Folk Songs and Economics
There is little economic theory in English folk music — most of the songs were developed when the subject was still fairly primitive, and few ordinary people understood much economics anyway. But here are a few brief thoughts on how songs in the Heritage Songbook illustrate basic economic topics.
Click on the link to find out about a particular economic topic and
Darling Nelly Gray: Labor and Industry *
The Farmer Is the Man: Supply and Demand *
The Flying Cloud: Game Theory *
Jefferson and Liberty: Economies of Scale *
Last Winter Was a Hard One: Financial Panics and Speculation *
The Longshoreman’s Strike: Game Theory and Labor Relations *
Darling Nelly Gray: Labor and Industry
Eli Whitney (1765-1825) was an equal opportunity revolutionary: He remade the economies of both the North and the South prior to the Civil War.
Whitney had a very strange career. He trained for the law — but the widow of the Revolutionary War general Nathaniel Greene pointed out the need for a device to remove the fibers from the burrs of short-boll cotton, and Whitney came up with a gadget to do it — the cotton gin. (It should be noted that Whitney did not invent the first cotton gin. There was already a device to do this for long-thread cotton. But that was a much harder crop to grow. A gin for short cotton was the holy grail of the cotton industry.)
Amazingly, the cotton gin did not make Whitney rich. His fortune was made in manufacturing firearms. And it was in that industry that he made his truly great invention.
Up to that time, weapons, and almost all other objects, were the work of craftsmen, made one at a time. Whitney changed that, by inventing interchangeable parts. The idea was that, by making many identical versions of the same component, it was easier to mass produce a final product. It also meant that, instead of a gunmaker having to know how to form a barrel and carve the firing mechanism and assemble all the parts, a laborer had to learn only one task.
The general concept of mass production was not new. Books had been mass produced since the 1450s. But Whitney made it possible to mass produce “stuff.” This was one of the two key discoveries of the Industrial Revolution (the steam engine, made efficient by James Watt, was the other; it made it possible to exploit power sources greater than human or animal muscle and more portable than millstreams).
It was the cotton gin which had the more obvious and immediate effect. Until Whitney introduced it in the 1790s, it had widely been believed that slavery was on the way out in the United States — as slavery was definitely on the way out in Great Britain. The United States Constitution permitted slavery at the time of its adoption, but it avoided the word itself, and most of the leaders of the nation thought slavery would die out within a few generations.
But, with the difficult task of extracting cotton fibers from cotton bolls suddenly solved by Whitney’s machine, it suddenly became possible to produce cotton at a much greater rate than ever before. Which meant that someone was needed to grow it. Someone who would work in the heat and humidity of the deep South, and who would work cheaply.
Given how terrible the job of cotton husbandry is, little wonder that the first thing to spring to mind was coerced labor — in other words, slaves. Especially since it was believed that Negro slaves, being the descendants of those who lived in the heat of Africa, were better able to stand the heat of the cotton fields. (As far as I know, this has never been verified scientifically. Blacks of course do not sunburn as easily as, say, the Irish, but that doesn’t mean that they are less susceptible to heat stroke; they may be more so, because their dark skin reflects less light energy.)
So the Deep South became a specialized economy, with only one real function: To grow the world’s cotton. As much land as possible was diverted to this end, and planters sought to create the largest possible plantations with the largest possible number of slaves. Any income that went in was not directed to improving the overall economy, or improving the lot of slaves; it went to buying more land and more slaves (McPherson, p. 97).
The Upper South — states like Virginia and Tennessee — was not so deeply involved in cotton planting; much of their land was not suitable for the crop, and in the eastern states, the soil was worn out anyway. (For more on this, see the portion in the Science page on Fertilizer.) But they could raise slaves to be employed in the Deep South. “Darling Nelly Gray” is an example of this very phenomenon: Nelly came from a border state (Kentucky) which was not a cotton state. But she was “sold south” to Georgia, which was a cotton state. Her case is somewhat unusual — it was rare for non-rebellious female slaves to be sold south — but it was entirely legal by the standards of the time.
