Utility Can be Dropped

Chapter 4, Section 7: Utility Can be Dropped

Let's get back to the concept of "utility". Although it's been popular in economics for quite long a time, I've decided not to use it any more after careful consideration. That's because the concept is a castle in the air, only an imaginary abstraction by economists, and doesn't exist in the real world; invisible means untestable, so it cannot be used in implication validation. From the viewpoint of economic explanation, when one more censer added one more ghost would have to be serviced, unobservable variables thus shall be avoided as much as possible. “Utility" is right so.

Years ago my teacher Alchian was with Becker and Friedman, and insisted "utility" be reserved. His reason was many economic goods, like friendship,  reputation and etc., cannot be traded on the market and therefore unmeasurable with money. Teacher Alchian called them non-pecuniary goods and thought only utility can be used for their measurement. After days of consideration, I had my conclusion for this problem: it's correct that some goods are not exchangeable on the market and thus don't have market price, yet economics has the postulate of substitution, and the so-called non-pecuniary goods can be mutually substituted with other pecuniary goods, so through the price changes of pecuniary goods we can still predict or explain the choice behaviors about those non-pecuniary goods. For example, now revising my Economic Explanations, I've increased my time spending measurable with money, and reduced the time chatting with my children about their life. The latter can be viewed as a loss of care to them, a non-pecuniary good. In the previously mentioned paper I published in 1972, my analysis of phenomena like children property rights, divorce, and child wife in old China all avoided any use of the utility concept.

I think, utility theory is popular in economics is mainly because the theory can provide a large room for the use of math formulas, which make papers look professional and easier to publish. Becker is the best of nowadays at the use of utility functions, and his analysis capability tops everyone I've seen. Yet I don't think good of his explanation capability: his predictions of worldly affairs usually go wrong. Utility is not something real, that makes the theory's implications need more steps before becoming testable, and one is very easy to make tautological mistakes in the course of reasoning. Asserting behaviors like jumping off a building, getting divorced, killing one's children, etc., are utility maximizing, cannot be wrong. But that's just a tautology. Of course Becker can't be this stupid, but you students shall realize in utility analysis it's very very easy to make such mistakes, and in fact gentlemen that's been set up are countless.

Alchian once had it quite right, that to explain human behaviors with utility analysis requires two conditions: first, we need to know how to rank different options with utility numbers; second, we need to know the sacrifice that has to be made for each option. I agreed, yet my reply was: if we know these, we don't need the concept of utility.

Inferior goods and Giffen Paradox

Chapter 4, Section 6: Inferior goods and Giffen Paradox

The concept inferior goods of economics is translated as "cixuan wupin", something inferiorly chosen, by Hong Kong education authorities, which is wrong! In mainland China it's translated as “didang wupin”, something low end, or "liezhi wupin", something low quality, which are wrong as well! My translation is "pinqiong wupin", which means poverty goods, though indecent yet correct.

What is an inferior good? I don't have a high income, so I drink beer, yet yesterday I won one hundred grand in my horse bet, which is a large amount, then I turn to drink wine. It's quite normal that one drinks beer when he is poor, and once income increased starts to drink wine. If the quantity demanded for a good reduces due to income increase, it's called inferior good. The beer above doesn't have to be low quality, inferiorly chosen, or low end at all. It can be excellent and wonderful, but I'd only drink more when I lose in horse bets, or when I am poor.

That's to say, when the relative price of beer and wine remains unchanged, the increase of my income can change my marginal rate of substitution, and lead to a decrease of the quantity demanded for beer. Logically, any good can be inferior good, and whether it is or not just depends on everyone's different choice.

The phenomenon above and its indubitable logic brings a great problem to economics. During the entire utility analysis, we have only three safe postulates: first, everyone maximizes his utility; second, the postulate of substitution; and third, the convexity postulate. These three are all constraints on behaviors, but since utility and indifference curve are only abstract and unobservable, they cannot give many potentially refutable implications and are not that useful in behavior explanation.

We thus need a postulate stronger enough to solve the difficulty caused by this unreal concept of "utility". We ask: when the sacrifice to obtain some economic good reduces, would one's quantity demanded for the good definitely increase? This is the heart of economics, and intuition seems telling us: of course it would! However, with only the above three postulates, the transition from the change in sacrifice to that in quantity demanded is not justifiable.

