­Making Economics Fun: Part II

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Marginal vs Average: Three Stories

Fantasy: How to Escape the Bad Guys

You are a hero with a broken sword, Conan or Boromir or your favorite Dungeon & Dragons character. You are being chased by a troop of bad guys, bandits or orcs. Fortunately you are on a horse and they are not. Unfortunately your horse is tired and they will eventually run you down.  Fortunately you have a bow. Unfortunately you have only ten arrows. Fortunately, being a hero, you never miss. Unfortunately, there are forty bad guys.

They are strung out behind you as shown with the fastest in front, close enough to count your arrows.

How do you use economics to get away? (Answer in the footnote)¹

Taxes: How not to Collect Them

You locate the 90th percentile of the  income distribution, say $150,000. People at the 89^th percentile are doing pretty well for themselves; nobody needs more money than that and the government can certainly find something useful to do with the excess. You announce that for next year the tax rate on everything above $150,000 is a hundred percent.

Next year you discover that nobody is earning more than a hundred and fifty thousand in any form visible to the IRS so the final bracket of your tax is not producing any revenue. Something must be done; the government still needs money. The 90^th percentile is now at $130,000, so you start your 100% tax there. Pretty soon …

First you shoot the dollar in front, then you shoot the dollar in front, then you shoot the dollar in front, then nobody earns any dollars.

Nobody is likely to propose a hundred percent tax rate, but the story illustrates the disadvantage of a graduated tax, the fact that it generates a greater incentive to conceal income or avoid earning it than a flat tax at the same average rate.

History: The Raven Banner

Clontarf was a battle fought in Ireland in 1014 between an army of Vikings led by Sigurd, the Jarl of the Orkney Islands, and an Irish Army commanded by Brian Boru, high king of Ireland.²

Sigurd, the jarl of the Orkney Isles, has called to his banner a Viking band,
And sailed to Dublin to make himself King of the Irish land.
But crowns are never so quickly won, the Norns, they well know - -
The king of the Irish blocks our way. We must to battle go.

The raven banner of the Orkney jarl brings luck in battle, but its bearer dies.
Two men have fallen 'neath its wings today, but still the raven flies.
The jarl tells a third to take it up. The third man answers no.
"The devil's your own, take it up yourself, and back to battle go."

"'Tis fitting the beggar should bear the bag," replies the jarl, "And I'll do so here."
He fought with the banner tied round his waist and fell to an Irish spear.
He died and the Irish broke our line. We had no chance but flight.
But I'm not hurried - - it's a long way home; I won't get there tonight.

The Norns have woven a bloody web, tapestry woven of guts and bone,
And parceled it out to the Orkney host - - our day in Ireland's done.
The grey wolf howls and the ravens soar above the arrow's flight,
And Odin is waiting beyond the fray for some of us tonight.

By keeping the banner flying Sigurd’s army could win the battle at a cost of a few extra lives; perhaps one or two more out of a thousand will die. But for whoever carries the banner it is a marginal cost of one life out of one.

Critics of the broad application of the economic approach to behavior sometimes object that people in the distant past were not like that; barbarian heroes fought for glory and damn the consequences. According to this account, out of a whole Army of Vikings only three men, including the Jarl, were willing to die in order to win the battle.

Our source is Njal Saga. We do not know how much of the story is true but medieval Icelanders, who knew a great deal more than we do about what real Vikings were like, believed it.

The Equimarginal Principle

You are in the supermarket with an armful of groceries, ready to check out. Should you search for the shortest line or go to the closest one? 

You should go to the closest one. If another was significantly shorter, everybody who came in between that and a longer line would choose the shorter, bringing its length back up. So the first approximation — you can create exceptions if you add some additional details — is that all the lines will be about the same length.

Driving along a busy highway you observe that the lane next to yours is moving a little faster so you switch lanes. Five minutes later you notice that the red pick-up truck that was behind you when you switched over is now even with to you. The logic is the same on the highway as in the supermarket. If one lane is moving faster people switch over to it and keep doing so until it is no longer faster.  There will again be exceptions, such as a lane that is slower because people are shifting into it in order to exit, in which case you may want to shift out. But as a general rule, switching lines doesn’t pay; everything is equal at the margin.

Only at the margin. You might be an unusually alert driver, one who spots differences in lane speed faster than most and switches back and forth accordingly, getting home two minutes faster — at some risk.

Which reminds me of a different story, one on engineering other people’s incentives. A friend of mine told me that she never had dents taken out of her car because driving a dented car made other drivers more careful.