In the North, they complained of “wage slavery” — and indeed many who worked for wages in the North had hardly more material goods than the slaves on some of the better southern plantations. Hence, for instance, the riots in the slums of the eastern cities, and the wild demonstrations in New York during the financial panics (for which see the section on Financial Panics below). But at least a wage slave could seek another job. Slaves could not (and, as post-war experience seems to show, they reacted with a sort of controlled laziness. Slaves, who had no reward for their labor, worked only as hard as the overseer required — and if an overseer on one plantation demanded more effort than the other overseers of the district, he would find himself subjected to all sorts of problems and complaints; usually he backed off eventually. The Southern economy tended to be far less efficient than a free economy. This is far from unique; Ireland in this period, where the laws saw to it that a tenant could not gain any benefits from his work, was also marked by an unusually unproductive labor force, which grew just enough food to feed the people a miserable and unvarying diet.)
Slavery came to be called the “Peculiar Institution.” The South in the pre-Civil War era might well have been called the Peculiar Economy. McPherson, p. 10, estimates that, in the three decades before the Civil War, average income of Americans roughly doubled, but income for laborers increased by only about half as much. In other words, the rich got richer faster than the middle class and the poor — and the planters of the Deep South in all likelihood led the way. The poor whites of the South tended to be far poorer than those of the north — some so poor that, even in the world’s most productive agricultural nation, they suffered from malnutrition (which produced, for instance, the very strange phenomenon of the “clay-eaters”). Chronic conditions such as tapeworms were more common in the south, and health care harder to obtain. (Admittedly a doctor in 1860 wasn’t good for much except setting bones, but in a world where almost everyone works outdoors, the ability to set bones is important!)
The differences between the sections were amazing. McPherson, p. 40, notes that “From 1800 to 1860 the proportion of the northern labor force engaged in agriculture had dropped from 70 to 40 percent while the southern proportion has remained constant at 80 percent. Only one-tenth of southerners lived in what the census classified as urban areas, compared with one-fourth of northerners…. In business the proportion of Yankees was three times as great, and among engineers and inventors it was three times as large. Almost half of the southern people (including slaves) were illiterate, compared to 6 percent of residents of free states.”
When the Civil War came, the South found that its extreme specialization did not serve it well. Cotton alone could not win wars. The South had too little industrial development, and too little transport — and could not build more, because it didn’t have the industrial base to improve its railroads; it could not built engines, and could produce only a limited amount of track. Most railroad “repairs” in the South consisted of cannibalizing less useful sections of track. Most weapons were captured. They had difficulty producing basic farm machinery. They could not even turn their raw cotton into finished clothing; McPherson, p. 95, says that in 1860 there were more cotton spindles in Lowell, Massachusetts than in the entire 11 states of the Confederacy! A popular song during the war was “The Homespun Dress” (see the text below), in which a southern girl boasts that her clothes may be ugly and uncomfortable, but at least they were not imported. During the War, the North could and did use such things as the McCormick Reaper to bring in more crops with fewer workers; the South had to keep workers in the fields to feed their armies.
The South had, on the whole, better generals than the North. It had a much simpler task, since it had only to defend its territory; the North had to attack. The South still lost — and it lost, more than anything else, because of its specialized economy.
The Homespun Dress
Oh, yes, I am a Southron girl,
And glory in the name,
And boast it with far greater pride
Than glittering wealth or fame.
We envy not the Northern girl,
Her robes of beauty rare,
Though diamonds grace her snowy neck
And pearls bedeck her hair.
For the sunny South so dear;
Three cheers for the homespun dress
That Southron ladies wear.
The homespun dress is plain, I know,
My hat’s palmetto, too;
But then it shows what Southern girls
For Southern rights will do.
We’ve sent the bravest of our land
To battle with the foe,
And we will lend a helping hand
We love the South, you know.
If you study the history of the late nineteenth century, the American farm economy was almost always in near-crisis. The farmers were forever complaining of low prices and saying that they were on the verge of bankruptcy.
And they were generally right. Why? Oversupply. As the west was opened, more and more land was available for farming — and, though the farming methods of the period were not efficient by modern standards, they were productive enough to consistently yield larger harvests than could be consumed by the population of the time.
The result was textbook: With supply of farm products (especially grains; also cotton) abundant, supplies for these commodities remained consistently low. Farmers sang of “seven cent cotton and forty cent meat,” and complained of bankers’ greed in songs such as “The Farmer is the Man.”
As Nevins and Commager write, p. 285: “Overexpansion led to overproduction; the purchase of larger farms and of expensive agricultural implements with which to farm them meant a load of debt which could be carried only while high prices obtained…. As in ages past, the farmers toiled long hours under the hot sun, lived without the comforts of community life, and in the end had little to show for their labors.” Laura Ingalls Wilder’s book The First Four Years, which she never published in her lifetime, is a catalog of this, in extreme form (since personal ill-health and extreme weather made the Wilders’ problems particularly severe): Almanzo Wilder owned too much land, bought too much machinery, and over the course of four years was forced to yield it all up, bit by bit, as he could not raise enough crops to meet the payments.