Let's take price as the sacrifice. When the price of an economic good reduces, by convexity postulate the quantity demanded for that good must increase, however a same indifference curve must be assumed. When the price of the good reduces, consumers of that good will have a increase in their real income, therefore the utility they maximize would be higher. A reduction in price originally enlarges the quantity demanded for that good, yet the accompanying increase in income or utility can either enlarge or decrease the quantity demanded — the decrease is right caused by "inferior good".

When the price of an inferior good reduces, the reduction itself enlarges the quantity demanded for the good, yet the price reduction leads to an increase in real income, and further to a decrease in the quantity demanded. Combined together, one plus and one minus, the quantity demanded can still increase. However, logically one plus and one minus can lead to a total decrease in the quantity demanded as well. The latter case is right the well-known Giffen paradox.

This was written in the third version (1895) of A. Marshall's Principles of Economics. Sir Robert Giffen (1827-1910) gave Marshall a paradoxical example. Bread is a main type of food, if the price of bread reduces, the purchase power of consumers will increase, they thus eat more meat while less bread. The price of bread reduces, yet the quantity demanded for it decreases. This paradox makes bread called a Giffen goods. Logically, Giffen goods doesn't have to be bread — it can be any goods. In other words, Giffen goods are inferior goods pushed to the extreme: the price reduction of a good leads to an increase in people's real income, and further to the decrease of the quantity demanded for the good. Logically this has nothing wrong.

Giffen goods are familiar to any freshmen that major in economics. They don't know — all economists have weirdly ignored either — that Giffen goods logically exist because we consider only the quantity demanded of each single individual and ignore the competition among them. Logically, Giffen goods cannot be traded on the market, used in back-door dealing, given and taken privately, exchanged in political deal, or allocated according to seniority. In other words, if Giffen goods can ever exist in a real world, that can only be Robinson's one-man world. Robinson's world doesn't have market or any other allocation related problems, yet Robinson has his needs, and need sacrifice as well. Because there is no allocation competition, Giffon goods can exist in this one-man world. However they cannot exist when there is social competition. That's to say, the competition among individuals eliminates Giffen goods. On the other hand, the twentieth-century masters of price theory, like Alchian, Stigler, Coase and etc., all reject the existence of GIffen goods. However, they cannot reject inferior goods. But rejecting one while keeping the other cannot be logically consistent. So I prefer my own handling to let competition eliminate Giffen goods. It will be further explained in Chapter 7, Section 1 of this volume. (That chapter is my own discovery, it rejects Marshall's scissors analysis, plain and clear, and one can easily see Giffen goods don't exist in social competition.)

(Translator: The “paradox” of GIffen goods, as well as inferior goods, originates not from the concept of utility, but from the special treatment of wealth and income. Wealth is nothing special but an economic good as well, and income is just part of one's wealth in a specific form. As an economic good, wealth has its substitution relationship with other economic goods, too, and one can choose whichever combination of wealth, beer and wine, which form a 3-dimensional surface. Once one wins a horse bet, or the price of bread reduces and leads to an increase in real income, as is in the Giffen example, the man just experiences an increase of his wealth. Whether this would lead to the decrease in the quantity demanded for beer or bread, just depends on the man's substitution preference in allocating the extra wealth.)

Convexity Postulate

Chapter 4, Section 5: Convexity Postulate

We can safely install another constraint to behaviors. That is, an indifference curve must curl inwards (concaving towards the lower left), like the bow weapon of Hua Rong the Little Li Guang, a fiction character in Water Margin, which "bends to a full moon". (Well, this is a joke, indifference curve doesn't have to curl that heavily.) This constraint (indifference curve neither is straight nor curls outwards) is called the convexity postulate, or the postulate of diminishing marginal rate of substitution.

Intention of the constraint is obvious. If utility stays unchanged (on the same indifference curve), the more A goods one has, the less willing he must be to substitute his B goods for more of A. This postulate is safe, if only the substitute happens on a same indifference curve. If the wealth or income of this man increases and he jumps to a higher indifference curve, his marginal rate of substitution will be totally changed. This is a great obstacle for the application of utility analysis to behavior prediction, and disables an important constraint to behaviors. Later we will get back to this.

