly what’s in the deal, but some of the things they have told us are actually quite encouraging. The New York Times has a summary that suggests lukewarm approval on their part. The TPP opens up Internet traffic, creating international regulations that prohibit the censorship of cross-border data. (With that in mind, I’m a bit baffled that the EFF is so strongly opposed; isn’t free data exchange your raison d’etre?) China hasn’t signed on, and this might well be why—they’d love to sell us products without tariffs, but they aren’t prepared to stop censoring the Internet in order to do that. It lowers barriers on the cross-border exchange of services (as opposed to only goods). Many services really can’t be traded much across borders (think restaurant meals and haircuts), and in practice this mostly means finance, which is a mixed bag to be sure; but in general I think allowing services to compete across borders is a good ideas. The TPP also places limitations on government-owned enterprises, though not very strict ones (probably because we in the US aren’t likely to give up the US Postal Service or the Federal Reserve anytime soon). Basically this is designed to prevent the sort of mass state expropriation that has destroyed the economies of several authoritarian socialist countries, like Cuba and Venezuela. It’s unlikely they would be strong enough to stop more legitimate nationalizations of industry or applications of eminent domain, since Japan, Canada, and probably even the US would have been unwilling to sign onto such an agreement. The leaked draft of the TPP would have given extremely strong protections to drug patents, but the fact that pharmaceutical companies are angry about it says to me that the strongest of these provisions must not have made it in. It sounds like patents are being made stronger but shorter, which like most compromises makes both sides mad. Best of all, it includes some regulations on human rights, labor standards, and environmental policies, which is something that has been sorely lacking in previous trade agreements. While the details are still sketchy (Have I mentioned how angry I am that they won’t release the full text?) it is claimed that the agreement includes a system of tariff penalties that can be implemented against countries that oppress LGBT people and other marginalized groups. Because Brunei, Malaysia, and Singapore currently criminalize homosexuality, they would already be in noncompliance from the moment they sign the treaty, and would be subject to these penalties until they change their laws. If this is true, it actually sounds like a step toward the “human rights tariff” that I would like to see implemented worldwide. In general, the TPP sounds like a mess, a jumble of awkward compromises that does some good things and some bad things, and doesn’t really satisfy anyone. In other words, it sounds like policy. # Monopoly and Oligopoly JDN 2457180 EDT 08:49 Welcome to the second installment in my series, “Top 10 Things to Know About Economics.” The first was not all that well-received, because it turns it out it was just too dense with equations (it didn’t help that the equation formatting was a pain.) Fortunately I think I can explain monopoly and oligopoly with far fewer equations—which I will represent as PNG for your convenience. You probably already know at least in basic terms how a monopoly works: When there is only one seller of a product, that seller can charge higher prices. But did you ever stop and think about why they can charge higher prices—or why they’d want to? The latter question is not as trivial as it sounds; higher prices don’t necessarily mean higher profits. By the Law of Demand (which, like the Pirate Code, is really more like a guideline), raising the price of a product will result in fewer being sold. There are two countervailing effects: Raising the price raises the profits from selling each item, but reduces the number of items sold. The optimal price, therefore, is the one that balances these two effects, maximizing price times quantity. A monopoly can actually set this optimal price (provided that they can figure out what it is, of course; but let’s assume they can). They therefore solve this maximization problem for price P(Q) a function of quantity sold, quantity Q, and cost C(Q) a function of quantity produced (which at the optimum is equal to quantity sold; no sense making them if you won’t sell them!): As you may remember if you’ve studied calculus, the maximum is achieved at the point where the derivative is zero. If you haven’t studied calculus, the basic intuition here is that you move along the curve seeing whether the profits go up or down with each small change, and when you reach the very top—the maximum—you’ll be at a point where you switch from going up to going down, and at that exact point a small change will move neither up nor down. The derivative is really just a fancy term for the slope of the curve at each point; at a maximum this slope changes from positive to negative, and at the exact point it is zero. This is a general solution, but it’s easier to understand if we use something more specific. As usual, let’s make things simpler by assuming everything is linear; we’ll assume that demand starts at a maximum price of P0 and then decreases at a rate 1/e. This is the demand curve. Then, we’ll assume that the marginal cost of production C'(Q) is also linear, increasing at a rate 1/n. This is the supply curve. Now we can graph the supply and demand curves from these equations. But the monopoly doesn’t simply set supply equal to demand; instead, they set supply equal to marginal revenue, which takes into account the fact that selling more items requires lowering the price on all of them. Marginal revenue is this term: This is strictly less than the actual price, because increasing the quantity sold requires decreasing the price—which means that P'(Q) < 0. They set the quantity by setting marginal revenue equal to marginal cost. Then they set the price by substituting that quantity back into the demand equation. Thus, the monopoly should set this quantity: They would then charge this price (substitute back into the demand equation): On a graph, there are the supply and demand curves, and then below the demand curve, the marginal revenue curve; it’s the intersection of that curve with the supply curve that the monopoly uses to set its quantity, and then it substitutes that quantity into the demand curve to get the price: Now I’ll show that this is higher than the price in a perfectly competitive market. In a competitive market, competitive companies can’t do anything to change the price, so from their perspective P'(Q) = 0. They can only control the quantity they produce and sell; they keep producing more as long as they receive more money for each one than it cost to produce it. By the Law of Diminishing Returns (again more like a guideline) the cost will increase as they produce more, until finally the last one they sell cost just as much to make as they made from selling it. (Why bother selling that last one, you ask? You’re right; they’d actually sell one less than this, but if we assume that we’re talking about thousands of products sold, one shouldn’t make much difference.) Price is simply equal to marginal cost: In our specific linear case that comes out to this quantity: Therefore, they charge this price (you can substitute into either the supply or demand equations, because in a competitive market supply equals demand): Subtract the two, and you can see that monopoly price is higher than the competitive price by this amount: Notice that the monopoly price will always be larger than the competitive price, so long as e > 0 and n > 0, meaning that increasing the quantity sold requires decreasing the price, but increasing the cost of production. A monopoly has an incentive to raise the price higher than the competitive price, but not too much higher—they still want to make sure they sell enough products. Monopolies introduce deadweight loss, because in order to hold the price up they don’t produce as many products as people actually want. More precisely, each new product produced would