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!):

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.

Should we raise the minimum wage?

JDN 2456949 PDT 10:22.

The minimum wage is an economic issue that most people are familiar with; a large portion of the population has worked for minimum wage at some point in their lives, and those who haven’t generally know someone who has. As Chris Rock famously remarked (in the recording, Chris Rock, as usual, uses some foul language), “You know what that means when they pay you minimum wage? You know what they’re trying to tell you? It’s like, ‘Hey, if I could pay you less, I would; but it’s against the law.’ ”

The minimum wage was last raised in 2009, but adjusted for inflation its real value has been trending downward since 1968. The dollar values are going up, but not fast enough to keep up with inflation.

So, should we raise it again? How much? Should we just match it to inflation, or actually raise it higher in real terms? Productivity (in terms of GDP per worker) has more than doubled since 1968, so perhaps the minimum wage should double as well?

There are two major sides in this debate, and I basically disagree with both of them.

The first is the right-wing view (here espoused by the self-avowed “Objectivist” Don Watkins) that the minimum wage should be abolished entirely because it is an arbitrary price floor that prevents workers from selling their labor at whatever wage the market will bear. He argues that the free market is the only way the value of labor should be assessed and the government has no business getting involved.

On the other end of the spectrum we have Robert Reich, who thinks we should definitely raise the minimum wage and it would be the best way to lift workers out of poverty. He argues that by providing minimum-wage workers with welfare and Medicaid, we are effectively subsidizing employers to pay lower wages. While I sympathize a good deal more with this view, I still don’t think it’s quite right.

Why not? Because Watkins is right about one thing: The minimum wage is, in fact, an arbitrary price floor. Out of all the possible wages that an employer could pay, how did we decide that this one should be the lowest? And the same applies to everyone, no matter who they are or what sort of work they do?

What Watkins gets wrong—and Reich gets right—is that wages are not actually set in a free and competitive market. Large corporations have market power; they can influence wages and prices to their own advantage. They use monopoly power to raise prices, and its inverse, monopsony power, to lower wages. The workers who are making a minimum wage of $7.25 wouldn’t necessarily make $7.25 in a competitive market; they could make more than that. All we know, actually, is that they would make at least this much, because if a worker’s marginal productivity is below the minimum wage the corporation simply wouldn’t have hired them.

Monopsony power doesn’t just lower wages; it also reduces employment. One of the ways that corporations can control wages is by controlling hiring; if they tried to hire more people, they’d have to offer a higher wage, so instead they hire fewer people. Under these circumstances, a higher minimum wage can actually create jobs, as Reich argues it will. And in this particular case I think he’s right about that, because corporations have enormous market power to hold wages down and in the Second Depression we have a huge amount of unused productive capacity. But this isn’t true in general. If markets are competitive, then raising minimum wage just causes unemployment. Even when corporations have market power, if there isn’t much unused capacity then raising minimum wage will just lead them to raise prices instead of hiring more workers.

Reich is also wrong about this idea that welfare payments subsidize low wages. On the contrary, the stronger your welfare system, the higher your wages will be. The reason is quite simple: A stronger welfare system gives workers more bargaining power. If not getting this job means you turn to prostitution or starve to death, then you’re going to take just about any wage they offer you. (I don’t entirely agree with Krugman’s defense of sweatshops—I believe there are ways to increase trade without allowing oppressive working conditions—but he makes this point quite vividly.) On the other hand, if you live in the US with a moderate welfare system, you can sometimes afford to say no; you might end up broke or worse, homeless, but you’re unlikely to starve to death because at least you have food stamps. And in a nation with a really robust welfare system like Sweden, you can walk away from any employer who offers to pay you less than your labor is worth, because you know that even if you can’t find a job for awhile your basic livelihood will be protected. As a result, stronger welfare programs make labor markets more competitive and raise wages. Welfare and Medicaid do not subsidize low-wage employers; they exert pressure on employers to raise their low wages. Indeed, a sufficiently strong welfare system could render minimum wage redundant, as I’ll get back to at the end of this post.

Of course, I am above all an empiricist; all theory must bow down before the data. So what does the data say? Does raising the minimum wage create jobs or destroy jobs? Our best answer from compiling various studies is… neither. Moderate increases in the minimum wage have no discernible effect on employment. In some studies we’ve found increases, in others decreases, but the overall average effect across many studies is indistinguishable from zero.

Of course, a sufficiently large increase is going to decrease employment; a Fox News reporter once famously asked: “Why not raise the minimum wage to $100,000 an hour!?” (which Jon Stewart aptly satirized as “Why not pay people in cocaine and unicorns!?”) Yes, raising the minimum wage to $100,000 an hour would create massive inflation and unemployment. But that really says nothing about whether raising the minimum wage to $10 or $20 would be a good idea. Covering your car with 4000 gallons of gasoline is a bad idea, but filling it with 10 gallons is generally necessary for its proper functioning.