Well, by the same indifference curve, the convexity postulate has a conclusion, which is not so useful. The conclusion says, if the price of a good decreases, the quantity demanded for this good on a same indifference curve must increase. That's because a price is always relative, when the price of a good A decreases it actually means the sacrifice of other goods needed for same amount of A reduces. In that way, the decrease in marginal rate of substitution would enlarge the quantity demanded for this price-lowered good.

The difficulty is, indifference curves and corresponding utilities are castles in the air, imagined by economists, and don't actually exist in reality. We cannot make sure whether one's choices would remain on the same indifference curve when the price of some good decreases. The logic reasoning for that is: when the price decreases, a consumer's real income would relatively increase, so he will jump to another higher indifference curve. One step further, when the marginal rate of substitution changes due to some other reason, what can we do?

Postulate of Substitution and Indifference Curve

Chapter 4, Section 4: Postulate of Substitution and Indifference Curve

In the first two chapters of this volume we have said, that to explain behaviors with a theory, the theory must install constraints to the behaviors. That individual maximizes his interest is a constraint, and with the concept of utility, that becomes one maximizes his utility. This constraint is a postulate and doesn't explain too many things. Asserting one maximizes his utility solely is tautology, and with the variation of constraints we can make predictions only when one economic good increases while all the others don't decrease.

The postulate of substitution adds another constraint, and widens the scope of explainable behaviors accordingly. The postulate says: everyone is willing to sacrifice any good he has for any other good. Do you agree or not? Are you willing to sacrifice your life for a bowl of fish ball noodles? This postulate says you are. If only the sacrifice is low enough and the gain is large enough.

When you cross a road to eat fish ball noodles, you are risking your life a little bit — the risk of a car accident is not zero. Like other fathers, I can sacrifice myself for my children — it's love. Yet because of work I don't have much time to stay with them — it's a substitution between love and livelihood.

Don't say that because you are principled, you'd never make a concession on matters of principle. Everyone has his own price, my soul can sell as well. The price is quite high, yet if you offer me a very big benefit while I need give up only a very minor principle, we can make a deal. This is substitution.

Due to everyone is willing to make substitutions, utility analysis thus creates the well know "dengyou quxian", or indifference curve, (normally translated into "wuchayi quxian", or no difference, in Chinese, which is neither elegant nor correct; "dengyou", or equally good, is my translation and gonna become classic). As one is willing to lose A while gaining B, we can find a curve for the two economic goods A and B, on which every point has a same utility. "Indifference" means same utility, and each point is indifferently preferable. Take A as the horizontal axis and B as the vertical, this curve must slope to the lower right, indicating one's indifferent substitution. The curve is a watershed, each point to the upper right of it has a utility higher than any on the curve, while the ones to its lower left go reversely.

Indifference curve enlarges the range of predictions. When there two economic goods, to be more preferable, it doesn't have to be A and B both increase, or A increases while B doesn't decrease: one increases while the other decreases can also be more preferable. There are an infinite number of indifference curves, each two of them don't intersect, and every upper right one has a higher utility number than any to its lower left. Under constraints, a man will choose the highest indifference curve he can reach.

Fisher's Contribution

Chapter 4, Section 3: Fisher's Contribution

Nowadays, the utility numbers economists use are mostly ordinal measure. Numbers of ordinal measure are not additive, but they can be ranked. Ranking is measuring. For an unadditive ranking, the margins between numbers are not comparable. 101 is greater than 99, and 99 is greater than 89. The former margin is 2, while the latter is 10, since the numbers are not cardinal measure, we cannot say the latter margin is five times larger.

Let's have some examples. In a Miss Hong Kong contest, the champion wins a score of 88, the runner-up 82, and the third place 79, then the ranking is settled. But we cannot say the margin between the champion and the runner-up is two times as large as that between the runner-up and the third place. Another example, when students take an exam, the teacher ranks them by scores. When I was studying in UCLA, one student asked the teacher how test scores were calculated. The teacher answered: "Test scores is just an arbitrary ranking, teachers that don't do this would be too stupid to teach in UCLA." The scores for essay questions are ordinal measure.

