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Economic Fables

Ariel Rubinstein

0. Introduction

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Bookkeeping with my father

1I sat that evening in the back of the auditorium where the first Senate session of the academic year was being held. The table on the stage was draped with a green tablecloth that reached the floor. Seated at the table were the patricians of the university, which is situated north of an almost dry riverbed. A microphone was connected to scratchy loudspeakers. The national flag and the university flag drooped side by side in their stands.

2The meeting opened with a string quartet whose young members had been asked to perform a classical piece to reflect the aesthetic taste of the Senate members, devotees of culture at a prestigious university. The rector then welcomed the participants, wishing them a year of fruitful research, a year of striving for excellence, and a year of peace. He noted a number of new programs at the university, ”all of which express our pursuit of excellence.” He went on to list the promotions, prizes and honors that members of the Senate had received during the summer months. Each honoree, when his name was mentioned, stood and made a slight bow, to the bored applause of a few of the more enthusiastic members of the Senate.

3The Senate then discussed the appointment of members of a committee set up to examine ways of promoting excellence at the university. One by one, the candidates were introduced and their unique qualities cited. There was an occasional burst of erudite chuckling in the auditorium when one of the presenters strayed from his written recitation and inserted a witty remark in the chronicle of the candidate’s meritorious deeds. The restraint disappeared when it came to female candidates. The first to leave the meeting had already begun to sneak out. And since to reach the exit they had to cross in front of the stage, they had no choice but to render an apologetic nod toward the self-satisfied rector.

4Until that evening, I had never spoken before the Senate. During the meetings, I actually thought that I had a lot to say. I sometimes felt compelled to jot down an outline of profound, daring and provocative points I would raise in response to the outrageous statements, full of pathos, being voiced there. I would write these things on the back of an ATM receipt I found in my wallet, in handwriting that even I had trouble deciphering. But at the end of the meeting, I would toss the note in the trashcan outside the auditorium. And if for some reason the note remained in my pocket and I found it the next day, I would praise myself for being smart enough to refrain from publicly expressing the ridiculous things I had wanted so much to say just the day before.

5The next item on the agenda was not supposed to dampen the festive atmosphere of the opening session. The administration proposed upgrading the program of studies in accounting to a status previously reserved only for main academic fields, and allowing the best students to receive a bachelor’s degree after studying only accounting. The head of the accounting department extolled the virtues of the new program, his description easily covering a whole page, embellished by numerous tributes to excellence: the excellence of the lecturers, the excellence of the students – past, present, and particularly, future. The rector thanked the speaker for his fascinating remarks, and almost routinely began to take a formal vote when, from the back of the auditorium, I raised my hand and asked for permission to speak.

6I approached the podium, with the pages of the speech I planned to deliver in my hand – three documents pertaining to the program and another small page, hiding between the folded pages. It was a photocopy of the diploma from a bookkeeping course offered at one of the evening classes of the Daughters of Zion in Bialystock. I had found the diploma in my father’s forbidden drawer, under the compartment of the starched sheets and above the compartment of the embroidered tablecloths, along with his immigration certificate, his officer ranks from the Civil Defense unit, and a booklet of unused coupons for water rations from 1948.


7My father was 21 when he received his only professional degree, bookkeeper. Four years earlier, he had immigrated to Palestine, but due to circumstances he was never willing to discuss, he returned to his parents’ home in Poland. In the photograph in the diploma, my father appears in a suit and tie, looking straight at the camera, a handsome young man, shy, yet proud. The left half of the diploma is in Polish, the right half in Hebrew:

8My father had a strong, confident voice, masculine, but soothing. When, rarely, he would raise his voice, it would frighten those around him. At home, everything was conducted according to his wishes. At one time he must have been a real ladies’ man. One of my aunts was secretly in love with him and, while I was growing up, sealed brown envelopes would still arrive at our house from a female admirer, a Dr. H. D., who apparently felt lost without him. During elections, he was the chairman of a polling station committee as the representative of the Mapai (the ruling party in Israel until 1977). On Memorial Day for Israel’s fallen soldiers, for a few minutes he was part of the guard of honor made up of veterans of the Haganah (the pre-State paramilitary defense organization), which President Ben Zvi reviewed before the siren was sounded at ten o’clock. I was proud of my father, but also a bit embarrassed that he was not one of the fathers capable of standing stiffly at attention for a complete hour, next to the memorial flame.

9With the establishment of the state, the word buchalteria was Hebraized to hanhalat heshbonot (bookkeeping), and my father became a government clerk. In time, he advanced, and almost made it to senior official. He was once photographed with the Minister of Transport at a ceremony inaugurating an airfield at the Dead Sea. On another occasion his name was cited in a news item in one of the daily newspapers. The article, which was cut out and kept in the bottom of the forbidden drawer, reported that one of the employees in his office had attacked him, and had been arrested and released on bail. No other details were provided.

10I discerned my father’s professional pride when I showed interest in the bookkeeping textbooks that rested in the bookcase, alongside the six volumes of the Mishnah (a codex of Jewish law), a Hebrew dictionary and a memorial booklet about the Jewish community of Bialystock. On the same shelves were summaries of lectures from the Economic History course that my father saved from his unsuccessful attempt to study economics at the university – the same texts the lecturer continued to read even when I arrived at the university. ”A person needs a profession in life,” my father told me many times when I was about to complete my military service and register for university. And he tried to convince me to study accounting, or at least economics.

