<Z e h> J o u r n a l

December 10, 2008

The foundations of modern economic theory were well established by the concepts recorded in the Talmud, Nobel-Prize winning mathematician Dr. Robert J. Aumann demonstrated in a lecture delivered at Touro College’s Lander College for Men on the evening of December 2. 

Dr. Aumann is a Professor at the Hebrew University in Jerusalem and a member of the United States National Academy of Sciences.  He was honored with Nobel Memorial Prize in Economic Sciences in 2005 for his work on conflict and cooperation through game theory analysis.

With his lecture, “Modern Economic Theory in the Talmud,” Professor Aumann demonstrated how ideas that only became clear 250 or 300 years ago in Western economics were anticipated in the Talmud.

The Cornerstone of Economics:  Incentives.

Professor Aumann opened with the basic idea of modern economic theory, which is incentives. 

“What makes the economic world go round is the idea of incentives,” Professor Aumann explained.  “If you match the economic system to the incentives of the people involved in the economic system, the workers, and the consumers and the entrepreneurs, then you will get a system that works. And if you do not match the incentives that are inherent in the system, to what the workers and the consumers and the entrepreneurs want, then your system will fail. 

“We’ve seen that happen in the previous hundred years.  We had this great fiasco which was communism and socialism which failed because it did not take into account that the basic incentives of people are to do better by themselves, to do better for themselves.

Professor Aumann pointed to an incident recorded in the Talmud which reveals how the fundamental importance of incentives was clearly recognized by the rabbis in Talmudic times.  An economic crisis required the rabbis to overlay a new program, called the pruzbol, over the basic Torah law, in order to keep in check the incentives of society.

According to Torah law, every seven years there was a release of debts.  Similar to bankruptcy law, but implemented across the entire nation, the Torah decrees a release of all debts at the close of every seven-year cycle.  This law of economic renewal is called “shmittah” or “release.”  However, to prevent a slowdown of lending, the Torah buttresses shmittah with a strong prohibition to lenders that they should guard themselves against refraining from lending to the needy as the seventh year approaches.

Unfortunately, by Hilell’s generation, the larger part of the lenders did indeed refuse to lend towards the close the shmittah year.  People were growing poor in the fifth and sixth years of each cycle, Professor Aumann explained, as lenders, concerned about defaults and the extinguishing of debt with the seventh year, refused to extend credit.

“Hillel ordained the pruzbol to fix the world,” the Talmud says, in the fourth chapter of Gittin.  Professor Aumann explained.  “The Torah says that in the seventh year, the shmittah, we do not harvest the agricultural products, and we also cancel all loans.  The Torah foresaw what was going to happen over there, the Torah says specifically, hey, you’ve got to watch out and not to close your hands not to say, I’m not going to lend people money because the loan will be cancelled… you shouldn’t do that. You should ignore that.   You should think of your fellow man, you should think of the common good. 

“Now Hillel saw that it’s written in the Torah, that you shouldn’t do it, but they did it.  People became poor in the fifth and the sixth year, and the seventh year, the economy slowed down…  He saw that the people refrained from lending money, so he enacted the pruzbol.”

The pruzbol operated similar to an assignment of a lender’s claims to the court during the shmittah years.  The court is able to preserve the claim on behalf of the lender so that the debt would not be cancelled with the shmittah release. 

In order to bridge the chasm between the real and the ideal, between the law of the society as it should operate in its fully developed state, and the way people actually acted when dominated by fears and selfishness, Hillel intervened to create the pruzbol.  When the fears about cancellation of loans was eased, the credit markets opened up again.  By making the claims  of creditors enforceable with the pruzbol through the shmittah, lenders allowed poor people to access the loans they needed.

“Tikkun olam,” literally, “fixing the world,” is required where the basic law of society creates wrong incentives, Professor Aumann explained.  “In spite of the fact that its well meaning and it sounds moral, and it sounds ethical, but if it gives people the wrong incentives, its not going to work.”

In the language of game theory, a branch of mathematics championed by Professor Aumann, the pruzbol “adjusted the incentives of society.”

Professor Aumann points out that although Viet Nam is still a communist dictatorship, they have a market economy, because in 1987 the Communist government realized their people were starving.  After asking how they are going to fix it, he said, the leaders found, “there’s one way to do that, when people work for themselves, not for other people, not for the common good.   This was an example of fixing the world to correspond to the incentives that people had.”

“We were mentioning the economic downturn that we are witnessing now, and indeed, a  lot of that economic downturn is caused by not fine tuning the incentives, incorrect incentives in all kinds of places.  These are all things that can and should be corrected,”  Professor Aumann commented.

Price control and competition.

The Torah itself specifically forbids cheating in business.  Specific verses forbid dishonest practices such as inaccurate weights and measures which merchants would use to their advantage to cheat others.