Ranking utilities with ordinal numbers doesn't have any logic problem. The assertion that someone takes A over B because the utility for A is larger, if relevant constraints properly handled, explains the behavior sufficiently. But when measuring utility with ordinal numbers, we know neither what the margin between A and B means, nor where a total utility for that man can be used. More than twenties years ago, the father of a Hong Kong middle school student called me, and said his son cannot answer the teacher's question about the use of total utility and thus failed an exam. The father asked for the answer, yet I asked in reply: "Does your son really not know the answer?" "No, he doesn't." "Good, your son actually knows more than his teacher!"

In 1892, I. Fisher (1867-1947), who later became the greatest economist of the twentieth century, published his doctoral dissertation, part of which is about utility theory. That's a genius book, and a key point in it is, to explain behaviors, cardinal ranking of utility is totally unnecessary, because at margin, cardinal ranking and ordinal ranking are of no difference, while for behavior explanation "margin" is sufficient. "Marginal" utility means the numerical change of utility brought by the increase or decrease of an item. When viewed at margin, neither addition into a total utility is necessary, nor comparison among different margins.

The idea that changes at margin suffice for behavior explanation originated from W. S. Jevons (1835-1882), and thrived due to Fisher's cherishing. In 1946 Stigler pointed out, if two products are produced through a single process, the average cost for each would be unable to know, yet the variation of marginal cost is knowable. To explain production behaviors, the information of average cost is unnecessary.

Later on when I was engaged in transaction cost research, I'd start only from changes at margin in any analysis. In the real world, transaction cost is not easy to measure. A viable means to explain behaviors is to see under different scenarios whether the transaction cost would go up or down. Change means "margin", and if there is no change, a behavior can never be explained. In dealing with transaction cost via changes at margin, it doesn't matter whether cardinal measure or ordinal measure is used. We cannot say cardinal measure is more accurate either, because accuracy here depends on the acceptance of observers, not the thoroughness of numbers.

Let me stress once again. Utility is just a free name for the ranking numbers of options, aiming at explaining a man's choices. This is what my teacher Alchian has said. Stigler has said: "Whether we assume one maximizes wealth, religious belief, elimination of love song singers, or his waistline, for rigorous demand theory it just makes no difference." R. H. Strotz has said: "Obviously, we don't have to find out whether the measurement of utility is in money, leisure time, octave, or inch, not to mention a psychological unit." These are all wisdom in the fifties of last century.

Utility is the Name of Numbers

Chapter 4, Section 2: Utility is the Name of Numbers

Generally speaking, to predict or explain behaviors/phenomena requires a measurement. To predict you'd take a right turn at a crossroad instead of a left one, is because turning right is faster, safer, or more comfortable, etc., which are all measurements. A measurement doesn't have to have many options, but at least two. To say A is bigger than B is a measurement, and that I assert under certain circumstance you'd choose the bigger over the smaller, is a prediction.

A measurement is ranking: ranked by big and small, by more and less, by heavy and light, etc. If the options for ranking are too plenty, A, B, C, D ... all used up but are still not enough, we then need numbers. Numbers are unlimited in amount. A measurement is thus defined as ranking with numbers. Yet these numbers have no content. When I say 17 and 29, you don't know what I am talking about. But if I say 29 pounds, you'd know it is the weight of some item, and also know 29 pounds is heavier than 17.

Because a selfish man maximizes his interest, we can use numbers to rank his options. If I assert under some circumstance this man would choose 29 over 17, you will certainly ask, what are exactly the 29 and 17?

Here right is the problem. I use numbers to rank your options, but the numbers don't have content, how does that happen? I can say the numbers you'd pick are in pounds, but "pound" means weight and that'd bring confusion. Anyway, I have to give a name to these ranking numbers, what shall I do? I therefore close my eyes, open a random page in dictionary, put down my finger on a word, reopen my eyes again and read it: utility. (Translator: Utility here corresponds to weight instead of pound.)

After more than one hundred years of nurture by countless scholars, at the time of mid-twentieth century, feasible definition of utility was simple: utility is the name of the numbers used in option ranking. It neither stands for happiness, nor enjoyment, nor welfare. Utility stands for option ranks, and as numbers are unlimited in amount, we let them come into play, and assert the option corresponding to a larger number is preferable, or vice versa, but never equally preferable.