11When I was a boy, my father would take me on two buses to Mr. Gur Aryeh, the eternal secretary of the committee for ”Workers Quarters B,” a small neighborhood with narrow paths, flowers and a towering palm tree, located between the aristocratic Rehavia and Talbieh neighborhoods. Gur Aryeh’s neighbours included a famous lawyer whose books are still cited, the father of an army Chief of Staff, an accountant, and a piano teacher who gave lessons only between 4 pm and 7 pm. Mr. Gur Aryeh, or ”the nudnik” (nagger) as we referred to him in our family (because he would phone frequently, and ask, slowly and clearly, as if he did not expect us to understand, ”is your father at home?”) would open the door for us at five o’clock sharp. First, he would offer me a piece of bittersweet chocolate from a yellow box he kept in a drawer. Then he would sit me down in an armchair, and I would gaze at a drawing of David’s Tower that hung on the wall, while my father discussed with him what to do about lost receipts. On the way back, between one bus and the next, we would stop at King George Street and my father would buy me a piece of peanut cake that had a whole peanut stuck in the center. Once a year we would ride to Mr. Gur Aryeh to pick up ”the material.” Then my father would sit during the evenings and do the bookkeeping for the committee. My father had wide ledgers with colored lines, lots of columns, and thirty rows corresponding to thirty apartments and tenants. From there, the numbers spilled over into two columns that had to balance before we could travel again to Mr. Gur Aryeh to return ”the material” and receive the check that my father would endorse and pass on the next day to the grocer to cover part of the tab in his notebook.

12When a new regulation was issued requiring that high government officers must be university graduates, my father was consigned to early retirement and became a teacher of bookkeeping in evening classes. The classes ran from 6:30 pm to 10 pm, with a break for burekas and Turkish coffee. He made his name as the author of the Exercise Primer in Bookkeeping Part 1. My father typed this slim book on a typewriter with a black ribbon that would get stuck whenever it was necessary to reverse direction. As a child, I used this typewriter to produce my street newspaper – a newspaper I founded, wrote, edited, and read, though not even a single edition was ever published. The bookkeeping primer bore my father’s patronymic nom de plume, Ben Israel Meir, a reference to his father, a man who died with ”Shema Yisrael” [the Jewish deathbed declaration of faith] on his lips and who left a slim booklet of polemical articles about the virtues of observing the Sabbath and the sins of our fellow Jews who went astray with communism, as well as sketches of figures from the halls of Torah study. Copies of the booklet will remain untouched in the National Library in Jerusalem and in a library in New York until the end of days, or until their pages disintegrate.

13The exercises in my father’s primer encompassed the entire theoretical world of Reuven, Shimon and Levy, the partners in ”Furniture, Inc.,” including movable property and cash, debtors and creditors, and a lot of doubtful debts. The transactions to be recorded were the sale on credit of six chairs to Mr. X and the payment of wages to the carpenter, Mr. Y. At the end of the exercise, the student had to deduct the annual depreciation on the company’s typewriter and, if he did not make a mistake, he would find that the business had a small loss. To this day I do not know how the loss was covered. There was also a sample test at the end of the primer, with questions such as: ”What is goodwill?” ”What is the role of bookkeeping in a business?” and ”Describe the duties of an accountant.” The publisher was Moskowitz Book Publishers, Bat Yam. Moskowitz had a machine for duplicating stencils and some dealings with a bookbinder from Holon. My father orchestrated the marketing; every so often he would phone Moskowitz and ask him to send thirty copies via Egged Parcels for the evening course of the Workers Council in Hadera. The booklet had sequels: Exercise Primer in Bookkeeping Part 2 and Exercise Primer in Bookkeeping Part 3. I was filled with pride when I found my father’s booklets at the university book store, among the books for students in the Accounting Department. When my father died, the books also disappeared from the evening courses of the workers’ councils.

14My father never spoke to me of his passion for women, or of his ambition to be a senior official, or even of his fears. I do not remember him ever saying ”I love,” ”I want” or ”I am afraid.” But one night I saw my father as I had never seen him before.

15The room was cluttered with household items: a bed, a bookcase and a radio that no longer worked, a dusty, empty fruit bowl, and lots of newspapers tossed on the floor alongside a pair of tattered slippers. On the dining room table, which also served as a work desk, there were plates with leftover food, left there since lunch. My mother was sprawled on the bed as always, surrounded by the stale stuffiness of unaired bedding. The broken wood shutters were closed and half-hidden by curtains that were once white lace and had since been refashioned by a decade of Jerusalem dust. My father sat in a brown dressing gown that was just about held closed with a threadbare cord. He sat with his back to the window, facing the bed where my mother was lying. I sat facing the window with my back to the bed.

16My father made another attempt to balance the accounts of the committee of the Workers Quarters B neighborhood. The nudnik had already called five times to ask for ”the material.” My father would read a list of numbers to me and I would add them with the proficiency of a young student of mathematics. I was 21 years old. I was so bored. The totals swung between a deficit and a surplus and did not balance. I was impatient. I felt suffocated. I wanted to flee. My father said we had to start over again from the beginning. And again the numbers moved around in the shadows cast by the chandelier (two of its three bulbs were burnt out), and again he dictated the numbers and I added them up. And then my father clutched his balding head and said that if he did not manage to balance the numbers, he would have to kill himself.


17With a tone of seriousness befitting the occasion, I began my address to the members of the Senate with the following words: ”I would like to express my strong objection to the plan to establish a program that focuses only on accounting.” And I immediately continued: ”Before explaining the reasons for my opposition, I would like to declare that I have a personal connection to the accounting profession. My late father’s only training was in buchalteria. In my childhood, without a computer, I would spend many hours helping him to balance the books, adding debits and credits, and he would occasionally explain to me the rationale of the discipline he so wanted me to study.”

18I then proceeded in a serious, business-like tone:

Those who are admitted to the new program will undoubtedly be the cream of our youth. When they graduate, they will find work in the top accounting firms and will become part of Israel’s elite, whose cultural make-up we are shaping, whether we like it or not. What will the members of this elite be like? They will be remarkably similar to, almost clones of, the images its critics portray. We are speaking of a talented and ambitious group of students who, at age 21, know what they are looking for in life. We will give them an entry ticket to the elite, extensive knowledge of accounting, and nothing else that this university could and should contribute to their education. Some might assert the cliché that accounting is an academic subject, but with all due respect to this new pillar of the scientific experience, I wonder how anyone can compare accounting to mathematics and biology and philosophy and linguistics. These are the subjects that we should be encouraging the outstanding students to study, rather than the elective course on ”Accounting for Residents Committees”.

