The Science of Demand (26) - Unofficial Translation of Steven Cheung's 经济解释 - 科学说需求

Section 6.  Inferior Goods and the Giffen Paradox

What are inferior goods? I normally drink beer given that I do not earn much. Luckily I won $100,000 at the races yesterday. With increased income, I switch to drinking wine instead. Having beer when less well-off and wine when better-off is human nature of certain people. Inferior goods are so called since the quantity demanded of them drops with increased income. Note that the aforementioned beer is not substandard, second choice, nor low-class. Yet no matter how highly exquisite beer may be, I would only drink more of it after losing at the races or when I am poor.

With the relative prices of beer and wine unchanged, any change in my income can bring about changes in intention to substitute at the margin. I may therefore drink less beer when my income rises. Logically, any kind of good can be inferior good, and whether it is or not depends on individual choices.

The above common phenomenon and its correct logic lead to a significant problem in economics. In the whole utility analysis we only have three failsafe postulates: the first one being every individual maximizes utility number under constraints; the second one the postulate of substitution; the third one the convexity postulate. All these three postulates restrain behavior, but since utility and indifference curves are abstract and non-observable, not many refutable implications can be derived, therefore their applications in explaining behavior are only limited.

What we really need is a more rigid postulate in restraining behavior so as to overcome the problem triggered by unreal utility. We have to ask: if the option forgone in obtaining an economic good is less, will the quantity demanded of that good necessarily increase? This is the focus of economics, and its intuitive answer is: certainly! However, if we were to apply the aforementioned three postulates, we can never arrive at this inexorable law between the change in option forgone and the change in quantity demanded.

Let’s replace option forgone with price. According to the convexity postulate, when the price of an economic good falls, its quantity demanded must increase. But this assumes that we stay on the same indifference curve with utility number unchanged. When the price of a good falls, the real income of a consumer in effect increases, hence his utility number increases, too. The fall in price itself will lead to an increase in the quantity demanded of that good, though the increase in income or utility number may cause the quantity demanded to go up or down – the latter being the effect of “inferior good”.

When the price of an inferior good falls, the fall itself will cause an increase in the quantity demanded of that good. But the fall in price leads to an increase in real income, hence reducing the quantity demanded of that inferior good. When the two are combined, one for and one against, the resultant quantity demanded may still increase. However, logically, this one for and one against may also lead to a fall in quantity demanded. The latter is the renowned Giffen paradox.

It was written by Marshall in the third edition of his masterpiece (1895). A Sir Robert Giffen (1827 – 1910) proposed the following paradox example to Marshall. Bread is a primary food. If the price of bread drops significantly, the purchasing power of consumers will increase, resulting in their consumption of more meat and less bread. The price of bread has decreased, yet its quantity demanded also decreases. The bread in this paradox is called Giffen good. Logically, Giffen good is not limited to bread – any kind of good can possibly be Giffen good. In other words, Giffen good is inferior good to the extreme: the fall in price of a good leads to an increase in real income, resulting in reduced quantity demanded of that good. This is logically correct.

All freshmen in economics are familiar with Giffen good. What they do not know – and surprisingly being overlooked by all economists as well – is that Giffen good can only logically exist because we view purely from the perspective of individual demand while ignoring competition among individuals. Logically, Giffen goods cannot be transacted in the market. And under a system with no market, such goods will not be used in back-door transactions, underhand transfers, political deals, or be allocated according to seniority. In other words, if Giffen goods were to exist in the real world, they could only logically exist in Crusoe’s one-man economy. Crusoe’s economy had neither market nor any of the allocation problems in a social system, though Crusoe still had his demand and options to forgo. Giffen goods could logically exist in a one-man economy with no competition among different individuals. Yet Giffen goods can never exist in a society with competition. In other words, human competition has eliminated Giffen goods. By contrast, twentieth century’s gurus of the price theory like Alchian, Stigler, Coase, etc., chose to arbitrarily veto the existence of Giffen goods. Their problem, however, is that they could not veto the existence of inferior goods. It is illogical to veto one but not the other. That is why I still prefer my approach of competition eliminating Giffen goods. I will provide further explanation in Point 5, Section 1, Chapter VII. (In that original chapter of mine, Marshall’s scissor analysis is plainly rejected, thus making it clear that Giffen goods would not exist in a competitive society.)