The same logic gives us the efficient-markets hypothesis. By the time you can predict that the price of a particular stock is going to go up it already has gone up — because lots of other people, including potential sellers, can predict it too. Unless you have some special expertise that lets you predict things other people cannot, you might as well save the time and effort of studying stocks and pick your investments by throwing darts at the listing page of the Wall Street Journal.

It applies to jobs too. Doctors make more than engineers but that does not mean you should choose to be a doctor.  There are always other people choosing careers; if being a doctor was unambiguously better they would become doctors instead of engineers, driving down the pay of doctors and driving up the pay of engineers.  It follows that if being a doctor is better in terms of pay it must be enough worse in other ways so that some of the people making the choice decide to be engineers.

Perhaps doctors have to work harder. Perhaps becoming a doctor takes more time, money, and effort. Even if you do not know what the disadvantages are, your first guess should be that all your options are on net equally attractive. The next step is to figure out where you are inframarginal, to look for a profession that is for some reason better for you than for most others choosing among the same alternatives.

Starting with the equimarginal principle as your first approximation works better than starting with the assumption that all you have to do is to look at wages. That, unlike most of what a student will find in an economics textbook, is an application of economics that is actually useful to him.

Rent Seeking

Economists are supposed to be objective social scientists, not preachers or moral philosophers; we have no expertise in questions of right and wrong, good and bad. The closest we come is to be in favor of economic efficiency, maximizing the size of the pie, the total value of all goods and services available for people to consume.³ It is not obvious, from that standpoint, what is wrong with theft. You steal a hundred dollars from me, making you a hundred dollars better off, me a hundred dollars worse off. Judged in terms of economic efficiency, don’t they cancel?

The answer is that the equimarginal principle applies to illegal markets as well as legal ones. If you can easily get $100 by stealing other people will enter the stealing business. As more and more people become thieves, the return to being a thief goes down. Potential victims are more likely to conceal their money, put bars on their windows. You try to pick a pocket and discover that one of your competitors has gotten to it first. The mechanism by which increasing the number of thieves reduces the return to theft is not quite the same as the mechanism by which increasing the number of doctors reduces their wages, but the underlying logic is the same.

As long as theft is more profitable than alternative professions, more people become thieves. The process stops when the marginal thief can make about as much stealing as working at McDonald's or whatever else is his most attractive employment. If all thieves are equally good both at stealing and alternative professions, none of them is better off as a result of theft; the entire amount stolen is being consumed by the diversion of labor out of productive activity into stealing.

In a more realistic picture there will be some inframarginal thieves, people either very bad at flipping burgers or very good at stealing; they will make a positive return just as the inframarginal driver saved a little time by switching lanes. But, if we include costs paid by potential victims in their efforts to avoid being stolen from, the net cost of theft could easily be more than the amount stolen. Whether or not that is the case there is a net cost, not merely a transfer. From the standpoint of economics, that is a reason to be against theft.

Next consider some American history with the same economic logic. Terry Anderson and P.J. Hill have argued that the homesteading act under which large parts of the US became private property was the largest mistake the US government has ever made, that it wiped out much of the land value of the US.

To see the logic of their argument, consider a piece of land beyond the current frontier of settlement as of 1870. There are no markets, no railroads, no roads, maybe hostile Indians. Someone who tries to farm it will lose $10,000 a year. As the frontier moves out the situation improves. By 1890 the loss is down to zero and the value of the land, based on the income stream it is expected to generate thereafter, up to $50,000.

Under the homesteading act of 1862, whoever settles on the land and farms it for five years will own it. You wait until 1890, when the land will finally be worth farming, only to discover that someone else has already claimed it; it was worth farming at a loss for a few years to get $50,000 worth of land.

If you had come a year earlier you would have had the same problem. As long as someone is going to settle the land at a date at which the money lost to establish his claim is less than the value the land will have once his claim is established, it pays someone else to come a year earlier. Running through the logic we just worked out for theft, we see that the land will get settled early enough so that the amount lost in premature farming just balances the eventual value of the land. Hill and Anderson concluded that the land should instead have been auctioned off. That way its value, instead of being dissipated by premature farming, would have been available to reduce taxes or pay for the government to do things.

This story has a sequel, because I got sufficiently interested to read up on the history of the conversion of public land to private property prior to the Homesteading Act. It turns out that attempts to auction off the public lands did not work very well.

