collusion

Krugman and rockets and feathers

pnrj critique of neoclassical economics, current events, macroeconomics, personal, public policy , , , , , ,

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.

Are unions collusion?

pnrj critique of neoclassical economics, ethics, market failure, public policy , , , , , , , , , , ,

Oct 31 JDN 2459519

The standard argument from center-right economists against labor unions is that they are a form of collusion: Producers are coordinating and intentionally holding back from what would be in their individual self-interest in order to gain a collective advantage. And this is basically true: In the broadest sense of the term, labor unions are are form of collusion. Since collusion is generally regarded as bad, therefore (this argument goes), unions are bad.

What this argument misses out on is why collusion is generally regarded as bad. The typical case for collusion is between large corporations, each of which already controls a large share of the market—collusion then allows them to act as if they control an even larger share, potentially even acting as a monopoly.

Labor unions are not like this. Literally no individual laborer controls a large segment of the market. (Some very specialized laborers, like professional athletes, or, say, economists, might control a not completely trivial segment of their particular job market—but we’re still talking something like 1% at most. Even Tiger Woods or Paul Krugman is not literally irreplaceable.) Moreover, even the largest unions can rarely achieve anything like a monopoly over a particular labor market.

Thus whereas typical collusion involves going from a large market share to an even larger—often even dominant—market share, labor unions involve going from a tiny market share to a moderate—and usually not dominant—market share.

But that, by itself, wouldn’t be enough to justify unions. While small family businesses banding together in collusion is surely less harmful than large corporations doing the same, it would probably still be a bad thing, insofar as it would raise prices and reduce the quantity or quality of products sold. It would just be less bad.

Yet unions differ from even this milder collusion in another important respect: They do not exist to increase bargaining power versus consumers. They exist to increase bargaining power versus corporations.

And corporations, it turns out, already have a great deal of bargaining power. While a labor union acts as something like a monopoly (or at least oligopoly), corporations act like the opposite: oligopsony or even monopsony.

While monopoly or monopsony on its own is highly unfair and inefficient, the combination of the two—bilateral monopoly—is actually relatively fair and efficient. Bilateral monopoly is probably not as good as a truly competitive market, but it is definitely better than either a monopoly or monopsony alone. Whereas a monopoly has too much bargaining power for the seller (resulting in prices that are too high), and a monopsony has too much bargaining power for the buyer (resulting in prices that are too low), a bilateral monopoly has relatively balanced bargaining power, and thus gets an outcome that’s not too much different from fair competition in a free market.

Thus, unions really exist as a correction mechanism for the excessive bargaining power of corporations. Most unions are between workers in large industries who work for a relatively small number of employers, such as miners, truckers, and factory workers. (Teachers are also an interesting example, because they work for the government, which effectively has a monopsony on public education services.) In isolation they may seem inefficient; but in context they really exist to compensate for other, worse inefficiencies.


We could imagine a world where this was not so: Say there is a market with many independent buyers who are unwilling or unable to reliably collude, and they are served by a small number of powerful unions that use their bargaining power to raise prices and reduce output.


We have some markets that already look a bit like that: Consider the licensing systems for doctors and lawyers. These are basically guilds, which are collusive in the same way as labor unions.

Note that unlike, say, miners, truckers, or factory workers, doctors and lawyers are not a large segment of the population; they are bargaining against consumers just as much as corporations; and they are extremely well-paid and very likely undersupplied. (Doctors are definitely undersupplied; with lawyers it’s a bit more complicated, but given how often corporations get away with terrible things and don’t get sued for it, I think it’s fair to say that in the current system, lawyers are undersupplied.) So I think it is fair to be concerned that the guild systems for doctors and lawyers are too powerful. We want some system for certifying the quality of doctors and lawyers, but the existing standards are so demanding that they result in a shortage of much-needed labor.

One way to tell that unions aren’t inefficient is to look at how unionization relates to unemployment. If unions were acting as a harmful monopoly on labor, unemployment should be higher in places with greater unionization rates. The empirical data suggests that if there is any such effect, it’s a small one. There are far more important determinants of unemployment than unionization. (Wages, on the other hand, show a strong positive link with unionization.) Much like the standard prediction that raising minimum wage would reduce employment, the prediction that unions raise unemployment has largely not been borne out by the data. And for much the same reason: We had ignored the bargaining power of employers, which minimum wage and unions both reduce.

Thus, the justifiability of unions isn’t something that we could infer a priori without looking at the actual structure of the labor market. Unions aren’t always or inherently good—but they are usually good in the system as it stands. (Actually there’s one particular class of unions that do not seem to be good, and that’s police unions: But this is a topic for another time.)

My ultimate conclusion? Yes, unions are a form of collusion. But to infer from that they must be bad is to commit a Noncentral Fallacy. Unions are the good kind of collusion.

MSRP is tacit collusion

pnrj critique of neoclassical economics, heuristics and biases, market failure, public policy , , , , , , , , ,

Oct 7 JDN 2458399

It’s been a little while since I’ve done a really straightforward economic post. It feels good to get back to that.