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Section 5.  The Convexity Postulate

We can safely assert further restraint on behavior: the indifference curve must be convex (curving toward the lower left corner) in shape. This restraint (indifference curve is neither straight nor concave) is called the “convexity postulate” or “postulate of diminishing marginal rate of substitution”.

Its implication cannot be more apparent. If utility number does not change (on the same indifference curve), the more a person has of A, the less eager is he to exchange B for A. This postulate is failsafe as long as substitution is made on the same indifference curve. However, when the wealth or income of this person increases, he would jump to another indifference curve with a higher utility number, and the intention to substitute at the margin may also change. This is a big conundrum in inferring behavior using the utility analysis, resulting in its theoretical framework losing the most significant restraint on behavior. Discussion of it is deferred.

The convexity postulate can draw a conclusion using the same indifference curve to predict behavior, though its usage is limited. The conclusion is, if the price of a good falls, the quantity demanded of this good on the same indifference curve must increase. Since prices are always relative, a fall in the price of a good means a reduction in the option forgone of other goods. As such, the decrease in the intention to substitute at the margin will lead to an increase in the quantity demanded of the discounted good.

The problems with indifference curves and utility numbers are that they are merely castles in the air conceived by economists. There are no such curves in the real world, therefore we have no way to find out whether a person’s choice will still be lying on the same curve when the price of a good drops. By logical deduction: when prices fall, the real income of a consumer increases, this consumer will consequently jump to a higher indifference curve. At a higher level, however, the intention to substitute at the margin may have changed. So how can we deal with it?

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Section 4.  The Substitution Postulate and the Indifference Curve

In the first two chapters of this Volume, we have said that in order to apply theory to explain behavior, behavior must be restrained by theory. The restraint of constrained maximization, when combined with the utility concept, becomes maximization of utility number. This restraint is a postulate, though cannot explain much of human behavior. It is a tautological statement saying that whatever one does is to maximize utility number. When changes in constraints are asserted, what we can infer is only limited to choices like an increase in one economic good without concurrent reduction of other goods.

When restraints are supplemented by the postulate of substitution, the scope in explaining behavior is enlarged. This postulate says: every individual is willing to give up whatever good to exchange for whatever other good. Agree? Are you willing to sacrifice your life to exchange for a bowl of fish-ball noodles? This postulate says that you are willing, as long as you get back more than you give up.

Crossing the road to have a bowl of fish-ball noodles bears a little bit of risk to your life, since the risk of traffic accident is higher than zero. Like other fathers, I am willing to sacrifice a lot for my children – this is love. Yet in order to work, I have not spent much time with my children – this is the substitution of livelihood for love.

Don’t say that you are a man of high principle that for certain matter of principle, you will never give in. There is a price for everything, every person included. For a reasonably high price, my soul can be sold. If lucrative “gains” can be obtained at the expense of giving up negligible principle, I would “transact” with you. This is substitution.

Since everyone is prepared to exchange, the utility analysis has created the renowned “indifference curve”. Since we are willing to exchange A for B, two economic goods, it is very easy to find a curve between A and B so that the utility number thereon remains the same. “Indifference” refers to having the same utility number on every point of the curve, i.e., every point is equally preferred. With A as the vertical axis and B the horizontal axis, this curve will definitely slope downward toward the right, representing indifferent substitution to every chooser. This curve therefore becomes a watershed. Every point lying to the right of the curve has a higher utility number than every point on the curve, and is thus preferred. The opposite is true for every point lying to the left of the curve.

