The Science of Demand (34) - Unofficial Translation of Steven Cheung's 经济解释 - 科学说需求

Section 7.  What is Quantity?

Quantity transacted and quantity demanded are two distinct matters.

Quantity transacted is an observable fact. The quantity bought and quantity sold of a good are always the same: the two are one and the same, merely different perspectives of quantity transacted.

Quantity demanded is not a fact but a non-observable concept. Without economists, “quantity demanded” will not exist. Quantity demanded refers to the quantity of a good that a demander intends to obtain at a certain price, while quantity supplied refers to the intent of a supplier, both quantities being non-factual. Since they are merely “intentions”, quantity demanded does not necessarily equal quantity supplied. The concept of equilibrium was conceived by economists of a situation when quantity demanded equals quantity supplied. “Equilibrium” is not a fact, either. It exists only in the cogitation of economists. Quantity bought should never be confused with quantity demanded; neither should quantity sold with quantity supplied.

Conceptually, quantity demanded refers to the highest quantity that a consumer intends to exchange at different prices (exchange values). The demand curve is therefore a line showing at different prices the highest quantities demanded.

Quantity – irrespective of quantity demanded or quantity transacted – is rather complicated yet very interesting.

I submit that “quantity” can be classified into “in substance” and “by proxy”, as well as a combination of the two. Let’s first discuss quantity in substance.

When you buy gold in the market, gram is the unit of measurement. Gold stands for gold, and one gram of gold stands for one gram of gold which is double that of half a gram, or half that of two grams. This is called quantity in substance.

When you buy for your girlfriend one carat of diamond, the size of the diamond is represented by carat, a unit of measure. However, other than carat, there are other “quantities” being measured and included in the price. Color (color97, color96, etc.), clarity (VVS1, VVS2, etc.), cutting, are all qualities separately measured and priced. As such, what you get after spending $100,000 to buy one carat of diamond is not simply one carat, but a combination of four kinds of qualities: carat, color, clarity, and cutting. If you go to a diamond wholesaler, he may put in front of you hundreds of diamonds. There are plenty of choices with different combinations of the four qualities. When you pick a one-carat diamond for $100,000, all four qualities have in fact been measured and priced, and you are paying for a combination of the four prices.

What does the quantity in the demand curve of diamond refer to? The answer being there are four curves with four prices and four quantities. Since carat can be conveniently ranked numerically, it is most often used as a representative of quantity. But if quantity is singly represented by carat, the other three qualities have to be assumed unchanged. Whenever quality is directly measured and priced, it is a quantity in substance. Essentially, if the other three qualities are to vary freely, the demand curve of diamond using singly carat as quantity may not necessarily slope downward from left to right.

I can cite another similar example. In the United States, when you buy eggs in the market, the unit of measure is “number” of eggs. The criteria for eggs as set by the Department of Agriculture can be divided into extra large, large, medium and small, as well as grading of AAA, AA and A. The latter is determined according to the firmness of yolk. The firmer the yolk, the more expensive is the egg. In this egg example, “number” has substance, since both size and firmness of yolk have substance, and are measured and priced, albeit not as delicately as diamond.

Let’s turn to the concept of “by proxy”. This was first envisaged in 1969 when I was investigating piece-rate contracts in Hong Kong’s factories. This concept, given prominent coverage in my 1983 article of “The Contractual Nature of Firms”, was considered significant by Coase. Subsequently, when writing the first edition of Volume III of this book in 2002, I applied this “proxy” concept again when analyzing the law of contractual performance and generalized contractual theories.

As an example, if a factory uses piece-rate, i.e., according to every product or portion of product, to calculate wages, this pricing has “substance” since it is directly based on product. If wages are calculated using hourly-rate, time itself is merely a proxy of quantity since it does not represent the worker’s contribution, therefore may not be worth anything. Time worked is merely an approximation of the production of a worker within a time-span. The reason for sometimes using piece-rate and sometimes hourly-rate involves extensively the issue of different transaction costs in monitoring and operation. This will be discussed in Volume III.

Noteworthy here is that even in our familiar product market, the adoption of proxy is still very common. The law of demand is always applied to depict the relationship between price and its directly-linked quantity. It can be made very complicated: if on top of pricing using a proxy quantity, a product is simultaneously priced using several substantive quantities, the way to approach it will be similar to the aforementioned diamond example. There may be several demand curves for the same good, but remember well, the law of demand restrains always the relationship between price and its directly-linked quantity.