It is announced that a parcel of land in the far West, somewhere around what is now Ohio, is about to be opened up for settlement. You are the representative of a consortium of entrepreneurs in Boston with the job of picking some good pieces of land and bidding on them. You arrive at the local courthouse where the auction is being held to discover that it is full of rough tough frontiersman with bowie knives in their boots and guns leaning up against the wall. They explain to you, very politely, that however it may be back East, around here, stranger, people don't bid against a settler for his land.

Although the land has not yet been opened for settlement, there are settlers living on it. You conclude that it might be risky to bid for pieces of legally unowned land against people who think they own them.  All of the good land ends up being bought at auction for the minimum legal bid.

There is also the political option. The illegal settlers argue that although they agree in principle with the idea of auctioning off the public lands there should be room for exceptions. They, after all, are brave American frontiersmen helping to expand the country; Congress should let each man buy his bit of land for a nominal price. Settlers are also voters so Congress is quite likely to agree.

As these examples suggest, there are practical problems to auctioning off an inhomogeneous resource belonging to a political institution. That may help to explain why homesteading was eventually set up the way it was.

Commitment Strategies

The plot of Doctor Strangelove, a popular movie from the nineteen sixties, hinges on a doomsday machine. The idea is due to Herman Kahn, a man who tried to think rationally about the implications of nuclear and thermonuclear weapons; Dr. Strangelove, the mad scientist the movie is named after, was probably intended as a parody of him. Kahn’s idea was a simple one: Instead of maintaining a large military, the U.S. builds a lot of hydrogen bombs designed to create as much fallout as possible, enough to end all life on Earth,⁴  and buries them in the Rocky Mountains with a trigger that will set them off if the Soviets ever launch a nuclear attack on the US. We tell the Soviets what we have done. The Soviets now know that if they attack us the world will end, so they don't. Kahn invented the doomsday machine not as a serious proposal but as a simplified version of what both we and the Soviets sere actually doing: Mutually assured destruction was a doomsday machine with human triggers.

There was one problem with Kahn’s idea that he may not have considered. If you are the last engineer coming out of the cave full of hydrogen bombs, what is the last thing you do?

(Answer in the footnote)⁵

The Doomsday Machine illustrates the idea of a commitment strategy. Sometimes the best way of achieving your objective is to set things up in a way that limits your future choices, to tie your hands.

That brings me to a talk I heard when I was a professor at UCLA. The subject was the limits of deterrence. The speaker told the following story:

Two guys in a bar get in an argument over which football team is better. The argument gets louder and louder; when it is over one of them is dead on the floor and the other is standing there with a broken beer bottle in his hand and a dazed expression on his face.

His point was that the killer could not be deterred by the threat of punishment because the killing is not rational behavior; the man regrets it as soon as it has happened. Crimes of passion cannot be deterred.

I got up at one end of the room, Earl Thompson⁶ at the other end, and we both responded more or less simultaneously⁷ that of course it was the result of rational behavior. It was a Doomsday Machine going off.

You are a big tough guy who likes getting his own way — as most of us do. You train yourself into an aggressive personality: You are a he-man and he-men don’t back down. You make it clear that if people cross you you beat them up. Your definition of crossing you comes to include things such as dating the girl you are trying to date or disrespecting your favorite football team. Most of the time your reputation as a bully pays off; people back down in order not to get beaten up.

One day you sit down in a bar. Another big tough guy sits down next to you. You order a beer and start explaining to him why your favorite football team is much better than any other football team — and he has the nerve to disagree with you. By the time the argument is over one of you is dead on the floor and the other is standing there with a broken beer bottle in his hand and a dazed expression on his face.

That quarrel is the human equivalent of a Doomsday Machine going off. Each of the two has programed himself with a commitment strategy: If you cross me I beat you up. Most of the time it pays — people don’t cross him and he doesn’t have to actually beat anyone up. Until he runs into somebody else with the same strategy.

Evolutionary biologists call it the hawk/dove game. In their version, hawks and doves are identical birds save for one difference: When two birds see a piece of food and both try for it, doves back down and hawks fight. A fight costs more than the food is worth, but as long as most of the other birds are doves a hawk usually doesn’t have to fight. If hawks, on average, do better than doves, hawks succeed in raising more chicks. The more hawks there are, the lower the payoff to being a hawk, so the ratio of hawks to doves adjusts until the payoff of both strategies is the same; the gain to a hawk from getting the food when the other bird is a dove just balances, on average, the loss from having to fight if the other bird is a hawk. It follows that if the cost of a fight goes up, the equilibrium number of hawks goes down.

