The Science of Demand (30) - Unofficial Translation of Steven Cheung's 经济解释 - 科学说需求

Section 3.  The Choice of Invariables

The law of demand restrains the relationship between price or option forgone (a variable) and quantity demanded (another variable). However, there are innumerable things that can affect quantity demanded, and price is merely one of those. If it has been raining incessantly for days, the price of umbrellas will rise, so will their quantity demanded. This phenomenon has not refuted the law of demand: the higher demand for umbrellas is not due to higher price but incessant rain.

“Quantity demanded” is different from “demand”. The former changes with price, whereas the latter changes due to changes in other things (variables). Raining incessantly for days (a variable) affects the demand for umbrellas, causing the whole demand curve to shift to the right. With this shift, quantity demanded goes up, yet this increase is not due to price change. Obviously, in order to apply the law of demand to restrain the relationship between the price and quantity demanded of umbrellas, we must assume no change in weather.

As aforementioned, there are innumerable things (variables) affecting quantity demanded, and price is merely one of those. For instance, you have a fight with your wife and your food intake drops; you are convinced by a fung-shui master that it is not your day when the sky is pure blue, therefore whenever the sky is pure blue, you stay at home, reducing your demand for taxi. There are countless examples like these.

In respect of the law of demand, which other things should not change? This is no simple knowledge. If you say other than price, all other things that can affect quantity demanded remain constant, the following question will arise: if all other things remain constant, how can price possibly change? But if you say all other things can change, then the umbrella example would have refuted the law of demand. Clearly, the law of demand necessitates certain criteria to choose which things should change and which should not.

When I was a student, I spent substantial time on the issue of the choice of “other invariables”. Given the significance of the question, yet all the then existing literary works were either not clear enough, or too complicated, or saying different perspectives could be used, I was forced to construct my own answer. My choice criterion is: as long as the implication of the law of demand is not refuted by facts, the less invariables the better – i.e., the more variables the better – since this would augment the extensibility of the explanatory power of the law of demand.

Under this criterion, the following three “non-change” and “change” delineations are “safe” – safe here means not refuted by facts.

1. All other things that have direct impact on price can change. This includes all the things that can cause price to change when supply changes: a bumper harvest (supply increases, price decreases); government reducing land supply (property prices go up). These things can change.

2. All other things that have direct impact on quantity demanded cannot change. This includes money income and all the factors that can cause quantity demanded to change when there are no changes in price or supply. The aforementioned incessant rain affecting the quantity demanded of umbrellas is a case in point. With recurring plane crashes every day, sales of air tickets will plummet; Gao Xingjian having won the Nobel Prize in Literature, sales of his works will soar, etc. This kind of things (variables) cannot change.

3. Price change will lead to a change in quantity demanded, and possible changes in other things. These “other things” may in turn affect quantity demanded. These “intermediate” things (variables) that indirectly affect quantity demanded can all change. To cite an example, a fall in the price of coffee can lead to an increase in quantity demanded of coffee itself. At the same time, this will also lead to an increase in the demand for sugar. Consequently, the price of sugar will go up, which in turn will cause the demand of coffee to fall. The demand for and price of sugar are “intermediate” things, which in here can change. That is, a fall in the price of coffee will lead to an increase in its quantity demanded, which is the law of demand, and in between these two, other things (variables) that have possible impact on the quantity demanded of coffee can all change.

This third delineation is imperative. We have to let these “intermediate” or “indirect” things change, since we would rather not worry about the impact of these variables on the law of demand. If we were to investigate into these variables, with twists and obstacles likely to arise, there will be a lesser chance of success. And if the law of demand were refuted by facts, we could always use these “intermediate” things as a remedy, though by so doing a majority of its explanatory power would be abated.

This third delineation can be reversed by viewing from the perspective of a change in quantity demanded leading to price change, and other variables (things) in between can all change. This is a repeat of the third delineation. The third delineation starts by using price as the independent variable and quantity demanded the dependent variable. Here the order is reversed with quantity demanded as the independent variable and price the dependent variable. The analytical effect is the same irrespective of whether the order is reversed. Out of the two, we today prefer the former: price as the independent variable. Marshall in his time chose the latter.

I believe the most fascinating analysis about “ceteris paribus” in the law of demand is the chapter on demand theory in Friedman’s book of “Price Theory”. However, Friedman’s analysis was so intricate that it was hard to explain clearly without using equation. The aforementioned was inspired by Friedman. On the surface, the analyses look unlike due to different perspectives, yet their theoretical implications are largely the same. As the saying goes, great minds think alike.

The Science of Demand (29) - Unofficial Translation of Steven Cheung's 经济解释 - 科学说需求

Section 2.  Friedman’s Analysis

Price is a variable, so is quantity demanded. The law of demand says that these two variables are inversely related (the demand curve must slope downward from left to right). However, using a single good as an example, besides the price of that good, there are infinite other variables or things that can affect its quantity demanded. The other things that can change but are assumed unchanged (or ceteris paribus) are called parameters. Although we have refuted the existence of Giffen goods in a competitive society, let’s not leave the theme of Giffen paradox so soon, since in remedying this paradox, we can learn a great deal on how to approach variables and invariables. This is crucial in comprehending the law of demand.