The Talmud, Bava Basra, 89a, records an interesting inference contained in the Torah’s prohibition against dishonest weights.  The Talmudic Sage Shmuel inferred from the Torah’s specific prohibition against dishonest weights and measures a corresponding obligation on the government to insure fair business practices in weights and measures.  That government regulation, however, Shmuel extrapolated, should only be limited to regulating weights and measures.   The Talmud records, in the name of Shmuel, “inspectors should be appointed for weights and measures, but not for prices.” 

Professor Aumann explained how the Medieval commentator Rashbam spells out Shmuel’s reasoning.  Directly quoting the Rashbam, he said, “It’s common sense, price control is not needed.   For if one seller sells dearly, another merchant who needs money, will undercut him, will sell cheaply, because he wants the business, and the buyers will go to this other merchant who sells cheaply, and then the first one will also sell cheaply, because otherwise he won’t get any customers.”

“Ladies and gentlemen,” Professor Aumann said, “this is the basic principle of the market economy.  This is what the market economy is all about.  Competition leads to prices finding their correct level.  You do not need to fix prices. You fix prices, then you get situations like you had in Russia and Poland and Viet Nam, where people were starving.

“It’s not entirely explicit in the Gemara, but it is entirely explicit in the Rashbam.  The Rashbam is 12th century.  This was first promulgated in the economic theory by Adam Smith in the 18th century.  So we’re talking about Adam Smith, the father of modern economic theory, being anticipated by the Rashbam, not by a few years,  but by 600 years he was anticipated.  And don’t think that this is a trivial matter.  Maybe to you and to me it’s easy to see that prices need not and should not be controlled.  It wasn’t at all clear to the contemporaries of the Rashbam, including, I’m sorry to say, the Rambam.”

Professor Aumann explained that the Rambam (Maimonides) held that inspectors should be appointed for weights and measures, and also for prices.  Professor Aumann speculated that Rambam’s ruling may have been influenced by the Scholastics, including Thomas Aquainas, and Muslim philosophers who advanced the idea of a “just price,” that there is a level of pricing which is correct, which is not determined by market forces.

In response to questions from the audience, Professor Aumann clarified that the idea of free markets, with no price controls, was not incompatible with the Torah’s prohibitions against overcharging in business.  The law against overcharging in business, called “onaah,” is measured against the rest of the market prices.   That is, in order to evaluate whether a merchant has overcharged, his price is compared to the prevailing market price of similar merchants.  “Onaah is misleading a particular customer,”  Professor Aumann said.

An audience member suggested that, in defense of the Rambam, price controls would be appropriate in certain inefficient markets, like monopolies or markets where relative price information is not readily available to the buying public.  In such inefficient or opaque markets, it might be advanced, government price control would be necessary.  Professor Aumann ceded this point and said the Rambam has been vindicated.

Moral Hazard.

The Talmud addresses how the decisions of self-interested human actors can alter the rules of probability and render impractical systems that are built on probability. 

Across the Talmud, according to Professor Aumann, the following case is brought approximately 26 times.  “There are 10 stores, all selling kosher meat, except for one, which is selling traife [non-kosher] meat.  If a man buys from one and doesn’t remember which one, then because of the doubt, the meat is forbidden.  But if he found the meat on the street, then we go by the majority.”  Kesubos 15a.

“The way this is usually summed up… anything which is in its place, in the original place where it was, is considered half-half, you can’t tell which, and when you have a half-half situation, you go l’chumra [rule stringently to prohibit].  But, if it left its original venue, then you go by the majority, you use probability theory.”

To paraphrase, since there are nine kosher stores opposite the one non-kosher store, according to the majority, the probability is higher that the meat is kosher, and, accordingly, the meat that is found on the street would be considered to have “left its original venue” in Professor Aumann’s words, and be deemed halachically kosher.  (Whether it is practically rendered permissible depends on the specific circumstances of each case.)  However, when the meat is found “in its place,” to use Professor Aumann’s words, that is, it was carried in the hands of the man who bought it, then the probability in reduced to 50-50, that is, either its kosher, or its not.  In such a 50-50 question, the law requires a stringent ruling to prohibit the meat.

This case turns on the issue of moral hazard, Professor Aumann explained.  A practical, modern-day application of the fundamental economic theory of moral hazard is the principle that underlies insurance. 

Professor Aumann gave an example.  A man could take out an insurance policy for the full value of his house.  However, if the man tried to purchase two policies, even if the man offered to double his premium, the insurance company would refuse to write him two policies.  These two policies would pay out more than the value of house itself.