add overall value to the economy, but the monopoly stops producing them anyway because it wouldn’t add to their own profits. One “solution” to this problem is to let the monopoly actually take those profits; they can do this if they price-discriminate, charging a higher price for some customers than others. In the best-case scenario (for them), they charge each customer a price that they are just barely willing to pay, and thus produce until no customer is willing to pay more than the product costs to make. That final product sold also has price equal to marginal cost, so the total quantity sold is the same under competition. It is, in that sense, “efficient”. What many neoclassical economists seem to forget about price-discriminating monopolies is that they appropriate the entire surplus value of the product—the customers are only just barely willing to buy; they get no surplus value from doing so. In reality, very few monopolies can price-discriminate that precisely; instead, they put customers into broad categories and then try to optimize the price for each of those categories. Credit ratings, student discounts, veteran discounts, even happy hours are all forms of this categorical price discrimination. If the company cares even a little bit about what sort of customer you are rather than how much money you’re paying, they are price-discriminating. It’s so ubiquitous I’m actually having trouble finding a good example of a product that doesn’t have categorical price discrimination. I was thinking maybe computers? Nope, student discounts. Cars? No, employee discounts and credit ratings. Refrigerators, maybe? Well, unless there are coupons (coupons price discriminate against people who don’t want to bother clipping them). Certainly not cocktails (happy hour) or haircuts (discrimination by sex, the audacity!); and don’t even get me started on software. I introduced price-discrimination in the context of monopoly, which is usually how it’s done; but one thing you’ll notice about all the markets I just indicated is that they aren’t monopolies, yet they still exhibit price discrimination. Cars, computers, refrigerators, and software are made under oligopoly, a system in which a handful of companies control the majority of the market. As you might imagine, an oligopoly tends to act somewhere in between a monopoly and a competitive market—but there are some very interesting wrinkles I’ll get to in a moment. Cocktails and haircuts are sold in a different but still quite interesting system called monopolistic competition; indeed, I’m not convinced that there is any other form of competition in the real world. True perfectly-competitive markets just don’t seem to actually exist. Under monopolistic competition, there are many companies that don’t have much control over price in the overall market, but the products they sell aren’t quite the same—they’re close, but not equivalent. Some barbers are just better at cutting hair, and some bars are more fun than others. More importantly, they aren’t the same for everyone. They have different customer bases, which may overlap but still aren’t the same. You don’t just want a barber who is good, you want one who works close to where you live. You don’t just want a bar that’s fun; you want one that you can stop by after work. Even if you are quite discerning and sensitive to price, you’re not going to drive from Ann Arbor to Cleveland to get your hair cut—it would cost more for the gasoline than the difference. And someone is Cleveland isn’t going to drive all the way to Ann Arbor, either! Hence, barbers in Ann Arbor have something like a monopoly (or oligopoly) over Ann Arbor haircuts, and barbers in Cleveland have something like a monopoly over Cleveland haircuts. That’s monopolistic competition. Supposedly monopolistic competition drives profits to zero in the long run, but I’ve yet to see this happen in any real market. Maybe the problem is that conceit “the long run”; as Keynes said, “in the long run we are all dead.” Sometimes the argument is made that it has driven real economic profits to zero, because you’ve got to take into account the cost of entry, the normal profit. But of course, that’s extremely difficult to measure, so how do we know whether profits have been driven to normal profit? Moreover, the cost of entry isn’t the same for everyone, so people with lower cost of entry are still going to make real economic profits. This means that the majority of companies are going to still make some real economic profit, and only the ones that had the hardest time entering will actually see their profits driven to zero. Monopolistic competition is relatively simple. Oligopoly, on the other hand, is fiercely complicated. Why? Because under oligopoly, you actually have to treat human beings as human beings. What I mean by that is that under perfect competition or even monopolistic competition, the economic incentives are so powerful that people basically have to behave according to the neoclassical rational agent model, or they’re going to go out of business. There is very little room for errors or even altruistic acts, because your profit margin is so tight. In perfect competition, there is literally zero room; in monopolistic competition, the only room for individual behavior is provided by the degree of monopoly, which in most industries is fairly small. One person’s actions are unable to shift the direction of the overall market, so the market as a system has ultimate power. Under oligopoly, on the other hand, there are a handful of companies, and people know their names. You as a CEO have a reputation with customers—and perhaps more importantly, a reputation with other companies. Individual decision-makers matter, and one person’s decision depends on their prediction of other people’s decision. That means we need game theory. The simplest case is that of duopoly, where there are only two major companies. Not many industries are like this, but I can think of three: soft drinks (Coke and Pepsi), commercial airliners (Boeing and Airbus), and home-user operating systems (Microsoft and Apple). In all three cases, there is also some monopolistic element, because the products they sell are not exactly the same; but for now let’s ignore that and suppose they are close enough that nobody cares. Imagine yourself in the position of, say, Boeing: How much should you charge for an airplane? If Airbus didn’t exist, it’s simple; you’d charge the monopoly price. But since they do exist, the price you charge must depend not only on the conditions of the market, but also what you think Airbus is likely to do—and what they are likely to do depends in turn on what they think you are likely to do. If you think Airbus is going to charge the monopoly price, what should you do? You could charge the monopoly price as well, which is called collusion. It’s illegal to actually sign a contract with Airbus to charge that price (though this doesn’t seem to stop cable companies or banks—probably has something to do with the fact that we never punish them for doing it), and let’s suppose you as the CEO of Boeing are an honest and law-abiding citizen (I know, it’s pretty fanciful; I’m having trouble keeping a straight face myself) and aren’t going to violate the antitrust laws. You can still engage in tacit collusion, in which you both charge the monopoly price and take your half of the very high monopoly profits. There’s a temptation not to collude, however, which the airlines who buy your planes are very much hoping you’ll succumb to. Suppose Airbus is selling their A350-100 for$341 million. You could sell the comparable 777-300ER for $330 million and basically collude, or you could cut the price and draw in more buyers. Say you cut it to$250 million; it probably only costs $150 million to make, so you’re still making a profit on each one; but where you sold say 150 planes a year and profited$180 million on each (a total profit of $27 billion), you could instead capture the whole market and sell 300 planes a year and profit$100 million on each (a total profit of $30 billion). That’s a 10% higher profit and$3 billion a year for your shareholders; why wouldn’t you do that?

