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.