The farmers’ political proposal was one which would sound ironic today: They wanted inflation. Their main proposal was “free silver” — that is, the circulation of silver-based money in addition to the gold-based money of the time. With more money in circulation, it would be easier for them to pay off their loans.
Eventually the cry was heard far enough that William Jennings Bryan could make his “Cross of Gold” speech and become the Democratic nominee for president. But he was never elected, and silver never became the primary basis for legal tender. The farm crisis, insofar as it was solved at all, was solved by shipping surplus grain to other overseas markets.
The Flying Cloud: Game Theory
A song about a young man turning pirate may seem like a bad example of game theory, but in fact this is a song entirely about decision under risk, which is the essence of game theory. Three times young Willie Hollander had to make career choices — strategic decisions. Each one had a potential payoff and a potential danger.
Young Willie started out as a cooper’s apprentice — that is, an apprentice barrel-maker. It was a respectable trade, but apprentices earned little pay, had little time off, and were little more than slaves to their masters. If the master was harsh, it could be a difficult situation.
So Willie had to make a his first choice: Stay on as a cooper’s apprentice, or run away to sea. The former meant several years of additional service before he earned his journeyman’s papers, but was almost 100% safe. The latter meant more excitement, and probably higher pay — but carried significant risks. Since we don’t really know anything about the ship he sailed in, we can’t say what the exact risks were — but a good basic number would be that he faced about a 2% chance of being killed in a particular voyage, and about a 5% chance, perhaps more, of suffering a career-threatening injury (it was a rare sailor who could still run the rigging after age forty; most by then had suffered “ruptures” — hernias and the like — which forced them ashore, half-crippled or worse; more than a few ended up losing limbs). And the longer the voyage, the greater the risk.
For whatever reason, Willie chose to go to sea. But it can’t have been a very satisfying choice; on his early voyages, he would have been rated no better than a landsman, and it’s unlikely that he had made it higher than ordinary seaman by the time he ended up in Valparaiso.
Captain Moore’s offer to hire Willie made things much, much more interesting. It seems not unlikely that the captain wanted Willie because of his skill as a cooper — ships at sea kept most of their vital supplies, including fresh water as well as flour, drink, and salt meat, in barrels. Coopers were vital to keep these barrels tightly sealed. Most legal ships had no trouble hiring coopers, but slavers were a much lower grade of vessel. If Captain Moore had lost his trained cooper, hiring Willie must have been attractive — sure, the kid wasn’t fully trained, but he was a lot better than nothing.
So Willie was probably offered a substantial pay raise — partly because slavers made large profits, and partly because of his skills. But he also faced an increased risk. My guess is that this story is set in the years around 1830-1840. I base this on the fact that there seem to be no ocean-going steam craft (which implies a fairly early date) but that the destination of the slaver is Cuba (which implies a date after the United States closed off the slave trade). By this time, Great Britain was actively working to stop the shipment of slaves. Also, slave ships, because of the misery and squalor in which they kept their cargo, did suffer higher losses among the crew.
So, as a wild guess, Willie was offered a three-fold increase in pay. But his odds of disaster had risen. On the Ocean Queen, he had a 2% chance of dying and a 5% chance of being maimed. On the Flying Cloud as a slaver, he suffered perhaps a 4% chance of dying, an 8% chance of being maimed, and a 10% chance of being captured and the ship being broken up — meaning that he might end up in prison and certainly would not be paid.
Since it was estimated that a slaver paid itself off after three voyages, the slave trade was still worth it, for the owners. And evidently Willie thought it was worth it for him, too.
After the slaving voyage, Willie was offered yet another decision under risk: Turn pirate, or go ashore. The latter was safe — but it meant significant economic loss. Having left one master, he probably could not hope to be given another apprenticeship. He surely didn’t have enough money to go into farming. Probably he would have had to return to being an ordinary seaman, with the low pay that entailed.
Or he could turn pirate. This was a really interesting choice. There were two risks: Death, and failure to take significant prizes. If the British were against slavers, all nations were against pirates, and would kill them if caught. And many pirates did not even capture enough to make a good living. Piracy was in fact a poor career choice — most pirates died both young and poor. But a few struck it rich, and for an ordinary seaman on a ship with a bad captain, almost anything sounded good.