Well, think about what will happen when Airbus releases next year’s price list. You cut the price to $250 million, so they retaliate by cutting their price to$200 million. Next thing you know, you’re cutting your own price to $150.1 million just to stay in the market, and they’re doing the same. When the dust settles, you still only control half the market, but now you profit a mere$100,000 per airplane, making your total profits a measly $15 million instead of$27 billion—that’s $27,000 million. (I looked it up, and as it turns out, Boeing’s actual gross profit is about$14 billion, so I underestimated the real cost of each airplane—but they’re clearly still colluding.) For a gain of 10% in one year you’ve paid a loss of 99.95% indefinitely. The airlines will be thrilled, and they’ll likely pass on much of those savings to their customers, who will fly more often, engage in more tourism, and improve the economy in tourism-dependent countries like France and Greece, so the world may well be better off. But you as CEO of Boeing don’t care about the world; you care about the shareholders of Boeing—and the shareholders of Boeing just got hosed. Don’t expect to keep your seat in the next election.

But now, suppose you think that Airbus is planning on setting a price of $250 million next year anyway. They should know you’ll retaliate, but maybe their current CEO is retiring next year and doesn’t care what happens to the company after that or something. Or maybe they’re just stupid or reckless. In any case, your sources (which, as an upstanding citizen, obviously wouldn’t include any industrial espionage!) tell you that Airbus is going to charge$250 million next year.