19At this point, the head of the Accounting Department interrupted me and shouted: ”You don’t know what you’re talking about!” I hurried to conclude my remarks: ”I ask each of you to use your independent judgment and answer the question of whether our curricula have true academic excellence as their objective, or whether our rhetoric is more Pravda than Pravda, and to vote accordingly.”

20I returned to my seat at the back of the hall and quickly buried my face in my father’s buchalteria degree. No one looked at me except for one humanities professor who passed me a note saying that she disagreed with some of the things I said. Another professor, his hair parted on the side, wearing a sporty suit and black tie, rose to the podium and, speaking fluently, said that he was very surprised by my remarks. ”We are not talking about buchalteria here,” he explained, his face expressing distaste as he said the word, and went on to more or less say that I did not understand the difference between buchalteria and accounting: ”Anyone can serve as a bookkeeper, but an accountant must have a BA degree. Accounting is an academic profession in every way, with international conferences and scientific journals…”

21Then a vote was held and the program was approved by a large majority. A few people were actually influenced by my remarks and voted against it. Others only abstained, but no one bothered to count them.

22During the following days, I was unable to forgive the head of the Accounting Department who had interrupted my remarks. I easily discovered that his comments were actually riddled with inaccuracies. I sent him and the rector a steady trickle of e-mail messages with evidence demonstrating that the approval of the program was based on erroneous information that he had presented. The embarrassed rector referred the program to some sort of committee and I said no more.

23The image of my father that accompanies me now is his picture on the certificate from the Daughters of Zion: young, handsome, serious, shy and proud. I would run into that head of department on campus and was curious to ask him who his father was, but I did not dare to ask as I was afraid I would discover that he also had ”a father”. I do not know what happened to that program in the committee. Perhaps it was buried there. Perhaps it will reemerge and be unanimously approved by the Senate. Or, perhaps it was approved there long ago. I am no longer interested in it. All I really wanted was to complete the one balance sheet that my father and I did not manage to balance at the formica table in the middle of the room opposite the window, next to my mother’s bed. After all, I just wanted to transfer one father from the liabilities side to the assets side.

Economics and me

24This is how I usually begin lectures on economics and social issues:

I would like to start with what I believe every academic should do when appearing in public, especially when speaking about political and controversial issues – to clarify the extent to which he is incorporating his professional knowledge in his remarks, whether he is expressing views with the authority supported by academic findings, and what part of his comments are nothing more than his personal thoughts and opinions. And so, I would like to declare unequivocally, without hesitation and even with a bit of pride, that my words here have absolutely nothing to do with my academic knowledge. Everything I say here is personal, based upon the entire range of my life experience, which also includes the fact that professionally I engage in economic theory. However, to the best of my understanding, economic theory has nothing to say about the heart of the issue under discussion here. I am not sure that I know what an option is; I am not attempting to predict the rate of inflation tomorrow nor the productivity index in manufacturing the day after tomorrow. Of course, I am aware of the fact that you have invited me here to speak because I am a professor of economics who is supposed to know all this, and my ignorance definitely embarrasses me. So you ask why I have come here? Because as an economic theorist, I would like to state that economic theory is exploited in discussions about current economic issues, and I don’t like it…, to put it mildly.

25This statement is not just a pretense to exempt myself from a commitment to ”scientific” criteria, and it is not intended simply to project an image that distinguishes me from other economists, or to boost my self-image. This introduction reflects what I truly believe. Nonetheless, it is clear to me that my remarks are received with skepticism. I myself would make fun of a professor of economics who begins a lecture by declaring that his remarks have nothing to do with economics, and speaks with an expression on his face that reflects his feeling of superiority over his colleagues and whose lecture could be seen as ”spitting in the well from which he drinks.” I am sure no one would invite me to speak about the government’s economic policy if I were a professor of astronomy or an historian of the Middle Ages. Moreover, it is clear to me that my reservations do not prevent my listeners from continuing to treat me as a professor of economics (at most, an unusual one) and not just as a concerned citizen. And I suspect that despite my warning, there are those who regard my remarks as if they are spoken by someone with an authority whose existence I deny.

26In this book too I make no claim to objectivity. I am not about to reveal to the reader some truth that I have discovered. On the contrary, everything I say here, even in an academic context (and I intentionally use the word ”academic” since I do not think that the word ”scientific” is appropriate for economics), is completely subjective, controversial and therefore perhaps describes me no less than it describes economic theory.

27At the Hebrew University of Jerusalem, where I studied, I had the opportunity to listen to many distinguished professors. Two of them in particular contributed to the fact that I found myself engaging in economic theory. One is unknown in the world of economics, someone who is not slated to become an advisor to a Minister of Finance, and who has not even written articles on mathematical economics; he is the mathematical logician Saharon Shelah. When my friends and I emerged from the lecture halls on Mount Scopus and Givat Ram, our notebooks would be filled with the definitions and proofs we had gleaned meticulously from the blackboards that Shelah had filled and overfilled in courses on set theory and mathematical logic. When we understood what we had copied, we were astonished by its wholeness, level of conceptualization and logic. We encountered a strict and uncompromising insistence on norms of simplicity and precision. We were introduced to and learned to appreciate the beauty of a model, a statement and a proof. But the abstract mathematical concepts we learned in these courses (as in other courses in the Mathematics Department), actually appealed to us because of the interest it awakened in us in the world around us. We somehow felt intuitively that the formal concepts we were learning were directly relevant to real life. In our discussions over coffee in the cafeteria, we searched for the meaning of the mathematical statements not only as links between mathematical concepts, but also as statements about what intrigued us so much as young students: the interaction between people.