The indifference curve has proved useful in restraining behavior. Between two economic goods, to be better off, one’s choice does not have to be more of both A and B, or more of A while B remains unchanged: more of one at the expense of the other may still be better. There are infinite indifference curves with no two of them intersecting. And the utility number of each curve lying on the right is definitely higher than that of the curve on the left. Under constraints, one will choose the indifference curve with the highest utility number.

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Section 3.  Fisher’s Contribution

Economists today generally treat utility numbers ordinally measureable. Though unable to be added together, ordinal numbers can be ranked. Ranking is a kind of measure. Non-additive ranking means that the intervals between numbers are not comparable. 101 is bigger than 99, while 99 is bigger than 89. The interval between the former is 2 while the interval between the latter is 10. But since they are not cardinal measures, we cannot say the interval between the latter is five times that of the former.

Let’s cite a few examples. In Miss Hong Kong Beauty Pageant, the winner has 88 points, the first runner-up 82, and the second runner-up 79. The positions are ranked, yet it cannot be said that the difference between the winner and the first runner-up is twice the difference between the first runner-up and the second runner-up. Another example is about school examination where the teacher arbitrarily uses marks to rank. When I was studying at the University of California, Los Angeles (UCLA), a student asked the teacher how examination marks were calculated. The reply was: “Examination marks are only arbitrarily ranked. Otherwise, the teacher will be too foolish to teach at the UCLA.” Examination marks of essay questions are ordinal measures.

Using ordinal measure to rank utility has no logical problem. When a certain person prefers A to B, the reason is A’s utility number bigger than B’s. And if the associated constraints are properly handled, this person’s behavior will be explained. However, in using ordinal measure to gauge utility, we will never comprehend what the difference between A and B represents, nor what usage this person’s total utility number has. More than twenty years ago, I received a call from the father of a Hong Kong high school student. He said that there was a question in his son’s examination asking for the usage of total utility. His son did not know how to answer and thus failed in the examination. This father asked me for the answer, and I asked back, “Does your son really not know?” “He doesn’t.” “Then your son knows much more than the teacher!”

In 1892, Irving Fisher (1867 – 1947), who subsequently became the greatest economist of the twentieth century, published his doctoral thesis. Part of the thesis was on the utility theory. This thesis shows how talented Fisher was. One of the key points in that was from the perspective of explaining behavior, cardinal measure of utility is not necessary. Since cardinal measure is no different from ordinal measure at the margin, thus in explaining behavior, viewing purely at the “margin” is sufficient. “Marginal” utility refers to the change in utility number by having a little more or a little less of a good. Viewing at the margin, nothing needs to be added together, nor is comparison of the intervals between utility numbers required.

William Stanley Jevons (1835 – 1882) incubated the argument that to explain behavior, one only has to start working from changes at the margin. This idea, valued by Fisher, was succeeded by others. In 1946, Stigler pointed out that if a production process simultaneously produced two products, the average cost of each product would not be known, yet we would know the change in marginal cost. In explaining production behavior, there is no need to know the average cost.

When I subsequently worked on transaction costs, I started purely from marginal changes. It is no easy matter to measure transaction costs in the real world. A commendable approach in explaining behavior is to determine whether transaction costs will increase or decrease under different circumstances. Change is “marginal”, and if there are no changes, behavior cannot be explained. In applying this marginal changes approach to handle transaction cost, whether the cost measure is cardinal or ordinal makes no difference. We cannot assume cardinal measure is any more accurate, since the accuracy of a measure depends on the observer’s recognition instead of the number’s thoroughness.

Let me reiterate. Utility is only a random assignment of numbers to arbitrarily rank options for explaining choice behavior. This is what my teacher Alchian said. Stigler said: “In our postulate, regardless of whether a person strives to maximize wealth, religiosity, eliminate people who sing love songs, or his own waistline, from the strict perspective of the demand theory, there are no differences.” Robert Henry Strotz said: “Clearly we do not have to determine if utility measure is supported by money, loose time, octave or inch. And we do not need to conceive utility measure as a psychological unit.” These are wisdoms of the 1950s.