"Utility" is an arbitrary name for the numbers of option ranking. It doesn't matter how big a number is, but what rank it takes: if the utility of a bigger number is set preferable over that of a smaller one, it cannot be reversed in the midway of analysis. This is a requirement by logic.

Roughly speaking, numbers have three applications, two of which are measurable. First, the non-measurable application is identification. If you go to a horse race and make a bet, there'd be a number for each horse, like 7, 3, etc. These numbers mean neither size nor speed, but are used only for identification. If you bet on the 7 and it wins, you can then have your prize.

The other two applications are about measurement. There are two types of measures because numbers can have two types of ranking. By one ranking, numbers can be added up, and that's called cardinal measure; while by the other, numbers can only be ranked but not added up, it's called ordinal measure.

A fish is 2 pounds and a chicken 3, with the two added up it's 5 pounds. So pound is cardinal. If you can't find an 8 feet rope, you can just add up a 3 feet and a 5. Foot is also cardinal. All cardinal measures can go through linear transformation. For instance: Fahrenheit degree of temperature is cardinal, and so is Celsius, thus with the Fahrenheit number at hand we can obtain the Celsius degree through a formula, securely. Pound and kilogram, or yard and meter, are all linearly transformable.

One difficulty for measuring utility is, utility is not always additive. The utility number for a pound of bread is 4, and that for an ounce of butter is 4 either, but when the two are eaten together, the utility number would be greater than 8. The utility for a cup of coffee is 4, and that of a cup of tea is 4 either, but when drunk together, the number of each cup would be less than 4. So when dealing with compliments like bread and butter, or substitutes like coffee and tea, additive utility would have insurmountable difficulties.

That said, economists once had devoted great energy to find a way so that utility can be cardinally measured. The most fabulous was the book cooperated by the twentieth century master of mathematics J. von Neumann (1903-1957) and economist O. Morgenstern (1902-1977), Theory of Games and Economic Behavior. In its second edition (1946), the authors pointed out, when there is risk, utility can be cardinally measured. Yet this cardinal measurement requires four assumptions, while two of them are problematic.

A Pathetic Development

Chapter 4: The Notion of Utility

Utility, a word frequently used by western economic scholars, is translated as "xiaoyong" (usefulness) in mainland China, while I think "gongyong" (worthiness) could be more appropriate. I've yielded to many other mainland translations, but this time I won't. The former translation "xiaoyong" is too real, and tends to make people feel there is really such a thing, which there is actually not. In China's cultural tradition,  there has never been such a concept of utility. As there is this cultural difference, one has the concept while the other doesn't, any translation of it can only be like blind men learn what an elephant is. Due to the same reason, some other concepts are almost untranslatable as well, like "cost", I don't think it's correct to be translated as "chengben" (expense), but I cannot come up with a better one either, so I just follow and yet express my attitude here that the translation is not so right.

Anyway, it's not so important for not having a perfect translation for "utility", because it had been more than a hundred years before western economic scholars made clear what the concept really means. With knowledge passed through generations, they thought they had understood, but actually not. It's not until the mid-twentieth century that the utility concept in economics receives an unambiguous definition. Yet as of today, many economic scholars still haven't got the correct definition. It can't be these scholars are too stupid to understand the concept, as many of them are indeed very smart. It's just they are unwilling: if they understand and agree the notion of utility detailed in this chapter, they'd lose their ambition to engineer any social improvement, and become nobodies like me.

Chapter 4, Section 1: A Pathetic Development

In 1789 and 1802, the English master of economic philosophy J. Bentham (1748-1832) originated the concept of utility, and influenced later generations vastly from then on. Bentham originally had three intentions. First, utility is an index of happiness or enjoyment. Second, everyone strives for a higher value of this index. The latter aspect led to the mathematization of selfishness, and after calculus was introduced into economics, utility functions flourished. Today they are still very popular in economics. Yet that's not because utility is indispensable in explanation, but because it makes mathematics applicable. Those skilled in math can thus have more showtimes.

Bentham's third intention was, when one's income increases, marginal utility of his income would decrease. He further made an assumption that everyone has a same version of income enjoyment, therefore the marginal income utility of a rich is low while that of a poor is high, the maximum welfare of the society would then be reached when all individuals have the same amount of income. This was the theoretical foundation of egalitarianism, and the predecessor of today's welfare economics.

