The Science of Demand (36) - Unofficial Translation of Steven Cheung's 经济解释 - 科学说需求

Section 9.  Price Elasticity of Demand

When price falls, quantity demanded rises – this is the law of demand. But when the price of a good falls, the total consumption value of buyers toward that good may either fall or rise. From the viewpoint of the seller, income after price reduction may either fall or rise. The key determinant is the price elasticity of demand.

Price elasticity is a coefficient calculated by a simple equation. In the late nineteenth century, some economists tried in vain to find this simple equation. By the end of 1881, while holidaying in Sicily with his wife, Marshall enjoyed working at the rooftop of a small hostel. One afternoon, he came down from the rooftop and said to his wife: “I have just found the elasticity of demand!”

Today, other than price elasticity, there are innumerable equations of other elasticity coefficients that can be made very complicated. Unfortunately, in respect of explaining behavior, elasticity coefficient has only limited application, hence is not crucial. (In estimating the change in social welfare – if you believe in this – elasticity coefficient is crucial nonetheless.)

Let’s just focus on the price elasticity of demand. A fall in price itself leads to less consumption; a rise in quantity demanded itself leads to more consumption. Whether the resultant total consumption will rise or fall depends on the relative weightings of these two. The key in Marshall’s then solution lies in treating the relative weightings in percentage terms. The price elasticity coefficient is calculated by having the percentage change in quantity as the numerator and the percentage change in price the denominator. When price falls, and the percentage increase in quantity in the numerator is greater than the percentage decrease in price in the denominator, then the elasticity coefficient will be greater than one, which is termed elastic. As such, any fall in price will lead to increased consumption (increase in seller’s income). If the elasticity coefficient is less than one, termed inelastic, consumption will fall.

When price is elastic (coefficient greater than one), price and consumption diverges. When price is inelastic (coefficient less than one), price and consumption converges. Be mindful that price elasticity coefficient is calculated at a particular price. There are countless prices on a demand curve, and price elasticity coefficients at different prices can be all different: elasticity coefficients greater than one for a certain portion of the curve, and less than one for another portion.

Price elasticity of demand does not offer much help in explaining behavior due to our difficulty (inability in fact) in foreseeing its ballpark figure. Even though quantity demanded is invisible, but due to the law of demand, we know that when price falls, quantity demanded will rise. We will not have this convenience using price elasticity coefficient.

Let’s quote an example. In 1997, Hong Kong’s Western Harbor Tunnel began operations. It was privately built and its operators undoubtedly yearned for more income. Toll at the outset was HK$30 but traffic was infrequent, resulting in several tactics to offer discounts. Subsequently, more traffic was generated, and toll was increased to HK$40. With a fall in income after such an increase (elasticity coefficient larger than one), toll was then reduced to HK$35. Service costs, repairs and maintenance, etc., are negligible for one extra car crossing the tunnel, therefore the main goal of the tunnel is maximizing its total income. Maybe total income would be far higher when toll were set at HK$20 than HK$35 or HK$30.

Another example is that over the years, every time before the Hong Kong government raises excise taxes on tobacco and alcohol, it will forecast how much additional revenue that would bring to its Treasury. Experience tells us that such government forecast is never accurate, with a standard not much different from that of low-skilled laborers. Were the Hong Kong government to ask me to forecast, my capability would at best be on a par with that of laborers! The problem being nobody knows the price elasticity of demand for tobacco and alcohol.

Unable to foresee price elasticity coefficient, we can nonetheless try guessing. Not long ago, I made two guesses for the publications of a publisher – one was right, the other wrong – resulting in a tie.

The first time was for the Chinese calligraphy DVD that I helped to produce for my teacher, Zhou Huijun. Teacher Zhou’s calligraphy demonstration is so amazing that there is no close substitute in the market, and given one lesson of calligraphy costs close to HK$200 while Zhou’s DVD can be constantly re-read, I believed if the price was HK$50, its elasticity coefficient should be less than one, therefore setting the price at HK$100 should not be a problem. Little did I know that the price was set too high. My guess of price elasticity coefficient was wrong.

The second time was for my two recent books on education and academia respectively that were re-organized from former articles. These two books were diligently compiled to my satisfaction. The publisher asked me on the pricing. After deliberate consideration, I said HK$100, doubling the normal price. Why? With my belief of no close substitutes in the market, price elasticity coefficient should be less than one. This time I was right: selling price was doubled yet sales volume was high.