You are no doubt familiar with the “Manufacturer’s Suggested Retail Price” or MSRP. It can be found on everything from books to dishwashers to video games.

The MSRP is a very simple concept: The manufacturer suggests that all retailers sell it (at least the initial run) at precisely this price.

Why would they want to do that? There is basically only one possible reason: They are trying to sustain tacit collusion.

The game theory of this is rather subtle: It requires that both manufacturers and retailers engage in long-term relationships with one another, and can pick and choose who to work with based on the history of past behavior. Both of these conditions hold in most real-world situations—indeed, the fact that they don’t hold very well in the agriculture industry is probably why we don’t see MSRP on produce.

If pricing were decided by random matching with no long-term relationships or past history, MSRP would be useless. Each firm would have little choice but to set their own optimal price, probably just slightly over their own marginal cost. Even if the manufacturer suggested an MSRP, retailers would promptly and thoroughly ignore it.

This is because the one-shot Bertrand pricing game has a unique Nash equilibrium, at pricing just above marginal cost. The basic argument is as follows: If I price cheaper than you, I can claim the whole market. As long as it’s profitable for me to do that, I will. The only time it’s not profitable for me to undercut you in this way is if we are both charging just slightly above marginal cost—so that is what we shall do, in Nash equilibrium. Human beings don’t always play according to the Nash equilibrium, but for-profit corporations do so quite consistently. Humans have limited attention and moral values; corporations have accounting departments and a fanatical devotion to the One True Profit.

But the iterated Bertrand pricing game is quite different. If instead of making only one pricing decision, we make many pricing decisions over time, always with a high probability of encountering the same buyers and sellers again in the future, then I may not want to undercut your price, for fear of triggering a price war that will hurt both of our firms.

Much like how the Iterated Prisoner’s Dilemma can sustain cooperation in Nash equilibrium while the one-shot Prisoner’s Dilemma cannot, the iterated Bertrand game can sustain collusion as a Nash equilibrium.

There is in fact a vast number of possible equilibria in the iterated Bertrand game. If prices were infinitely divisible, there would be an infinite number of equilibria. In reality, there are hundreds or thousands of equilibria, depending on how finely divisible the price may be.

This makes the iterated Bertrand game a coordination game—there are many possible equilibria, and our task is to figure out which one to coordinate on.

If we had perfect information, we could deduce what the monopoly price would be, and then all choose the monopoly price; this would be what we call “payoff dominant”, and it’s often what people actually try to choose in real-world coordination games.

But in reality, the monopoly price is a subtle and complicated thing, and might not even be the same between different retailers. So if we each try to compute a monopoly price, we may end up with different results, and then we could trigger a price war and end up driving all of our profits down. If only there were some way to communicate with one another, and say what price we all want to set?

Ah, but there is: The MSRP. Most other forms of price communication are illegal: We certainly couldn’t send each other emails and say “Let’s all charge $59.99, okay?” (When banks tried to do that with the LIBOR, it was the largest white-collar crime in history.) But for some reason economists (particularly, I note, the supposed “free market” believers of the University of Chicago) have convinced antitrust courts that MSRP is somehow different. Yet it’s obviously hardly different at all: You’ve just made the communication one-way from manufacturers to retailers, which makes it a little less reliable, but otherwise exactly the same thing.

There are all sorts of subtler arguments about how MSRP is justifiable, but as far as I can tell they all fall flat. If you’re worried about retailers not promoting your product enough, enter into a contract requiring them to promote. Proposing a suggested price is clearly nothing but an attempt to coordinate tacit—frankly not even that tacit—collusion.

MSRP also probably serves another, equally suspect, function, which is to manipulate consumers using the anchoring heuristic: If the MSRP is $59.99, then when it does go on sale for $49.99 you feel like you are getting a good deal; whereas, if it had just been priced at $49.99 to begin with, you might still have felt that it was too expensive. I see no reason why this sort of crass manipulation of consumers should be protected under the law either, especially when it would be so easy to avoid.

There are all sorts of ways for firms to tacitly collude with one another, and we may not be able to regulate them all. But the MSRP is literally printed on the box. It’s so utterly blatant that we could very easily make it illegal with hardly any effort at all. The fact that we allow such overt price communication makes a mockery of our antitrust law.

Monopoly and Oligopoly

pnrj core principles, Top 10 things to know about economics , , , , , , , , , , , ,

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!):

monopoly_optimization

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.

derivative_maximum

monopoly_general

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.

linear_demand

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.

linear_supply

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:

marginal_revenue

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:

linear_monopoly_solution

They would then charge this price (substitute back into the demand equation):

linear_monopoly_price

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:

elastic_supply_monopolistic_labeled

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:

perfect_competition_general

In our specific linear case that comes out to this quantity:

linear_competitive_solution

Therefore, they charge this price (you can substitute into either the supply or demand equations, because in a competitive market supply equals demand):

linear_competitive_price

Subtract the two, and you can see that monopoly price is higher than the competitive price by this amount:

linear_monopoly_premium

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:

linear_Cournot_1

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.

linear_Cournot_2

The two equations to focus on are these ones:

linear_Cournot_3

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.