I often cite the sale of vitamin capsules as an example of proxy quantity in the product market. When you go to buy multivitamin capsules, they are apparently priced by the bottle. However, the bottle itself, bearing no relationship to vitamin, has “no substance”. The bottle is just a proxy unit of vitamin capsules for pricing. The proxy here is clearly shown, with a label on the bottle specifying the number of capsules inside and the different ingredients of each multivitamin capsule. These different ingredients have been separately measured and priced, yet we are buying multivitamin capsules by the proxy bottle.

In terms of proxy bottle with no substance, this example of multivitamin capsules is the most detailed and clear-cut example commonly seen in the market. However, since price is set for each bottle, a consumer could only pursue, at the margin, his highest use value per bottle to equal each bottle’s price. Unless by a none in a million coincidence, the marginal use value of the capsules, particularly the marginal use value of each type of vitamin, will not be identical to their prices. This is different from the diamond example.

In the aforementioned instance of vitamin capsules, the law of demand is only applicable between the price of each bottle and the number of proxy bottles. Though the number of capsules and the ingredients of each type of vitamin have all been measured and priced, the demand curves of these qualities may not necessarily slope downward from left to right. Consumers may consider certain ingredients of some vitamins too many, hence they would be willing to pay more for less. Yet this has not refuted the law of demand, since the demand curve of this law only restrains the relationship between the price of each bottle and the number of bottles. In other words, since the “quantities” of the different vitamins are not directly linked to the price, the law of demand is not applicable.

Let me switch to the example of watermelon. Watermelon is usually sold by weight, in pound or kilogram. The weight of watermelon is different from the bottle in the earlier example: weight itself represents certain quality of watermelon. The question is: in buying watermelon, a consumer values its composition of sugar, water and vitamin C, as well as the tastiness of its fibers. These qualities have never been measured. Buyers can at best estimate when picking. Hence these important qualities have to be entrusted to weight.

When there is a bumper harvest of watermelons in California, roadside watermelon stalls often do not sell by weight but by each watermelon. Though the watermelons differ in size, their prices are the same. There is therefore another proxy of quality in addition to weight.

This reminds me of the cedar round market in the United States. The trunk of cedar is not prone to be eaten by worms, therefore is often crosscut into circular pieces of about one foot in diameter and six inches in thickness as foot mats in gardens. These round cedar pieces differ in size, yet their prices are usually identical. Sellers first allow customers to select the better ones themselves, then mark down the price of the remaining stock for sale. After further time has been allowed for customers to further choose, the remaining will be marked down for sale again. Such practice is obviously due to sellers trying to avoid the costs of identifying different grades of cedar pieces and determining their respective prices. Instead, sellers let customers decide themselves. As such, after different rounds of markdowns, a decrease in price does not necessarily lead to an increase in quantity demanded. This, however, has not refuted the law of demand, since when price declines, so does the quality of cedar pieces.

With the above examples, I would like readers to realize that, in the hands of different people, the same demand curve can have completely different power. On one hand, theory has to be simplified; on the other, focus has to be precisely clenched, and phenomena in the real world have to be subtly observed. Generally speaking, explaining behavior cannot be accomplished simply by coupling government statistics with a few equations.

The law of demand confines the regularity between “price” and its related “quantity”. Quantity may be “in substance” or “by proxy”, or a combination of the two. Of essence is that there must be a direct linkage between price and quantity: “quantity” must be the quantity directly expressed by “price”. However, as seen from the diamond example, there are several demand curves in buying a diamond. In the example of multivitamin capsules, one demand curve represents a combination of multivitamins, and quantity is entrusted to “non-substantive” bottle. Here, the demand curve is only limited to the price of each bottle and the number of bottles. The composition of different vitamins is pre-determined in multivitamin, yet the different ingredients are not separately expressed by different prices, and each of them cannot be separately transacted, hence there is no individual demand curve for each vitamin. Certainly, we can find in the market bottles of single vitamin, but that belongs to the scope of another demand curve.

In the watermelon example, the demand curve refers to price and weight, or price and number of watermelons. Not measured are qualities like sugar, water and fibers, though consumers have in mind a rough combination. In the example of round cedar pieces, the demand curve refers to price and piece of cedar, albeit each piece is different. After customers have finished one round of buying, the price of the remaining lower-quality pieces is reduced for another round of sale. This then falls into the scope of another demand curve.

Price and quantity of the law of demand can be as delicate as an imperfection in a diamond, as approximate as one whole watermelon; as mammoth as all agricultural or industrial products of the whole economy, or even worldwide demand for real estate. However, irrespective of how delicate, approximate, or mammoth, the approach remains the same. What is price? What is quantity? Which price does the demand curve refer to? Which quantity? Is quantity in substance or by proxy? These questions are inevitable.