To safeguard the explanatory power of the law of demand, it is a crucial topic about which thing can change and which cannot. There are two reasons. First, economists hope that in managing the variation or non-variation of other things, the predicament that the law of demand cannot be derived due to the Giffen paradox could be remedied. Second, the law of demand cannot assume the aforementioned other things all vary or all constant. That is, besides a good’s price and quantity demanded, the law of demand is also founded on the premise that certain things are allowed to change, while some other things are restrained not to change. As such, choosing things that can change and cannot change becomes a science.

Let’s discuss the first point: using the choice of invariables to refute the Giffen paradox. I will mainly discuss Friedman’s 1949 article, “The Marshallian Demand Curve”. I consider the Marshallian demand curve elucidated by Friedman not Marshall’s but Friedman’s himself. I also consider the focus of the article brilliant but not without problem. Knowing how talented Milton was, this extraordinary article was repeatedly studied by me as a student, altering my view on economics. Whoever does not believe Milton is indeed the twentieth century’s dean of economics should take a close look at that article. I sincerely admire Friedman, and am whole-heartedly grateful for his teachings, though at times disagree with him. This is an utterly opposite phenomenon between Western and Eastern academia.

Friedman’s “The Marshallian Demand Curve” is rich in content and profound in thought. It will take a long while to discuss in length, so we will only comment on one of its main points here.

Friedman was concerned that the utility analysis could not derive the law of demand – i.e., could not deduce that the demand curve must slope downward toward the right. This law is indispensable, and if utility number remains unchanged (or real income unchanged), then the convexity postulate is the same as the law of demand. The problem is if we assume money income unchanged (generally assumed), a fall in price will lead to a rise in real income, then the law of demand will be perplexed by the Giffen paradox. Friedman asked: “Should the demand curve assume money income unchanged or real income (utility number) unchanged?” His answer was that either one was about the same! As such, the demand curve, only allowed to slope downward toward the right, becomes a law.

The prediction of Friedman was, in a society without unemployment, a fall in price of a good will not lead to any rise in real income. This is due to price changes only causing a shift in the allocation of resources instead of an increase in income in the society. That is, the Giffen paradox in the utility analysis is merely the result of partial equilibrium. If we view the world from the perspective of general equilibrium of the society as a whole, the Giffen paradox is untenable. As such, the law of demand is established.

Generally speaking, this Friedman’s analysis is correct. The problem is exceptions still exist. For instance, in a bumper harvest, the price of agricultural produce will fall significantly, yet people’s real income will rise. And when the government provides substantial subsidy for education, school fees will tend to fall to almost zero. Though the income of the society as a whole will not rise, the real income of students will increase, hence logically the Giffen paradox might appear in the stratum of students.

No capable economists would disagree that if the law of demand were untenable, the entire economic framework would fall apart and be destroyed. Strictly speaking, Friedman’s aforementioned article does not resolve the Giffen paradox issue, yet this article is important in the sense that his partial equilibrium analysis has the substance of general equilibrium. More importantly, in demand analysis’ choice of variables and invariables, this article and Friedman’s “Price Theory” in 1962 have taught us a great deal.

The Science of Demand (28) - Unofficial Translation of Steven Cheung's 经济解释 - 科学说需求

Chapter V.  The Law of Demand

In the economic explanation paradigm, the law of demand, as far as I know, is the only indispensable theory. Either explicitly or implicitly, all the aforementioned postulates are incorporated in the demand curve of this law. All the other economic theories, if not dispensable, can be substituted by some others. The most important law of marginal output in the output theory, made famous by me when I first started, has seldom been used by me again when I grew older, since it can be substituted by the law of demand. That’s right – the food that we eat is a consumer good as well as a factor of production.

Until now at least, the law of demand is the only theory that has not been substituted by its counterparts. Being just a single curve, it incorporates much content, has plentiful variations, and involves profound concepts. Therefore, mastering the law of demand is never easy. And I say so from the economic explanation paradigm. The discussions and analyses throughout this whole book are all demonstrating either the content of this law, or how this law should be applied.

The law of demand says that whenever the price of a good declines, its quantity demanded will rise. From archaic days till now, irrespective of time or place, there are no exceptions. Using the vertical axis as price and the horizontal axis as quantity, the demand curve therein must slope downward from left to right. Certain books say that there are exceptions, for their authors are not treating economics as an empirical science. The reason is simple. In applying theory to explain phenomena or behavior, the theory itself must be refutable by phenomena or behavior. I have in Chapter I made this point clear. Supposing there are exceptions, and whenever refuted implications encountered are treated as exceptions, what then is empirical testing?

The law of demand is the spirit of economics. In any economics publications, I am able to assess the standard of the author simply by looking at his mastery of this law. This law needs not be literally mentioned, though content-wise it must be strictly followed – in my doctoral thesis, “The Theory of Share Tenancy”, I deliberately avoided mentioning “demand” to flaunt to my teachers.