One right and one wrong, with the same inference method. Price elasticity coefficient is largely determined by the more or less of substitutes and their prices. Interestingly, I believe substitutes for Teacher Zhou’s calligraphy DVD are in all likelihood even less than that of my two books. But my guess was wrong.

The implication here is obvious. Whoever could always accurately guess beforehand the elasticity of demand in the market must be awfully rich. Even approximately right could have already made a fortune. No such person has ever existed in the world, clearly reflecting that elasticity coefficient can never be foreseen.

The Science of Demand (35) - Unofficial Translation of Steven Cheung's 经济解释 - 科学说需求

Section 8.  Consumer’s Surplus

Consumer’s surplus, having numerous applications in explaining behavior, is a crucial topic in the demand theory. This concept, coined and flourished in the late nineteenth century by Alfred Marshall, was first put forward by French economist, Jules Dupuit, in 1844. Arthur Cecil Pigou (1877 – 1959), Marshall’s student, audaciously brought that into his strongly-advocated welfare economics. Unfortunately, Pigou considered it futile of consumer’s surplus in explaining behavior (nothing had this welfare guru contributed to explaining behavior). Ever since Marshall, this “consumer’s surplus” has largely been used in measuring welfare, squandering a tool that could have been crucial in explaining behavior.

Applying consumer’s surplus to explain behavior was a flash in the pan limited to the Chicago School of Economics in the 1950s – 60s. The Chicago School then was interested in pricing arrangements, and this when combined with joint sales or tie-in sales formed a field of knowledge unique to the School. Even though such knowledge is incredibly amazing, very scarce are literary works in this area. This is mainly due to the oral tradition of a founding member of the School, Aaron Director (1901 – 2004). All his lifetime, Director enjoyed reading, thinking, discussing but writing. I am likely the last person inheriting Director’s tradition.

To elaborate on consumer’s surplus, it is best to start from Smith’s concept of value. As aforementioned, Smith considered the use value of water very high yet its exchange value very low. Simply put, the difference between use value and exchange value is consumer’s surplus.

Let’s use water as an example. With no water, other drinks, or fruits, etc. around at home, you feel thirsty and for some reason cannot go out to drink, how much will you pay for a glass of clean water? $1,000 may be an underestimation. When there is water at home, the price of one glass may be just $0.01. The highest use value of your first glass is $1,000 which you are willing to pay, yet you only need to forgo $0.01, the difference is therefore your surplus. Certainly, with water at home and you can keep on drinking until you have had enough, the highest use value of your last glass will only be $0.01. At the margin, when the highest use value of water equals its price (exchange value), there is no consumer’s surplus. Yet before reaching this margin, when the use value of every glass of water is higher than its exchange value, there is surplus for every glass. And the sum of the surpluses of all the glasses equals consumer’s total surplus.

Suppose the market price (exchange value) of an apple is $2, and you buy five. The highest use value of the fifth (margin) apple must also be $2, otherwise you would buy a little more or a little less. There is no consumer’s surplus for this fifth one. However, you are willing to pay $10 (your highest use value) for the first apple, $8 for the second one, $6 for the third one, $4 for the fourth one, while only the fifth one is for $2. The price you pay for each one is just $2. As such, your consumer’s surpluses are $8, $6, $4, $2, $0 respectively, or $20 in total.

To you, the total highest use value is $30 ($10 + $8 + $6 + $4 + $2), total exchange value $10 ($2 x 5), consumer’s surplus $20 ($30 – $10). Your highest average use value for five apples is $6 ($30 ÷ 5), average surplus for each apple $4 ($6 – $2), total consumer’s surplus is also $20 ($4 x 5).

Suppose I sell apples. Under competition, when other stalls sell each apple for $2, I can only follow suit. But if I am the only seller, and know that you are willing to pay $30 for five apples, I would certainly love to keep that $20 surplus to myself. So what can I do? There are three methods.

The first method is the most difficult. I will sell the first apple to you for $10, the second one $8, the third one $6 … As such, you pay a total of $30 instead of $10. Your consumer’s surplus ($20) is extracted by me. The difficulty is you will cheat me by saying that an hour ago you bought four apples from me, and now you are buying the fifth one.

Trying to cheat me? I still have two other methods to extract your surplus. One of them looks generous enough. Each apple sells for $2, and it is entirely up to you how many to buy (I know that for $2 an apple, you will buy five), though you have to pay a $20 entrance fee upfront. This entrance fee is your consumer’s surplus.