For a pirate, then, there were three possible outcomes in a given period of time: Get rich, die, or neither of the above, which probably meant being forced to remain a pirate. We might guess that, after one year, the probabilities were as follows:
15% strike it rich
40% be captured and probably executed
45% survive to do it again.
Of course, the Flying Cloud is described as being a very fast ship with a heavy armament — perhaps, like the battle cruisers of a later war, she was expected to outrun what she could not outgun. Would this affect the odds? It obviously adds another twist to the model of the game.
At each stage of the game, Willie had a choice to make. In each case, we can calculate the expected payoffs, and make a decision what to do. In the first and second cases, Willie could be said to have won the game. In the third, he definitely lost.
I suppose you could argue that songs like “Cole Younger” also illustrate game theory. Not so much by the robbers as by their victims. The three men in the bank in effect “conspired” to foil the robbers by not telling them that the safe was open and by being very stubborn about not cooperating. They bet their lives against the money, on the basis that the alarm had been raised and the robbers had only limited time to find the money and run. That one turned out to be, in game theory terms, rather a draw — cashier Heywood lost his life, but the robbers managed to gain almost no money, and in the end, three robbers ended up dead and three were in prison.
Jefferson and Liberty: Economies of Scale
Thomas Jefferson was one of the greatest American political thinkers. His ideas influenced the nation for generations. But he was not a very successful president (the economy did not grow very fast in his time) — and, in the end, the nation turned away dramatically from his ideals.
Jefferson dreamed of a nation of small farmers and artisans. He thought — probably correctly — that such a society would be more free and more egalitarian than the true capitalist system that threatened to replace it. Many people still dream of going back to a small-town existence. So — why don’t we?
Because such an economy can’t compete, that’s why. In a true Jeffersonian economy, there can be no cars or computers, no televisions or recording industry. There is no one to make them! To build these items requires a very large production facility, larger than was possible in a Jeffersonian world.
Even if people were willing to settle for a lesser technology, there was another problem: Specialization, and economies of scale.
This is easy to model. In a Jeffersonian world, roughly 80% of the population are farmers. They grow their own food, make their own clothes, in all likelihood build their own homes and furniture, and turn to others only when they need someone with highly specialized skills (blacksmiths, physicians). The farmers produced only about 20% more food than they themselves needed, and the artisans similarly could produce only a slight excess.
Compare this with a specialized economy. A Jeffersonian wife with a spinning wheel can make only enough clothes for her family. A cloth worker in a factory can make enough cloth, or sew enough garments, to clothe hundreds of people. A home-building syndicate, with a specialized carpenter, and bricklayer, and paneller, and so forth, can build a home in a tenth the time, and for significantly less cost, than an individual.
In a specialized economy, though no one can meet all their own needs, they can produce enough excess to supply many, many people. They may make only one of (say) ten things necessary for life — but they make enough of that one thing to supply twenty or thirty other people. Whereas the Jeffersonian economy produced surplus goods of only about 20% in excess of immediate need, the specialist economy can potentially yield 200-300% more — or even more if sufficiently automated.
And, as a result, many, many more people can be born, raised, fed, and clothed. They need a medium of exchange (since they need to determine how many pints of wheat are worth as much as a shirt, or how many horseshoes one needs to forge to be able to pay for a house), and they lose independence — but they can support a lot more people.
A non-Jeffersonian economy can produce enough excess to allow rapid population growth. And hence they simply squeeze out the Jeffersonians, who are starving to death on their independent farms.
This gives us a brilliantly simply concept for an economic model. (You can surely come up with others if you want them. But this one is nice and easy.) We need only two parameters: The efficiency of the economy (call it h), and the economy of scale rate (call it s). Our other variable is population (p).
Let’s assume that the population increases directly in proportion to production. We said that a Jeffersonian economy had a productive excess of 20%. So if the initial population is 100, it produces enough food and other goods for 120 people. (In other words, h=1.2.) Therefore, in the next generation, we assume that it will have 120 people. These 120 people will produce enough food for 144, so the next generation will have 144 people. And so forth. The formula for the population is then as follows:
P(n+1) = h * P(n)
This can, incidentally, generalized as
P(n) = hn * P(0)
(A rule which allows us to calculate the population even for fractions of generations.)