28During my third year of study, I met the second teacher who is responsible for my academic pursuit, Menachem Yaari. As part of my work on a seminar paper, Yaari referred me to a wonderful book by Amartya Sen called Collective Choice and Social Welfare. This book has a very unusual structure. Each chapter has a parallel chapter with the same number but with an asterisk. In the chapter without an asterisk, a textual discussion is conducted about the various axioms of social choice theory, while in the chapter with the asterisk the textual discussion becomes a chain of precise definitions, arguments and proofs. When I read this book, I realized two things: First, that economics is interesting – a real revelation for me. And second, that the connection between our everyday world and the world of mathematical symbols is far deeper than I had thought previously during our coffee-bar debates. Before reading the book, I was like a child gazing at leaves, hills and shadows and imagining heroic figures in them, and feeling afraid of what I could see. After reading Sen’s book, I realized that what we did in the cafeteria was actually an innocent foray into the core of economic theory. This is because economic theory is concerned precisely with the abstract concepts related to the interaction between people (the chapters without an asterisk). And the working tools of economic theory are mathematical models (the chapters with an asterisk).

Economic fables

29Economic theory formulates thoughts via what we call ”models.” The word model sounds more scientific than the word fable or tale, but I think we are talking about the same thing.

30The author of a tale seeks to impart a lesson about life to his readers. He does this by creating a story that hovers between fantasy and reality. It is possible to dismiss any tale on the grounds that it is unrealistic, or that it is too simplistic. But this is also its advantage. The fact that it hovers between fantasy and reality means that it can be free from irrelevant details and unnecessary diversions. This freedom can enable us to broaden our outlook, make us aware of a repressed emotion and help us learn a lesson from the story. We will take the tale’s message with us when we return from the world of fantasy to the real world, and apply it judiciously when we encounter situations similar to those portrayed in the tale.

31In economic theory, as in Harry Potter, the Emperor’s New Clothes or the tales of King Solomon, we amuse ourselves in imaginary worlds. Economic theory spins tales and calls them models. An economic model is also somewhere between fantasy and reality. Models can be denounced for being simplistic and unrealistic, but modeling is essential because it is the only method we have of clarifying concepts, evaluating assumptions, verifying conclusions and acquiring insights that will serve us when we return from the model to real life.

32In modern economics, the tales are expressed formally: words are represented by letters. Economic concepts are housed within mathematical structures.

33And an economic model looks like this:

2 knows its actual value. In such a situation some new aspects appear. 1 will try to conclude from 2's behavior what the true bargaining cost is, and 2 may try to cheat 1 by leading him to believe that he, 2, is “stronger” than he actually is. In such a situation one can expect that the bargaining will continue for more than one period. I hope to deal with this situation in another paper.
Two players, 1 and 2, are bargaining on the partition of a pie. The pie will be partitioned only after the players reach an agreement. Each player, in turn offers a partition and his opponent may agree to the offer “Y” or reject it “N”. Acceptance of the offer ends the bargaining. After rejection, the rejecting player then has to make a counter offer and so on. There are no rules which bind the players to any previous offers they have made.
Formally, let S = [0, 1]. A partition of the pie is identified with a number s in the unit interval by interpreting s as the proportion of the pie that 1 receives. Let s, be the portion of the pie that player
i receives in the partition 5: that is sx = s and s2 = 1 – s.
F be the set of ail sequences of functions f = {ft}t=1, where f1 Є S, for t odd f : St–1 ->S, and for t even ft : St-> { Y,N}. (St is the set of ail sequences of length t of elements in S.) F is the set of ail strategies of the player who starts the bargaining. Similarly let G be the set of ail strategies of the player who in the first move has to respond to the other player's offer; that is, G is the set of ail sequences of functions g = {gt}t=1, such that, for t odd gt: St> {Y,N} and for ( even gt: St-1–>S.
The following concepts are easily defined rigorously. Let σ(f, g) be the sequence of offers in which 1 starts the bargaining and adopts f Є F, and 2 adopts g Є G. Let T(f, g) be the length of σ(f, g) (may be ). Let D(f, g) be the last element of σ(f, g) (if there is such an element). D(f, g) is called the partition induced by (f, g). The outcome function of the game is defined by

Thus, the outcome
(s, t) is interpreted as the reaching of agreement * in period t, and the symbol (0, ) indicates a perpetual disagreement.
For the analysis of the game we will have to consider the case in which the order of bargaining is revised and player 2 is the first to move. In this case a strategy for player 2 is an element of
F and a strategy for player 1 is an element of G. Let us define σ(f, g), T(g, f), D(g, f) and P(g, f) similarly to the above for the case where player 2 starts the bargaining and adopts f Є F and player 1 adopts g Є G.
The last component of the model is the preference of the players on the set of outcomes. I assume that player; has a preference relation (complete, reflexive, and transitive)
i. on the set of S x N U {(0, )}, where N is the set of natural numbers.

34The use of formal language has its advantages. Formal language imposes self-discipline on the storyteller. A teller of economic tales who uses formal language is obliged to spell out his assumptions precisely. When he uses expressions like ”thus” or ”therefore” or ”it follows that…,” he is exposed to objective criticism: the conclusion he draws from the assumptions must be formulated as a mathematical statement which must be accompanied by a proof.

35A description of an economic model is like the introduction in a tale, presenting the heroes, their interests and the setting in which they operate. An array of rules by which the model is ”allowed” to develop from its beginning to its end is called a solution concept.

36Many solution concepts can be applied to the same model. We examine a solution concept according to the reasonableness of the assumptions it expresses, and we prefer solution concepts that can be applied to a large set of models. Formal language encourages the narrator to honor the requirement that the conclusion of the economic tale must be derived from the assumptions he formulated in describing the model and from the solution concept to which he is committed.

37However, formal language also has its disadvantages. It creates the illusion of being scientific. Those unfamiliar with formal models tend to regard them as representing ”absolute truth,” though they are nothing more than tales. In addition, formal models narrow the target audience to those who were immersed in them. From my teaching experience I have learned that even the best economics students with the highest affinity for the subject have difficulty with the language of formal models, perhaps due to their persistent confusion between the formal model and its interpretation, and between the mathematical concepts and the words that accompany them. Moreover, when it comes to questions of economic policy, the model’s formal mantle enables economists to create the false impression that their pronouncements are scientific and authoritative, and to conceal from the layman the assumptions the model uses. The barrier between the secret formal language and ordinary human speech almost completely prevents anyone who is not a member of the economic fraternity from criticizing ”professional” economic claims.