The last method does not require entrance fee. Every apple sells for $6 (your highest average use value of five apples), but you must buy a pack of five, or else none I would sell. When you buy a pack of five and pay $30, the $20 surplus is extracted by me. (Do not mix this up with the phenomenon of a pack of 6 bottles of beer, since beer is subject to competition, and you also have the option of buying bottles individually. Selling by a pack of six bottles, essentially at a discount, is for saving transaction costs with economy of scale.)

The price of all-or-nothing ($6 an apple as aforementioned) is the average of the highest use values, inclusive of consumer’s surplus. On a commonly-used demand curve, at each price you can buy as many or as few as you like. But if at each price you are required to buy all or nothing, then this demand curve becomes a all-or-nothing demand curve. On this curve there is no consumer’s surplus. In Section 6. What is Price? I have said that price is marginal use value, but in respect of a all-or-nothing demand curve, price is average use value. (Use value, irrespective of “marginal” or “average”, always refers to the highest.) That is to say, the commonly-used demand curve that allows you to buy as many or as few as you like is a curve of marginal use values; whereas the all-or-nothing demand curve a curve of average use values. (In the former case, whether it is an inferior good makes a little difference, though unimportant.)

There is a minor complication in the above analysis. When consumer’s surplus is extracted, the consumer’s income or wealth will fall a little, therefore he may buy a little less. On the other hand, if that good is an inferior good, the consumer will buy a little more due to his becoming poorer. Here we assume such complication does not exist.

As discussed earlier, a seller with a patent, or monopoly, or the so-called oligopoly, has the propensity to extract consumer’s surplus. Certain issues, to be later explored, deter him from doing so. The point I would like to make here, however, is that the analyses of pricing behavior of patent, monopoly or oligopoly in common textbooks are often rubbish.

Back to our earlier apple example. If each apple sells for $2 with no extraction of consumer’s surplus, given the specified quantity demanded (five in the example), from different perspectives, three definitions of consumer’s surplus exist:

1. Consumer’s surplus is the difference between the highest exchange value a consumer is willing to pay ($30) and actual exchange value ($10).

2. Consumer’s surplus is the difference between a consumer’s total use value ($30) and total exchange value ($10).

3. Consumer’s surplus is the biggest difference a consumer is willing to pay under a choice of all or nothing.

This apple example is not a castle in the air that does not exist in the real world. Let me quote a hypothetical example first before reverting to the real world.

Suppose a certain local government leases a big pond to me, allowing me to turn it into a fish farm for customers to fish. If the supply cost for each angler is $20 and I charge $20, this angler will patronize eight times a year. I know his average use value for eight times is $50. The question is, if I charge $50, he will only patronize three times a year. What should I do if I want his patronage eight times a year as well as charge him an average of $50? One way is to charge him $20 each time, but he has to pay an annual membership fee of $240 ($30 x 8) for the right to angle. This $240 is the consumer’s surplus for angling eight times. Given the charge each time is $20, as long as the $240 membership fee does not decrease his demand, he will still patronize eight times a year. That is, charging $50 each time will largely reduce this customer’s marginal quantity demanded, whereas $20 each time has no discernible marginal effect. Whether paying the $240 membership fee is a choice between patronizing eight times or none at all. This is the same as the “all-or-nothing” arrangement.

Certainly, readers will ask: given the demand curve of each customer is different, how can we determine the membership fee for individual customer? This is a good question to be answered in Volume II.

Let’s revert to the real world. Hong Kong these days has many “clubs” such as the American Club, the Jockey Club, golf clubs, country clubs, etc. They all charge entrance fees plus annual or monthly fees in return for the provision of cheaper food and services. These membership fees, annual or monthly fees are all extracted from consumer’s surplus. Such extractions may not be to the utmost, and the relatively cheap supplies within the clubs encourage more patronage for further extraction of consumer’s surplus. Thirty years ago, membership of a certain golf club in Hong Kong was valued at over HK$6 million. How lofty was the consumer’s surplus of old member!

I believe the most fascinating instance of extracting consumer’s surplus belongs to the former pricing arrangements of Disneyland (unsure if they have now been changed). Two options were offered by the theme park to potential customers. One was first paying a considerable admission fee, then once inside the park, for whatever item to enjoy, a separate fee is charged. The second option was buying a multi-item catalogue for admission as well as enjoying the listed items. These two arrangements were clearly both avatars of “all-or-nothing”.

Obviously, since the demand curves of customers are all different, the more pricing arrangements, the “fuller” the “extraction” of consumer’s surplus. No wonder Disneyland had so many pricing arrangements for students, senior citizens, the rich, the not-so-rich, etc. These different arrangements involve another important topic that we will analyze in Volume II – price discrimination.