Why wouldn’t the insurance company want to take twice the business?  Professor Aumann asked.  “If you have two insurance policies, you have a positive incentive to burn down your house.  And even if you’re an erliche yid, and you wouldn’t dream of doing such a terrible thing, even then, you’ll be a little less careful, or maybe a lot less careful.  You won’t worry if you left the gas on when you go away for a vacation… Your actions influenced the probability that this is going to happen. 

“The size of the premium is based on the probability that the house will burn down.  But now the insured influences in a very clear way the probability.  His actions change the probability.  Moral hazard is when the actions of the person who is involved in this probability calculation, when the incentives of this person change the probabilities that underlie the problem.”

This is precisely what’s happening in the case of the questionable meat, Professor Aumann said.  “This person, he forgot which store he bought the meat from, but he bought the meat…  He made the choice by himself.  When he made the choice, then you right away have an issue of moral hazard.  When does moral hazard have nothing to do?  When he found it.  When he found it, he didn’t determine from which store it came… He could not influence the probability. But when the person himself made the choice, then there’s no probability.  The laws of probability do not apply to your choice when you are motivated to go one way or another.”

Consistent Fair Division.

The Mishnah in Kesubos 93a advances a mystifying approach to resolve a monetary dilemma. The case involves the division a man’s estate among three women who each have a marriage contract entitling them to a different amount from his estate.  But how is the estate divided when there is not enough to fully satisfy all three claims?

“If a man with three wives dies, and one [holds] a kesuba of 100 zuz, one of 200, one of 300, and there’s only 100 in the estate, then the three women divide equally.  If there’s 200 in the estate, then the one of 100 take 50 and those of 200 and 300 take 75 each.  If there’s 300, then the woman who has the kesuba of 100 takes 50, the one of 200 takes 100, and the one of 300 takes 150.”

“It’s a very strange Mishnah,” Professor Aumann said.  “Now each of those methods of division makes sense.  But they’re inconsistent with each other.  What’s the general rule?  Is it equal division, or is it proportional division, and in the case of two hundred it’s in fact neither.

“The principle is equal divison of the contested amount… All three divisions over here have the property that any two women divide what they together get in accordance with the principle of equal division of the contested amount.”

“Equal division of the contested amount” arises in a case where two parties have competing claims to a single amount of money, but the size of each claim is different.  When the two competing parties have different size claims, according to Professor Aumann explained, then the party with the smaller claim, in essence, has ceded his claim on the amount claimed by his adversary that is greater than his claim. 

To illustrate, Professor Aumann brought the case of “shneyim oksim b’talis.”  “Two men come to court, and they’re both holding onto a garmet, a talis. And one says ‘It’s all mine,’ and the other one says, ‘Half of it is mine.’  He doesn’t claim all of it, he only claims half of it.  Then the Mishnah says, divide, 75, 25, three quarters, one quarter. 

“Rashi explains over there, that the reason for dividing ¾. ¼, because on half of the talis, there’s no argument.  The one who says, half of it is mine, cedes half of the talis to the other one, the one that says, ‘kulo sheli,’ [‘all of it is mine.’]  So what’s the argument is about?  The argument is about half the talis.  You have an argument about something, split, 50-50.  Half of the talis is split, 50-50, so each one gets a quarter.  The other half goes all to the one who said, ‘kulo sheli,’ [all of it is mine’], so the result is three quarters, one quarter.  The principle over here is equal division of the contested amount.

Returning to the three competing claims of the wives in Kesubos, Professor Aumann summarized, “all three divisions over here, have the property, that any two women divide what they together get, in accordance with the principle of equal division of the contested amount.”

Professor Aumman explained one of the examples listed above in the Mishnah.  “In the case where the estate is 200, so the one who has a kesuba of 100, she gets 50…  The third [with a claim of 300]… gets 75, together how much do they get.  They get together 125.  If they want to divide this 125 between them, according to the principle of equal division of the contested amount.  What is the contested amount?  The contested amount is 100.  Because the woman who has the kesuba of 100, she doesn’t claim 125, she claims only 100, so she cedes 25 to the other woman.  How much is left?  What is then the contested amount?  It’s 100.  This is divided equally between them.  So the first one gets 50, and the last one gets 50, plus 25, is 75.  So you get back exactly these numbers.

“Now ladies and gentlemen, this may sound that no matter what you do, you get back the numbers, but that’s not true.  For each of the three estates, there’s only way of dividing the estate so that any two women divide what they together get…  And not only with these amounts.  But no matter how large the estate is, no matter what the kesubas are, no matter how many women there are, even if there a thousand women, like by Shlomo ha Melech, it doesn’t matter.  There’s always a way of dividing the estate in order to fulfill this principle.  And there’s only one way.  There’s always one, and only one way.”

The applications for this principle may arise, this reporter speculates, in the operations of modern-day bankruptcy law, which is built on the equal division of the property of a bankrupt debtor among each class of creditor.