Similarly for the bar room brawl. A legal system that punishes the guy who did the killing raises the cost to him of running into another hawk, which lowers the average benefit from committing to the bully strategy; the equilibrium number of bullies goes down. You have reduced the number of killings not by deterring bullies from getting into fights but by deterring people from becoming bullies.

Sex, Marriage, Barter

If a psychologist wants to get his audience’s attention, he talks about sex. Economists are more likely to talk about the income distribution but sex works for us too. I like to use the marriage/dating/sex market to explain the problem with barter.

If I am sleeping with you, you are sleeping with me. If I am married to you, you are married to me. On an ordinary market all you have to do is find someone who wants to buy what you want to sell and someone else who wants to sell what you want to buy. On a barter market you have to find one person who both has what you want and wants what you have, which is much harder. That explains why so many people are lonely, frustrated, and single.

Putting it that way not only gets the students’ attention, it also helps them see the advantage of money over barter.

The problem for an economics professor is how to persuade the students that economics is not boring, not just about money, may even be relevant to their lives. Armies running away are more interesting than prices going up or down, dating and marriage more important to students, or almost anyone else, than how the GNP or inflation rate is defined. How to choose a profession is important to students. So is how not to be fooled by people who tell you to invest in fuel oil because winter is coming and the price will go up. The explanations of both come out of the same economics as the efficient markets hypothesis.

The same principles apply to teaching economics outside the classroom. Probably the writing of mine that has done most to spread economic understanding is my explanation of how to grow Hondas⁸:

We have two technologies for producing automobiles: We can build them in Detroit or we can grow them in Iowa. Everyone knows how automobiles are built. To grow them you grow the raw material they are made out of, called “wheat,” you load it on a ship and send the ship into the Pacific. It comes back with Hondas on it.

That way of looking at trade tells you that an auto tariff protects American auto workers from the competition not of Japanese autoworkers but of American farm workers, that it is a tax on one of two alternative technologies in order to favor the less efficient.

Twenty years before I came up with that argument and published it, James Ingram published a longer and more elaborate version. Mine is a paragraph, his is most of two pages. In his, “A Fable of Trade and Technologies,” a mysterious entrepreneur, Mr. X, announces that he has made a great invention, a way of producing practically everything. To keep it secret he sets up his factory on the coast surrounded by a twelve-foot-high electrified fence, hires workers sworn to secrecy. He buys a wide variety of inputs, sells high-quality low-cost finished goods, “including textiles, cameras, watches, chemicals, and TV sets.”

He is a hero, a wonderful example of American progress, until “a small boy, vacationing with his family at a nearby seaside resort, tried out his new skin-diving equipment, penetrated Mr. X’s underwater screen, and observed that Consolidated Alchemy’s ‘factories’ were nothing but warehouses and that its ‘secret technical process’ was nothing but trade.” Now he is denounced as a fraud and his business shut down — although what he is doing, converting inputs to outputs, has exactly the same effect as what he pretended to be doing.

Ingram tells a better story than I do but also a much longer one, hence harder to remember and repeat, which is probably why my version went viral and I only discovered his when my friend Steve Landsburg pointed me at it.

1. First you shoot the bad guy in front. Then you shoot the bad guy in front. Then you shoot the bad guy in front. Then they all run slowly.

You can only impose an average cost of one chance in four of dying; that is not enough to discourage them, since they can count your arrows and are still coming. But you can impose a marginal cost of one chance in one on whomever runs fastest.

The story, puzzle, and picture are from my Price Theory: An Intermediate Text.

2. The poem is “The Raven Banner” by Malkin Grey (Debra Doyle). The account it is based on is from Njal Saga. I am simplifying a little — there were multiple leaders on the Norse side and they had Irish allies.

3. I explained what economist mean by economic efficiency in an earlier post.

4. My guess is that this was and is impossible, that although nuclear weapons are very powerful they are not as powerful as many people at the time imagined, but that is irrelevant to the economic point and including it would make both Doctor Strangelove and Red Alert, the novel it was based on, into less powerful, stories.

5. Cut the wire to the detonator.

6. Earl Thompson, one of my favorite economists, was the person who persuaded me that commitment strategies are a useful way of thinking about the world.

7. The scene may have improved over time in my memory.

8. David Friedman, Hidden Order, Chapter 6. Also Price Theory, Chapter 6.