Hotelling’s tale of the main street

38Harold Hotelling’s model of the main street is a simple model that is considered to be among the more successful ones in economic theory. Two newsvendors compete for the custom of their city’s newspaper readers located along the city’s main street. Each vendor seeks to have the maximum number of customers buy the newspaper at his stand. In a simple version of the model, the freedom of action of each vendor is limited to choosing the location of his stand. The price of the newspaper is set by the publisher, so the vendors cannot compete against each other by lowering prices. Nor can they use violence to secure or enlarge their market share, and they do not have the legal right to appeal to the courts with claims such as ”for generations, the whole street has been mine” or ”it is only fair that I will control half of the street.” As my teacher Menachem Yaari once noted, the economic agents in our models have desires but no rights.

39At dawn, each vendor sets up his stand somewhere along the street. At lunchtime, each newspaper reader takes a break from his other pursuits and realizes that he cannot get through the day without reading the newspaper. The reader sees where the two newsvendors are located, and sets out to buy a newspaper from the closest one. (If the two stands are equidistant from the reader, the chances of the reader buying the newspaper at either stand are equal.) The diagram below illustrates the distribution of customers between the two vendors. The vertical line marks the center point between their locations. Everyone situated to the left of the vertical line buys from vendor 1, and everyone to the right of this line buys from vendor 2.

40That was the introduction to the tale: we have described the characters participating in the situation and specified each one’s range of choice and objectives. The conclusion of the tale is a description of the choices made by the two vendors. In other words, the two unknowns in the model are the locations of the two newsvendors.

41We noted earlier that the principles by which the tale’s conclusion is tested – that is, the solution of the two unknowns – can be found in the solution concept. The conventional solution concept for situations like the above is called a Nash equilibrium. This is discussed at length in Chapter 2. Here, I describe it in the context of Hotelling’s model. The Nash equilibrium in this model must be a pair of locations, one location for each of the two vendors. In order to award this pair the title of ”Nash equilibrium,” the location of each vendor must be the best one for him given the location of the other one.

42First, let us examine the situation in which both vendors are located in the center, the median point in the street with an equal number of buyers on each side. When one vendor is located in the center, the other will have less than half of the market share if he does not set up his stand in the center too. And if he does set up in the center, he will get half of the market share. Therefore, it is best for each one to set up his newsstand in the center when the other is located there. Consequently, a Nash equilibrium is achieved when both vendors set up their stands in the center.

43Any other pair of locations is not a Nash equilibrium. If the two vendors set up in different spots, each can increase his market share if he moves closer to the other. Both setting up at the same location different from the centre point is also not an equilibrium: each one, by shifting toward the center, can increase his market share (and get more than half of the total, assuming that the other does not move.

44We are thus left with a single equilibrium: the two vendors set up in the center. This situation, a single-equilibrium model, is ideal from the perspective of the narrator of the economic tale because the result of the equilibrium can then be regarded as the inevitable conclusion of the tale.

45By the way, in this model, the competition leads to an outcome that is not ideal from the buyers’ standpoint. If one of the vendors sets up at a location other than the center, none of the buyers will suffer and some will benefit, i.e., those who are now closer to the nearest one.

46Hotelling’s model has been applied to many situations. For example, instead of a main street of a city, economists apply the model to a situation in which two cola manufacturers must choose the sugar content in the product (and they cannot offer a range of products). The conclusion drawn from the model in this case is that both manufacturers should produce an identical product. Political scientists interpret each location point on the main street as a political position in a one-dimensional space (political right versus left, for example). Each candidate positions himself on the political map, aspiring to receive the maximum number of votes. Each citizen is situated somewhere in the political space and chooses the candidate closest to his own political views. Everyone agrees on the political geography and on the concept of distance in the political space. The model’s single equilibrium is interpreted in this case as follows: if there are two parties operating in the political space, and if the subject of dispute is primarily one-dimensional, the platforms of the two parties will be identical, in the center of the political spectrum. Only a cynic would say that this conclusion matches the political reality in the real world. Even in the United States, the two political parties are far from identical. But Hotelling’s model sheds light on the logic behind the efforts of the two parties, Democratic and Republican, to capture the center.

The tale of the three tailors

47Imagine an island with six hundred residents, all dressed in identical clothes that require mending every month. Three tailors work at mending the clothes. For as long as anyone can remember, the residents of the island have been divided equally between the three tailors. Once a month, each resident goes to the same tailor whose services his father had used. Tradition, or decree, has set the price of the monthly repair at $5. Assume that the tailors have only minimal, negligible expenses. Each of the tailors would like to have as many customers as possible. However, even with great effort, none of them can do more than three hundred repairs a month. The residents feel that there is ”hidden unemployment” in the tailoring sector. The tailors are often seen reading a newspaper, or dozing. It seems that two tailors would be enough and that it would be better if one of the tailors were to quit tailoring and find himself another job. In the language of economists, the situation is inefficient.

48Let us say that all the tailors have various other employment options that influence their decision about whether to remain in the tailoring profession or to quit. Tailor A can expect to earn $900 a month in another profession, while Tailor B can expect to earn $600. Tailor C has limited alternative employment options and can earn only $300 outside the tailoring field. Each of the tailors will choose to abandon his sewing needles if his income from tailoring falls below his alternative income (”opportunity cost”). Currently, when the price of mending a piece of clothing is $5, it is not worthwhile for any of the tailors to leave this line of business because each tailor has two hundred customers and a monthly income of $1,000.

49One day, the idea of the free market reaches the island. The traditions are shattered and the decrees canceled, and each tailor can decide on the price he charges for repairs. Each resident compares prices and turns to the tailor who offers his services at the lowest price. If more than one tailor offers the lowest price, the residents of the island will divide their custom equally between them. Each tailor attends a short course in modern business management and internalizes his role in the new economic regime: he must become familiar with the market and maximize his profits. What will happen on the island in the new situation?