For the diversified economy which allows economies of scale, we add a scale parameter. For example, suppose we want our economy to increase its efficiency 25% if we double the population (actually a rather low rate of economy of scale). It then turns out that our parameter s is about 0.32. (To figure out the parameter, just divide the logarithm of the increase in efficiency by the log of the increase in population — in this case, log[1.25]/log.) In this case, our formula becomes
P(n+1) = h * P(n) * [P(n)/P(0)]s
So let’s run an experiment. Let’s use h = 1.2 in both the Jeffersonian and diversified economies, but use our scaling factor of s = .32 in the diversified economy. How many generations does it take for the diversified economy to have ten times as many people as the Jeffersonian?
Just eight generations, believe it or not:
|Generation||Jeffersonian economy||Diversified Economy|
And the Diversified Economists drive the Indians, er, Jeffersonians, into the sea.
And that’s if we assume that, in the initial population, there is no advantage to the diversified economy at all! If we give it any advantage (e.g. a productivity edge of just 10%, or h=1.22 instead of 1.2), things get even more extreme (in the case of that 10% productivity edge, the diversified economy becomes ten times as large as the Jeffersonian after only seven generations, with a population of 4117 verses 358).
Here is a historical scenario to examine: in 1840, when the Jeffersonian economy really broke down, the American population was about 18 million. The 2020 population, in round numbers, will be 300 million. Consider values for h and s which produce such an increase. They won’t need to be very high.
This doesn’t mean that everything can scale infinitely, of course. At some point, a factory reaches the maximum possible efficiency (if nothing else, because it will run up against the second law of thermodynamics). And, in all likelihood, the system will have run into a supply bottleneck even before that — there won’t be enough land, or enough energy, or enough molybdenum, or something. In a high-population, high-energy, no-population-control society, this can be disastrous. (See what happened in Ireland when the potato supply failed!) But, by then, the economy-of-scale society will have crowded out all the alternatives.
This does not mean that we absolutely cannot return to a sort of “semi-Jeffersonian” world. This was the dream of people like E. F. Schumacher. In the long run, it’s the only sustainable sort of economy. But it will take more people agreeing to it than have ever agreed to it so far. And, in all probability, a much lower world population.
In the century after the War of 1812, the United States suffered half a dozen major financial downturns: The Panic of 1819, the Panic of 1837, the Panic of 1857, the Panic of 1873, the recession of 1893 (not always called a panic, for some reason) and the Panic of 1907. These varied in severity (that of 1837, which lasted through two presidential terms, was probably the worst), but all resulted in major unemployment and bank failures.
Indeed, it was bank and business failures which seemed to start each downturn. As a result, unemployment rose dramatically. Several panics resulted in riots, and someone would usually respond with some sort of employment scheme.
If there is a common thread to all these events, it is over-extension of credit followed by collapse as people started demanding payment in hard currency. The nature of the crisis varied, but always it seemed to involve a mismatch between investment and the ability to back the investments — what we would now call over-leveraging.
The Panic of 1819 resulted from a great credit bubble in the wake of the War of 1812. Commodity prices rose fast, and land speculation was rife. In 1817, the government switched to requiring (and making) payment in hard currency, and the myriad unbacked bank notes collapsed. It is considered the first serious recession in American history, though it ended quickly enough that James Monroe was re-elected President in 1820 without major opposition. (The only unopposed election after George Washington.)
The Panic of 1837 was far worse, lasting (depending on which source you consult) at least three and perhaps as many as seven years and ruining the re-election prospects of Martin van Buren. It is blamed by some on overdevelopment in the west, which naturally involved a lot of settlements on a shoestring. The fault is arguably that of Andrew Jackson, who attacked the Bank of the United States. And Jackson also insisted on a hard money policy. In 1836, congress tried to repeal the specie circular (requiring payment for federal land in gold and silver), but Jackson pocket vetoed it. The first signs of trouble began even before van Buren took office: In February 1837, rioters protested against high prices by attacking warehouses in New York. In May, banks began to suspend payment in specie, and these were not entirely resumed until 1842.
The Panic of 1857 destroyed over 4000 businesses. It started in August of 1857, when the New York branch of Ohio Life Insurance and Trust failed. Nevins and Commager, p. 244, call it “brief [but] disastrous,” and note that it inspired calls for a protective tariff and a better banking system. In this case, the national political effects were slight — everyone was too worried about slavery — but on the local level, there were all sorts of proposed remedies.