Well, in that case there’s no point in you charging $330 million; you’ll lose the market and look like a sucker. You could drop to$250 million and try to set up a new, lower collusive equilibrium; but really what you want to do is punish them severely for backstabbing you. (After all, human beings are particularly quick to anger when we perceive betrayal. So maybe you’ll charge $200 million and beat them at their own conniving game. The next year, Airbus has a choice. They could raise back to$341 million and give you another year of big profits to atone for their reckless actions, or they could cut down to \$180 million and keep the price war going. You might think that they should continue the war, but that’s short-term thinking; in the long run their best strategy is to atone for their actions and work to restore the collusion. In response, Boeing’s best strategy is to punish them when they break the collusion, but not hold a grudge; if they go back to the high price, Boeing should as well. This very simple strategy is called tit-for-tat, and it is utterly dominant in every simulation we’ve ever tried of this situation, which is technically called an iterated prisoner’s dilemma.

What if there are more than two companies involved? Then things get even more complicated, because now we’re dealing with things like what A’s prediction of what B predicts that C will predict A will do. In general this is a situation we only barely understand, and I think it is a topic that needs considerably more research than it has received.

There is an interesting simple model that actually seems to capture a lot about how oligopolies work, but no one can quite figure out why it works. That model is called Cournot competition. It assumes that companies take prices and fixed and compete by selecting the quantity they produce at each cycle. That’s incredibly bizarre; it seems much more realistic to say that they compete by setting prices. But if you do that, you get Bertrand competition, which requires us to go through that whole game-theory analysis—but now with three, or four, or ten companies!

Under Cournot competition, you decide how much to produce Q1 by monopolizing what’s left over after the other companies have produced their quantities Q2, Q3, and so on. If there are k companies, you optimize under the constraint that (k-1)Q2 has already been produced.

Let’s use our linear models again. Here, the quantity that goes into figuring the price is the total quantity, which is Q1+(k-1)Q2; while the quantity you sell is just Q1. But then, another weird part is that for the marginal cost function we use the whole market—maybe you’re limited by some natural resource, like oil or lithium?

It’s not as important for you to follow along with the algebra, though here you go if you want:

Then the key point is that the situation is symmetric, so Q1 = Q2 = Q3 = Q. Then the total quantity produced, which is what consumers care about, is kQ. That’s what sets the actual price as well.

The two equations to focus on are these ones:

If you plug in k=1, you get a monopoly. If you take the limit as k approaches infinity, you get perfect competition. And in between, you actually get a fairly accurate representation of how the number of companies in an industry affects the price and quantity sold! From some really bizarre assumptions about how competition works! The best explanation I’ve seen of why this might happen is this 1983 paper showing that price competition can behave like Cournot competition if companies have to first commit to producing a certain quantity before naming their prices.

But of course, it doesn’t always give an accurate representation of oligopoly, and for that we’ll probably need a much more sophisticated multiplayer game theory analysis which has yet to be done.

And that, dear readers, is how monopoly and oligopoly raise prices.