Well, whether one's income increase would lead to a decrease of his marginal utility of income, is quite questionable. What economists all agree on today, is that utility indexes of different individuals are not comparable. The importance of one more dollar to a big rich doesn't have to be less than that to a street beggar. This only point would suffice to crush welfare economics. In 1950, P. Samuelson (1915-2009) pointed out in one profound paper, that no matter how much the total income of a society increase, as long as the income of some members (even only a single individual) has a decrease, economists would then be unable to affirm social welfare is improved.

Even Samuelson, the No. 1 figure of welfare economics, said like that, why are there still many practitioners of welfare economics today? I guess there two reasons. First, like previously mentioned, these economists think they are capable of engineering social improvements. Second, they need improve their own welfare: by advising the government in welfare engineering, they can have more income. In fact, the government loves to cut broad thongs of another's leather, sending taxpayers' money to economists: before the implementation of some policies that satisfy their own interests, government officials always need the words of corroboration from such scholars.

Scientifically speaking, the most important question on utility is Bentham's first intention: utility is an index of happiness. As the proverb goes: you are not a fish yourself, how can you know the happiness of it? How could you ever know whether I am happy or not, or whether I am more happier than yesterday? Leopards cannot change their spots, so are many economists, who always take themselves as capable as God. Today there are still people that view utility as an index.

In 1915, a self-taught Russian economist E. E. Slutsky (1880-1948) published — in Italian — an influential paper. After he passed, the paper was translated into English in 1952. One point of this great work was that, if we are going to explain human behaviors with a utility theory, then the concept of utility must be freed from subjective happiness or enjoyment. Mustn't it? To explain human behaviors, we need predict their choices, or under varied conditions how the choices would change. Whether one's choice is based on an increase of happiness, doesn't matter at all.

Since Bentham, participants in utility theory research almost included every important economists. Unfortunately, efforts of these countless geniuses earned only a history full of pathos. In 1950, G. J. Stigler (1911-1991) published a long paper titled The Development of Utility Theory to retrospect the history of utility thoughts over the past more than one hundred years. The paper was very knowledgeable, and also very graceful. In its conclusion Stigler could not help losing his temper: he thought economic scholars had had so little intention in theory validation, that all the efforts virtuosoes had payed in utility theory made nearly no contribution to our explanation of human behaviors!

I loved a paragraph of Stigler's conclusion in that work so much that in 1968 I had him write them down on a white paper, so that I can place it on my table as a motto of research. Today the ink has faded, but the scripture remains. I post it here so that the readers can appreciate the handwriting and keenness of this genius of the twentieth century. The words are as follow:

"The criterion of congruence with reality should have been sharpened — sharpened into the insistence that theories be examined for their implications for observable behavior. Not only were such implications not sought and tested，but there was a tendency，when there appeared to be a threat of an empirical test, to reformulate the theory to make the test ineffective. Economists did not anxiously seek the challenge of the facts." 

George J Stigler

Anyway, the theory of utility is still very popular today, so I have to spend some words to elaborate its key points.

In 1972 I published a paper about some phenomena like "blind marriage" and "child wife" in Chinese traditional marriage. In its last section I criticized the theory of utility heavily and deemed it totally useless. Economic Journal (Royal Economic Society) wanted to publish it but required me to reduce another five pages, so I simply removed the last section. After publication, two exerts wrote to me and blamed that I shouldn't have removed the section they thought the most important. Later the manuscript of this section cannot be found any more.

That I was against the theory of utility, was mainly because "utility" is only an imaginary concept by economists, a castle in the air, not fact, invisible and untouchable, so it's very difficult to derive refutable implications under this theory, and most would be only tautology.

At the time, R. H. Coase was on my side, while on the opposite side were three man I appreciated a lot: M. Friedman, G. Becker and my teacher A. A. Alchian. They opted to keep the theory of utility, as many economic goods — like friendship, reputation, family love, etc. — cannot be measured with money. As money cannot be used, they thought utility should come into play. In the following I will explain why I don't agree their point, but let me first show what the notion of utility that everyone agrees is.