The Panic of 1873 was second only to the Panic of 1837 in severity; it lasted five years, and would have swept the Republicans out of office in 1876 were it not for the chicanery of the Hayes/Tilden election. It started rather suddenly, on September 18; supposedly 37 banks and brokerages failed on that very day, and Jay Cooke and Co. also failed. Once again, the cause seems to have been inflation resulting from too much paper money. On September 20, the stock market was closed for ten days. Labor disruptions in the form of mass strikes continued as late as 1877.
The Panic of 1893, called “dreadful” by Nevins and Commager, p. 472, lasted almost five years. One of the factors was the usual speculation. But currency manipulation also played a part, as the government mismanaged the nation’s supply of precious metals. The problem of silver and gold shows the danger of government price controls, at least when the prices are not rationally set. For many years, the government had coined both silver and gold. A 16:1 price ratio of silver to gold went back to the time of Andrew Jackson (Current/Williams/Freidel, p. 559). Silver at that time was in relatively limited supply, meaning that the 16:1 ratio actually made it uneconomic to sell silver to the government. Few silver dollars went into circulation. But silver was found in the West in the 1870s, and suddenly there was a silver surplus. Suddenly, instead of silver being worth more than 16:1, it was worth less, and equating it with gold at that rate meant that a silver dollar was said to contain only enough silver to be worth 57 cents of a gold dollar. (Remember that, at this time, coins were basically like the old shekels and drachmas of Hebrew and Greek culture: A coin contained a certain amount of metal, and it was the metal, not the coin itself, which had value.)
The result was an economy built on false valuations — a “bubble.” Which popped spectacularly. The downturn had started to afflict the west as early as 1887 due to falling agricultural prices (Current/Williams/Freidel, p. 558) — Kansas lost half its population from 1887 to 1892, according to Morison, p. 789, inspiring the motto “In God we Trusted, in Kansas we Busted.” The Silver Purchase Act of 1890, and balance of payment problems (the British pulled out of American railroad securities, sensing their essential weakness — the Philadelphia and Reading in 1893 failed to the tune of 125 million dollars!), meant that the government was short of gold and in danger of default — an obvious source of panic. Throw in a very high tariff, and you had “the worst industrial depression since the 1870s” (Morison, p. 796). Current/Williams/Freidel, p. 558, say that 8000 businesses failed in six months, with a million people (20% of the labor force) being thrown out of work. Jacob S. Coxey proposed a series of ideas which were rejected at the time — “Coxey’s Army” was halted by police in Washington (Current/Williams/Freidel, p. 559) — but which were largely adopted during the New Deal (and Coxey, who lived until 1951, was actually around to be vindicated). The troubles of the workers, especially in Chicago, led to the famous Pullman Strike of 1894. The tide did not begin to turn until President Cleveland forced the repeal of the Sherman Silver Purchase Act, reducing the problem of two currencies with unequal values.
The Panic of 1907 began on October 1 as the Knickerbocker Trust failed; once again there had been an extensive overcapitalization of new businesses. J. P. Morgan was able to stand firm and prevent the collapse of the dollar (the last time — indeed, the only time — a private businessman was able to directly control the economy), but the downturn still lasted about two years.
There is an interesting point here about speculation and the herd mentality.
The investment market historically has had a bad tendency to play “follow the
leader.” If some stock-buying strategy is deemed a success, everyone pursues
it. If western land speculation made one person rich, everyone tries it.
At best, such strategies are self-defeating; at worst, self-destroying. The
stock market illustrates this.
Take a very simple strategy — say, “Pick the one of the world’s ten largest companies with the highest P/E ratio” (where the P/E ratio is share price divided by earning per share, a common measure how stocks “ought” to be valued). Suppose you buy shares of X Corporation as a result. This will force the price of X Corporation up slightly. But supposing everyone follows this strategy. The price of X Corporation will rise at least enough that it no longer has the best P/E ratio, whereupon everyone will shift to buying
the company with the next-best P/E ratio.
Theoretically, the result would be what mathematicians call a “predator-prey” cycle, of sinusoids out of phase. In practice, because not every stock trader can strike at the same moment, it will all be a bit fuzzy because of time delays. Theoretically, if you can move ahead of everyone else, you can make a little profit by being ahead of the game. In practice — good luck.
And if the delays in the system are significant, the problems get worse. Suppose everyone keeps buying Corporation X even after the P/E ration becomes unacceptable. The price is now far too high for the P/E ratio, and will crash. Investors who over-bought at the highest price will go bankrupt, reducing the capital in the system, and everything starts to fizzle.