Section 1.  Observation and Testing

In the previous chapter we said that with the three postulates of the utility analysis, given the existence of the Giffen paradox, we are unable to confirm the inexorable law between the decline in price and the increase in quantity demanded. A demand curve can be derived from the utility analysis, though this curve may not necessarily be sloping downward toward the right. In other words, the utility analysis cannot deduce the law of demand. On the other hand, the law of demand is not confined to the relationship between changes in price and quantity demanded. A good number of goods do not have market price, or under certain systems there is no market, yet the law of demand is still applicable. Without market price, we can instead use option forgone. In other words, any change in constraint can be interpreted as change in option forgone. The law of demand is still applicable to economic goods that cannot be exchanged due to their nature or the non-existence of a market. The approach, being a bit more complicated, will be explored later.

If the three postulates in the utility analysis could deduce the law of demand, then it would have been both rigorously logical and remarkably beautiful. However, from the perspective of explaining behavior, as long as we acknowledge that the law of demand itself is a postulate, or agree to my proposition that Giffen goods are not logically allowed to exist in a competitive society, then the three postulates in the utility analysis are superfluous. This is because the law of demand not only incorporates all the behavioral constraints of these postulates, but also one additional point: Giffen goods do not exist in a society. With changes in price or option forgone leading to a change in quantity demanded, the law already encompasses the postulate of substitution; and by refuting the existence of Giffen goods, its restraint on behavior is greater than that of the convexity postulate. Moreover, the selfish postulate that we mentioned in Chapter II – constrained maximization of an individual – is also incorporated in the law of demand, since as long as the choice stays along the same demand curve, it must follow the postulate of constrained maximization. In other words, as long as we accept the law of demand, the indifference curve analysis is redundant.

The price or option forgone in the law of demand is factual and observable in principle. However, quantity demanded refers only to the intended quantity of demanders which does not exist in the real world. As such, the law of demand itself is not testable. We must, therefore, assert additional test conditions, i.e., by specifying changes in observable constraints, before we can apply the law to yield hypothesis that is refutable by facts. In the next chapter I will demonstrate with a few real-world examples.

My point here is that if the price or option forgone in the law of demand is like quantity demanded – non-observable and non-factual – then the law of demand will be unable to derive any refutable implications, thus losing its function in explaining behavior. Simply one non-observable variable – quantity demanded – is hard enough to resolve, though resolving is still possible. We therefore have no options but to face the challenge of having an unreal quantity demanded.

Abstractive castle in the air is generally the starting point in theorizing, but for the sake of empirical testing, our hypothesis has to be inferred to observable phenomenon or behavior. In other words, abstract is necessary, though in general the less the better. As regards observation, there are three categories. The first one is non-observable and non-existent in practice. It is therefore insane to claim that they are observable. Quantity demanded belongs to this category. So does utility. The less from this category is certainly the better in testing. After decades of testing work, quantity demanded is the only non-observable “item” that I have to accept. The second category is real and observable. Price belongs to this category, and its level of difficulty gets relatively higher when approaching from the perspective of option forgone is required. The third category is observable in principle yet hard to observe in practice. We need to find indirect substitute for testing. The often-said marginal product in economics belongs here. Though it does exist, if not controlled in an artificial laboratory, it is close to non-observable. If “marginal” product is only imaginary and non-factual, then the “marginal product theory” in economics will suffer a crushing defeat. Note that quantity demanded belongs to the first category of observation which does not really exist but is only conceived by economists. We have to face it nonetheless. How we approach it could show the difference between an adult and a child.

“Utility” is also unreal. It is a great pity that the utility analysis could only derive the demand curve but not the law of demand. On the other hand, as will be shown in Section 5 of this chapter, the law of demand does not require any utility concept. The law of demand possesses greater restraint on behavior than the indifference curve analysis, but since it encompasses more concepts and variations which require ingenious handling, it is not at all easy to master.

Today’s development of economics indeed uses too many non-observable “intentions” or “motives” to tell nice and credible tales. But since these cannot be tested, the very nature of empirical science is contravened. To explain behavior requires the derivation of hypothesis that can be empirically tested. The less usage of variables or jargons which are non-existent in the real world, the better it is. Storytelling and scientific explanation are two distinct matters.

So complicated is the world that it is preferable to use simple theory to explain real-world phenomena. Utility analysis is usable, though it makes theory more complicated. Innumerable articles using the utility theory to “explain” behavior have their emptiness mercilessly exposed after the veil of mathematical formulae is lifted. The strengths of the utility analysis include its beauty, neatness and orderly structure if applied by masters, while its weakness lies in its proneness to fall into the trap of tautology. The law of demand can do without any content of “utility”, therefore is less liable to fall into this same trap. Without “utility” means the loss of a layer of façade decoration, forcing us to focus on the aspect of explaining behavior. Due to the relative simplicity of the law of demand, we can come up with variations more readily, and a simple theory with infinite variations displays the beauty of a different art. That said, rigorous utility analysis can nonetheless explain behavior. It is far from useless, though it needs not be used. The law of demand is another matter. Without the law of demand, never can economic hypotheses be tested!