50The continuation of the Tale of the Three Tailors must provide answers to the following questions: Which tailors will remain in this occupation? What will be the terms of commerce between the tailors and their customers? As is customary in economics in this type of context, we will use a solution concept called competitive equilibrium. The concept of equilibrium imposes the following requirements for the rest of the story: (1) All customers will pay the same price for the repair of his clothes. (2) Each tailor knows the price of the service and compares the income he believes he can make in this work and his potential income outside this field. If the income in the other profession is higher, the tailor will leave the tailoring business. If the income outside of this field is lower, he will remain a tailor. (3) The number of customers the remaining tailors are interested in serving (supply) is equal to the number of islanders interested in this service (demand). Now, all six hundred islanders are interested in the service at any price. Since the tailors have no expenses, each one is interested in serving three hundred customers (the greatest number of repairs he is capable of doing a month). Thus, this condition demands that precisely two tailors remain in this business.

51The logic underlying the concept of competitive equilibrium is that if the price of tailoring services is so high that the supply of tailoring services exceeds the demand, then the price will decline until one of the tailors closes his business. And if the price is low and the demand for tailoring services is greater than what the tailors are able to supply, the price will rise until another tailor returns to this sector.

52We will now see that there is competitive equilibrium when the price of a repair is $2.50 (or any other price between $2 and $3), and only tailors B and C remain in this business sector. Each of the tailors (B and C) will have three hundred customers and each has an income of $750, which is more than either could receive in his alternative employment. Tailor A, meanwhile, earns $900 outside of the tailoring business. If he returns to this sector, he would earn $750 at most, less than what he is earning in another occupation.

53In every competitive equilibrium, the price of the tailoring service will be lower than the price that prevailed in the old regime: If the price of the service were $5 (or higher), the tailor who quit the profession would figure that he could earn more as a tailor than he does in his new line of work. Only the two tailors whose alternative employment options are less profitable will remain in the tailoring sector; and the total output of the residents of the island will grow. An ”invisible hand” generates the competitive equilibrium price and mobilizes the self-interest of the tailors and the islanders to correct the inefficiency created by the traditions and decrees that were recently canceled.

54How does the market arrive at the competitive equilibrium price? The usual explanation offered in Introduction to Economics classes goes like this: The price of mending clothing prior to the cancellation of traditions and decrees was $5. After canceling the traditions and decrees, a price war erupts. One of the tailors who was ”re-educated” concludes that it would be better for him to lower the price to $4.90 and thus create a situation in which all of the islanders would seek his services. Before long, the other tailors take note and also lower prices. And thus the price drops lower and lower until a certain stage when one of the tailors offers the service at a price less than $4.50. At this point, the tailor with the best employment alternative closes his tailoring business and engages in a different profession, and the island remains with only two active tailors.

55Several assumptions in this story are not obvious. First, is it indeed so clear that the tailors will lower their prices after the cancellation of the traditions and decrees? We expect them to act only in pursuit of their own personal interests. But if a tailor is concerned only with his own earnings, it would actually be better for him not to lower the prices because he understands that any profit he would gain from increasing his clientele would be temporary and insignificant compared to the large loss he would incur in the future when the other tailors respond to this move and also lower their prices. The tailor would not need to speak with his colleagues in order to refrain from lowering prices. (Explicit collaboration between the tailors might be prohibited on the island under antitrust legislation.) Stated simply, no tailor would want to start a price war.

56Second, let’s assume that the tailors are not so wise and fall into the trap the competitive atmosphere lays for them. Is it clear that the consumers will indeed choose the least expensive tailor? Until now, they have used the services of the same tailor their father and grandfather used. Now they need to compare prices frequently. If the price differentials between the tailors are not large, some customers will decide that the price savings are not worth the bother involved in comparing prices. Thus, a tailor may actually raise his price a little, relying on the fact that most of the customers will not bother to find another tailor offering the service at a lower price. If customers do not compare prices, the market might stabilize at a higher price than the competitive equilibrium price.

57Finally, let us assume that all of the residents of the island regard the search for the least expensive tailor as a real national mission, an act that will serve the society as economists demand, and let us assume that the tailors are not so smart, and that price competition rages and leads to a drastic drop in prices, and that one of the tailors abandons the profession and finds alternative employment (and does not become jobless on the streets of the island), and that it enlarges the national pie. Then we come to the question: is this story as happy as it sounds?

58The change generated by the competitive economic regime on the island did indeed lead to growth in the ”national pie.” However, the improvement also led to a change in the distribution of income. The situation is worse for the tailors and better for their customers. Is the income distribution better now? Are the tailors now receiving fairer compensation for their work? Is the price for mending clothes now more reasonable? There are no objective answers to these questions. Economics has no way of choosing between the new situation and the previous situation. The island’s residents, all of them, are the ones who must make the choice.

The bargaining tale

59A pie is to be divided between two diners; let’s call them A and B. Both want as much of the pie as possible. Without an agreement on how to divide the pie, both will remain without anything. Both are hungry and want to eat their piece of pie as soon as possible. Unless they are willing to compromise, the allocation of the pie will be delayed, to the chagrin of both of them. The desire to receive as large a piece as possible leads to haggling; impatience leads the two sides to compromise.

60A bargaining process is a procedure that enables the parties involved to reach an agreement. In the model of bargaining presented here, the negotiation takes places along a time axis. Each day, one side offers a proposal and the second responds, accepting it or rejecting it. Every time one side rejects the proposal submitted to him, he must submit a counter-offer, but not before the next day. In this way, the two sides to the negotiation exchange proposals until one of them accepts a proposal from the other and there is an agreement. At this point, the bargaining ends.

61From the perspective of each of the two parties involved, each day that passes without an agreement is like losing a part of the pie. This loss might express the cost of time wasted in the bargaining process, or the mental effort involved in negotiating. Let us stipulate that from A’s perspective, the loss incurred from each day of bargaining is equal to 2 % of the pie. B is more impatient and from his perspective the loss from each day of bargaining is equal to 3 % of the pie. Accordingly, if A has to choose between reaching an immediate agreement that would give him 57.5 % of the pie and reaching an agreement the next day according to which he would get 60 % of the pie, he would wait until the next day: The postponement would give him an additional 2.5 % of the pie, more than offsetting the 2 % loss he would suffer from prolonging the negotiation for one more day. On the other hand, if B has to choose between an immediate agreement that would give him 40 % of the pie and an agreement for 42.5 % to be signed the next day, he would choose to conclude the negotiation immediately: If he tarries, he will gain an additional 2.5 % of the pie, which is less than the 3 % loss he would incur, from his perspective, by prolonging the negotiation for one more day.