This is just a stock market model, but it applies to anything. It’s where most of the panics came from. Most means of getting rich by simply moving money (as opposed to producing product) are such that they work well on a small scale. Sub-prime mortgages where you know a buyer will fail and be foreclosed are a good idea if you are the only bank doing it — the rest of the housing market will let the bank sell the foreclosed house at a good price, and meanwhile the bank has gotten whatever they have gotten from the person with the subprime loan. But when there are enough such gimmicks that the housing market can’t absorb the houses, you have a bubble.
Any strategy that has to divide a certain pile of cash too many ways doesn’t work. It’s basic mathematics. To beat the market, in the long run, you have to do something the market isn’t doing. Of course, if the market isn’t doing it, it may be because it’s a stupid idea (selling dog-biscuit flavored pizza treats, say), and you’re going to get killed. But it’s the only choice you have. Fail to do so — and next winter will be a hard one.
The Longshoreman’s Strike: Game Theory and Labor Relations
Most books about labor strife talk about the history, pointing out that, for many years, the American government maintained a strongly pro-business, anti-labor policy. Then, in the twentieth century, we saw a swing toward labor. Now, in the twenty-first century, we are seeing a dramatic move away from labor again as businesses are convincing workers to go without unions and as government employees are treated increasingly not as people who help society but as burdens on it.
There is an irony here, in that everyone is trying to make a cooperative “game” into a zero-sum game. Properly speaking, if labor and management work together to increase productivity, they can both see rewards. But this is a complicated interaction. Whereas it’s very simple for the workers and management to see each other as The Enemy.
And that makes modelling easy — and also gives us an easy opportunity to show how game theory works in the real world. It also gives us a lesson in what is known as a “mixed strategy” — that is, instead of always doing the same thing, how a player in a game (or a union or management representative in a negotiation) cannot always do the same thing.
Let’s break this down into a very simple model: Labor has two choices, to hold out or to give in to management. Management has two choices, to hold out or give in to labor. For the company as a whole, the worst thing is probably that they both hold out; the union goes on strike, the company shuts down, and it loses all its profits. Let’s call that a -2 value for the company. If the company gives in and labor holds firm, then the company owes more in labor
costs, so the value for the company is -1. If the company holds firm and the
union gives in, then the company doesn’t have to pay as much in wages but has
disgruntled employees; again we’ll call that a score of -1. If both give in,
we have a compromise; call that score 0. Then we can fill out what is called a “payoff matrix:”
|Give in||Hold out|
If we express it by comparing labor’s payoff with management’s, we get a different matrix, perhaps something like that shown below, showing M(anagement’s) payoff in the upper right, L(abor’s) in the lower left.
|Give in||Hold out|
Be it noted that this is the infamous game of “Prisoner’s Dilemma,” about which more has been written than I can possibly reproduce here. This potentially tells us a great deal about labor relations: The best strategy for both labor and management is to give in (compromise), but the equilibrium strategy for both is to hold out, hurting both the union and the management and the company as a whole.
|Give in||Hold out|
|Give In||Best Case:
And so we have bitter results like the Longshoreman’s Strike, which did management little good and hurt the workers terribly.
Strikes themselves often illustrate another class of problem well known to game theorists, the game of “Chicken.” The classic example is of two or more cars racing toward a cliff, with the winner being the last one to swerve to avoid going over the edge. A strike is an equally good illustration, since the union doesn’t want to end the strike and make concessions, and management doesn’t want to give in and make concessions; if they both hold out long enough,
the company can fail and both sides go over the cliff. The payoff for the labor version of Chicken often looks something like this:
|Give in||Hold out|
Of course, these are all cooked-up situations. if the company has a large stock of product on hand, and workers who are overpaid compared to comparable workers at other businesses (say, the situation which pertained in the American auto industry around 2008), then the company can afford to have the workers go on strike, and its payoff for holding out increases. On the other hand, if the company is just barely able to meet demand, and has a skilled and irreplaceable work force, then the company’s payoff for giving in increases, because it doesn’t want to risk even a moment’s shut-down. By adjusting the payoffs in each cell of the matrix, we adjust what is the best strategy for each side. This is where game theory is at its best. The real trick is to figure out just what a particular outcome is worth to each side — technically, not game theory but what is known as utility theory, although the two are almost always taught