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Section 2.  Utility Being a Numerical Assignment

In general, a measure is required in inferring or explaining behavior or phenomena. Inferring that one would turn right instead of left on a crossroads can be due to it being faster, safer, or more comfortable, etc. These are all measures. Not many options are required to measure, though two are needed at the very least. It is a measure in saying that A is bigger than B. And if I say under certain circumstances one will pick a big one instead of a small one, this is inference.

To measure is to rank: in order of size, in order of quantity, in order of weight, etc. Supposing there are too many options for ranking, and if it is still not enough after exhausting A, B, C, D …, then we will use numbers. Numbers are infinite. The definition of measure is to use numbers to arbitrarily rank. Yet number itself has no content. When I say 17, 29, you would have no idea what I am talking about. But if I say 29 pounds you would know that I am referring to the weight of an object, and that 29 pounds is heavier than 17 pounds.

To describe a selfish person maximizing his self-interest, we can use numbers to rank his options. If I say under certain circumstances, this person will choose 29 instead of 17, you will then ask: what does 29 or 17 stand for?

The problem lies exactly here. I have to use numbers to rank your options, yet number itself has no content. What can we do? I could say the numbers you have chosen represent pounds, but “pound” also refers to weight which may cause confusion. Somehow a name has to be given to these numerically-ranked options. What can we do? I therefore close my eyes, casually open an English dictionary, put my finger down and then open my eyes, the word is utility.

In the mid-twentieth century, after the cultivation of numerous scholars over more than a century, the only creditable definition of utility is this simple: utility is a numerical assignment in ranking options. It represents neither happiness, nor enjoyment, nor welfare. Utility represents options ranking, and since there are innumerable options, we arbitrarily use numbers and proclaim that bigger numbers are preferable to smaller ones, or smaller numbers are preferable to bigger ones, but not that big or small numbers are equally preferable.

“Utility” is an arbitrary numerical assignment in ranking options. Whether the number is big or small is not critical. Of essence is the sequence: if we say the utility of a big number is preferable to that of a small one, we cannot reverse that halfway and say a smaller number is more preferable. This is a requisite of logic.

In general, there are three usages of number, out of which two are for measurement. The non-measure usage of number is for identification. For instance, when you go horse racing, on each horse is a number like number 7, number 3, etc. These numbers do not indicate big or small, fast or slow, but are for identification purposes only. If you bet on horse number 7 and that particular horse wins, you can go to collect your winning.

The other two usages of number are in relation to measure. Two types of measure exist since there are two kinds of rankings in numerical measure. One kind of ranking that can be added together is called cardinal measure; the other kind of numbers that can only be ranked but not added together is called ordinal measure.

A fish weighs 2 pounds and a chicken weighs 3 pounds, the two added together is 5 pounds. If you are in vain looking for an 8-foot long rope, then adding up a 3-foot rope with a 5-foot one gives you 8 feet. Foot is therefore cardinal. All cardinal measures can be linearly transformed. For instance, Fahrenheit is a cardinal measure, so is Celsius. By knowing the degree in Fahrenheit, we can safely use an equation to find out the exact degree in Celsius. Pound and kilogram, yard and meter, can all be linearly transformed.

A problem in measuring utility is that utilities cannot necessarily be summed. The utility number of one pound of bread is 4 while the utility number of one ounce of butter is also 4, when both of them are eaten, the utility number will be greater than 8. The utility number of a cup of coffee is 4 while the utility number of a cup of tea is also 4, but the utility number per cup, when both of them are drunk, will be less than 4. When dealing with complements (like bread and butter) or substitutes (like coffee and tea), there is no easy solution to the so-called additive utility issue.

Nonetheless, economists have spent substantial effort on devising certain solution to cardinally measure utility. The most remarkable is the book “Theory of Games and Economic Behavior” written by twentieth century’s mathematics guru, John von Neumann (1903 – 1957), and economist, Oskar Morgenstern (1902 – 1977). In the second edition (1946) of this popular book, the authors pointed out that in the presence of risks, utility could be cardinally measured. However, four assumptions are required for such measurement, out of which two are problematic.