This kind of argument is actually pretty common among Republicans, come to think of it. Take the Laffer Curve, for instance; it’s basically saying that since a 99% tax on everyone would damage the economy (which is obviously true) then a 40% tax specifically on millionaires must have the same effect. Another good one is Rush Limbaugh’s argument that if unemployment benefits are good, why not just put everyone on unemployment benefits? Well, again, because there’s a difference between doing something for some people sometimes and doing it for everyone all the time. There are these things called numbers; they measure whether something is bigger or smaller instead of just “there” or “not there”. You might want to learn about that.

Since moderate increases in minimum wage have no effect on unemployment, and we are currently under conditions of extremely low—in fact, dangerously low—inflation, then I think on balance we should go with Reich: Raising the minimum wage would do more good than harm.

But in general, is minimum wage the best way to help workers out of poverty? No, I don’t think it is. It’s awkward and heavy-handed; it involves trying to figure out what the optimal wage should be and writing it down in legislation, instead of regulating markets so that they will naturally seek that optimal level and respond to changes in circumstances. It only helps workers at the very bottom: Someone making $12 an hour is hardly rich, but they won’t benefit from increasing minimum wage to $10; in fact they might be worse off, if that increase triggers inflation that lowers the real value of their $12 wage.

What do I propose instead? A basic income. There should be a cash payment that every adult citizen receives, once a month, directly from the government—no questions asked. You don’t have to be unemployed, you don’t have to be disabled, you don’t have to be looking for work. You don’t have to spend it on anything in particular; you can use it for food, for housing, for transportation; or if you like you can use it for entertainment or save it for a rainy day. We don’t keep track of what you do with it, because it’s your own freedom and none of our business. We just give you this money as your dividends for being a shareholder in the United States of America.

This would be extremely easy to implement—the IRS already has all the necessary infrastructure, they just need to turn some minus signs into plus signs. We could remove all the bureaucracy involved in administering TANF and SNAP and Medicaid, because there’s no longer any reason to keep track of who is in poverty since nobody is. We could in fact fold the $500 billion a year we currently spend on means-tested programs into the basic income itself. We could pull another $300 billion from defense spending while still solidly retaining the world’s most powerful military.

Which brings me to the next point: How much would this cost? Probably less than you think. I propose indexing the basic income to the poverty line for households of 2 or more; since currently a household of 2 or more at the poverty line makes $15,730 per year, the basic income would be $7,865 per person per year. The total cost of giving that amount to each of the 243 million adults in the United States would be $1.9 trillion, or about 12% of our GDP. If we fold in the means-tested programs, that lowers the net cost to $1.4 trillion, 9% of GDP. This means that an additional flat tax of 9% would be enough to cover the entire amount, even if we don’t cut any other government spending.

If you use a progressive tax system like I recommended a couple of posts ago, you could raise this much with a tax on less than 5% of utility, which means that someone making the median income of $30,000 would only pay 5.3% more than they presently do. At the mean income of $50,000, you’d only pay 7.7%. And keep in mind that you are also receiving the additional $7,865; so in fact in both cases you actually end up with more than you had before the basic income was implemented. The break-even point is at about $80,000, where you pay an extra 9.9% ($7,920) and receive $7,865, so your after-tax income is now $79,945. Anyone making less than $80,000 per year actually gains from this deal; the only people who pay more than they receive are those who make more than $80,000. This is about the average income of someone in the fourth quintile (the range where 60% to 80% of the population is below you), so this means that roughly 70% of Americans would benefit from this program.

With this system in place, we wouldn’t need a minimum wage. Working full-time at our current minimum wage makes you $7.25*40*52 = $15,080 per year. If you are a single person, you’re getting $7,865 from the basic income, this means that you’ll still have more than you presently do as long as your employer pays you at least $3.47 per hour. And if they don’t? Well then you can just quit, knowing that at least you have that $7,865. If you’re married, it’s even better; the two of you already get $15,730 from the basic income. If you were previously raising a family working full-time on minimum wage while your spouse is unemployed, guess what: You actually will make more money after the policy no matter what wage your employer pays you.

This system can adapt to changes in the market, because it is indexed to the poverty level (which is indexed to inflation), and also because it doesn’t say anything about what wage an employer pays. They can pay as little or as much as the market will bear; but the market is going to bear more, because workers can afford to quit. Billionaires are going to hate this plan, because it raises their taxes (by about 40%) and makes it harder for them to exploit workers. But for 70% of Americans, this plan is a pretty good deal.