62A solution, we said, is the principle that links the beginning of the tale to its conclusion. Here we will use the solution concept called perfect equilibrium. A perfect equilibrium is a pair of plans of action (”strategies”), one for each party to the negotiation, such that for each of the strategies the following holds: after each chain of events that might occur during the negotiation, the negotiator’s strategy is the best one for him vis-à-vis the strategy of the other party. In particular, if a proposal is made that offers one side too little, a proposal that according to his strategy he should reject, then if the player who holds the strategy reconsiders his moves he would indeed choose to reject the proposal. In other words, if a bargainer’s strategy includes a threat to reject low offers, then the threat must be credible.

63One can show that the bargaining game could have only a single conclusion: the negotiation ends immediately. If A (the more patient bargainer) makes the first offer, he will receive the entire pie, and if B makes the first offer, A will receive 98 % of the pie. The proof of this statement is not presented here, but the following section provides an illustration of the logic behind the result.

First, let us examine the following pair of strategies: each negotiator, when it is his turn to make a proposal, demands half of the pie for himself. And when his turn comes to respond to a proposal, he agrees only to a division that awards him at least half of the pie. In other words, each side always plans to offer an equal division of the pie and threatens to reject any proposal that gives him less than half of the pie. This pair of strategies is not a perfect equilibrium, because the threat to reject any proposal in which the bargainer would receive less than half of the pie is not always credible: sometimes it is not worthwhile for the negotiator to carry out the threat. For example, if A strays from his strategy and offers B only 49 % of the pie, then B, according to the strategy, is supposed to reject the proposal. But if he carries out the threat and rejects the proposal, he expects – according to this pair of strategies – the next day, when he makes his counter-offer, he will end up with only 50 % of the pie, assuming that A now keeps to his strategy. If B accepts A’s proposal to give him 49 % of the pie, he would lose 1 % of the pie, but would avoid the loss incurred by prolonging the negotiation, which from his perspective is equivalent to losing 3 % of the pie. Therefore, in this situation, B’s threat to reject the proposal to receive only 49 % of the pie is not credible, and it is best for him not to act in accordance with his strategy.
On the other hand, the following pair of strategies is a perfect equilibrium: A always demands 100 % of the pie for himself and agrees to any proposal that awards him at least 98 % of it. B demands 2 % of the pie for himself and accepts any proposal, including one that gives him nothing. A’s strategy includes a threat to reject any proposal that gives him less than 98 %. This is a credible threat. If B offers A less than 98 % of the pie, A will indeed reject the proposal, as his strategy suggests, as he expects to reach an agreement the next day to receive the entire pie, and the increase of more than 2 % is larger than the 2 % loss he expects to incur from an additional day of negotiation. B’s strategy includes no threats at all because he plans to accept any offer.
This pair of strategies ceases to be a perfect equilibrium if we substitute the numbers appearing in the description of the strategies with other numbers. For example, let’s examine the following pair of strategies: A always demands 60 % of the pie for himself and agrees to any proposal that gives him at least 58 % of it. B demands 42 % of the pie for himself and accepts any proposal that awards him at least 40 % of the pie. If A strays from his plan and offers B 39.5 % of the pie, B would do well to accept the proposal. If he carries out the threat to reject the offer, he can expect to reach an agreement the next day that would give him 42 % of the pie. The additional 2.5 % would not compensate him for the ”cost” (3 %) of one more day of negotiation.

64The model of negotiation described here, with the assumption that each player incurs a loss that is equivalent to a fixed share of the pie for each day that goes by without an agreement, ”predicts” that the player whose time is less ”expensive” will receive all (or nearly all) of the pie. The model perhaps clarifies the common intuition that a player whose time is more expensive is in a weaker negotiating position vis-à-vis a player whose time is less expensive. But the model does not describe reality, where things are always more complex, whether because the players’ considerations are more complex and also include psychological considerations such as ”if I already rejected an offer of 60 %, I won’t agree now to receive less,” or because the negotiators do not always act in a rational way, or because negotiations in real life are conducted according to less rigid rules than this procedure of exchanging proposals.

65I thought about this model just before completing my doctoral studies in Jerusalem. I was inspired by the market in the Old City in Jerusalem where I occasionally bargained when purchasing a Bedouin rug or Armenian plate. I really hate to bargain. Once, when I was fed up with the bargaining games in the market, I said to a trader, ”Why don’t we play a different game: you make an offer and I’ll simply say ’yes’ or ’no’?” Ostensibly, I was trying to exploit my so-called professional expertise to design a different mechanism that would spare me the exhausting bargaining process. The trader smiled scornfully and threw out a price that I immediately rejected. But then the man provided me with an insight that put my dreams of using the bargaining model to reform the world into a proper perspective: ”Tell me, did you think that I thought there was some offer I would make and that you would accept?” And then he added: ”For generations, we have bargained in our way and you come and try to change it?” I parted from him shamefaced.

Tellers of tales

66We have seen three examples of economic tales. Let’s again ask ourselves the question: what is the connection between an economic model and reality? Different economists have different answers to this question. According to one view, an economic model is supposed to serve as a basis for making predictions about the real world, not the world of tales. Those holding this view perceive an economic model as an attempt to predict human behavior, based on data about the actions and interests of the economic units included in the model. According to this approach, a model is supposed to be an objective description of the real world, not a tale. The designer of the model would be happy to add more and more details to it to improve its ability to predict. If the model does not provide enough good predictions, it must be augmented with additional details. But the increased complexity of the model exacts a steep price: it is hard to understand and is difficult to solve.

67According to another view, the objective of the economic model is to sharpen perception. A model is an intellectual exercise. Just as a soldier use simulations in training, the economist exercises his intuitions on a model before offering advice. The use of formal models helps to develop our intuitions about the way things occur in life. Thus, for example, economists who specialize in game theory have advised various governments to auction off public assets such as government companies and wavebands for huge sums. Others have been members of strategic teams hired by firms that participate in public auctions. These economists did not rely on a particular model, but claimed that their work with formal economic models sharpened their senses. I am not unequivocally opposed to this approach and I assume that those who claim that economic models have sharpened their perception are genuine in expressing what they feel. I also find myself from time to time looking at something from a perspective I have acquired from the study of economic theory. But I am quite sure that if instead of devoting my adult life to economic models I had engaged in a non-academic profession, I would view life from standpoints that are less abstract but no less useful.

68Both of the approaches I have mentioned so far look for a purpose in an economic model. Students look for a purpose in the material they study, because ”Otherwise, why study?” The research agencies and university presidents like to hear about purposefulness since it is easier for them to finance research that has a practical aspect. We economists are delighted when we find evidence of purposefulness in our work, because we are full of guilty feelings about devoting our lives to meaningless studies when the world faces innumerable problems.

69I would like to advocate another approach, which does not aspire toward purposefulness and the practical use of a model. According to this approach, an economic model is not essentially different from a model in logic. A model in logic is not a prediction of how humans judge whether a phrase in ordinary language is true or false. It is not a recommendation for a thinking person and it is not designed to educate people to think correctly. I contend that economics studies the logic of life, but does not engage in predictions or recommendations. We deal with the wide range of considerations that economic decision makers might take into account. We are satisfied even if the economic model is merely interesting. To be interesting it must focus on considerations that at least some people weigh before making a decision and taking action.

70In particular, I do not think that the bargaining models that I myself have studied have significant predictive value; I am not more qualified than any reader (but also not less qualified than my colleagues) to give advice on how to conduct negotiations, and I do not feel that dealing with these models has sharpened my ability to understand the process of bargaining in the market. There are many models of negotiation and many solution concepts, and each combination of model and solution concept has its own internal logic. At most, we find links between natural ways of thinking and bargaining processes. That is all.

71Yes, I admit that it is tempting for me to think of myself as a teller of tales, a philosopher, a researcher of the social sciences, in fact, anything but an economist. Whenever I am asked ”What is your profession?” ‒ for example, on the form for entering the U.S. ‒ I do not answer ”economist” but instead adopt the neutral title of lecturer. Besides the immigration official and the sleepy passenger in the seat next to me, no one will see the form, but I still always refrain from defining myself as an economist. I have limited knowledge of current economic issues. During most of my life, these issues have not interested me. I usually toss the economics section of the newspaper in the bin together with the sections on sports, fashion and health.

72This book reflects my debate with myself about economic theory. On the one hand, I am captivated by the charm of formal models: tales emerge from the formal symbols, and these tales have almost miraculous powers over me. On the other hand, I am obsessively occupied with denying any interpretation contending that economic models produce conclusions of real value. I feel attracted to economics as a branch of philosophy and as an academic field in which an intelligent discussion of social arrangements is, or at least can be, conducted. But I also feel disgust for economics as an academic field that tends toward conservatism and helps the strong in society maintain their dominance, and thus serves people for whom I have little empathy.

Snow in Jerusalem

73My perspective on economic models is completely subjective and describes me no less than it describes economic theory.

74When I was a boy and winter came, I would peek in the morning from the window of my room at the two green trees outside and hope to see them white. I longed so much for snow that I wanted to be a meteorologist. A meteorologist, I thought, is the first to know when it is going to snow. But several nights that started with a forecast of snow – ”tonight snow will fall in the hilly areas” – left me bitterly disappointed in the morning. Then several mornings that dawned with an unheralded white vista led me to the conclusion that the meteorologist was not the first to know when it would snow. Instead, it was Aryeh Mansdorf, the neighborhood grocer – he was the first to wake up and say his morning prayers before setting out to arrange the bottles of milk.

75Later, I wanted to be a lawyer who would defeat his adversaries in battles of intellect and razor-sharp logic. In order to prepare myself for this heroic task, I borrowed Samuel Hugo Bergman’s book ”Introduction to Logic” from the labor union library. This book did not make me a master of debate and did not equip me with a wealth of rhetorical tricks. The only thing I remember from it is the description of tin soldiers lining up in the courtyard. A resounding defeat in a classroom debate on ”Youth Movements, For and Against” (I was ”against”) made it clear to me that personal charm is more helpful in winning an argument than understanding the law of syllogism.

76I had the good fortune to grow up in one of the most wonderful areas of Jerusalem. Rabbi Meizel from the synagogue my father attended on holidays; the communist Sala Marcel, who made a point of eating pork just to annoy everyone; Aunt Hannah, who left her husband in Siberia and immigrated to Israel with her two children; the ritual slaughterer from the Yemenite courtyard; the widow whose son got caught up in crime; and the intellectual Yaacovson, who wrote a book explaining the rationale of the Jewish commandments — all these characters instilled in me a sense of great awe for those people who understood the complexities of human interaction so well. As far as I’m concerned, the opinion of such people is just as authoritative for making social and economic decisions as the opinion of an expert using a model.

77So, I do not know when it will snow and when prices will change. I am not an advocate of justice and have done nothing to change the social order. I do not feel entitled to advise anyone on the basis of my professional knowledge. I find myself denying that the models I work on can serve as a basis for predictions and, in general, I do not think that the appropriate test of economic models is whether they are useful.

78If the models we develop in yellow notepads or on blackboards constitute a basis for predicting human behavior, it would be miraculous in my eyes. There are no miracles in economics, but there are wonders. In my studies in the Department of Mathematics in Jerusalem, I learned to see wonders in the world of formalities. I sometimes also see them in economic theory. I approach economics as someone with a sense of curiosity who is trying to understand the logic of human interaction a bit better. This may not be much, but perhaps it is not so little either.


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