Chapter 15

Economic Efficiency

Positive statements are statements about what is; normative statements are statements about what ought to be. Economics is a positive science. An economist who says (correctly or incorrectly) that a one-dollar increase in the minimum wage will increase the unemployment rate by half a percentage point is expressing his professional opinion. If he goes on to say, "Therefore we should not increase the minimum wage," his statement is no longer only about economics. In order to reach a "should" conclusion, he must combine opinions about what is, which are part of economics, with values, opinions about what ought to be, which are not.

Of course, one of the main reasons people learn what is is in order to decide what ought to be. Economists have values just as everyone else does. Those values affect both their decision to become economists instead of ditchdiggers or political scientists and the questions they choose to study. But the values themselves, and the conclusions that require them, are not part of economics.

Economists frequently use terms, such as "efficient," that sound very much like "ought" words. Once one has proved that something leads to greater efficiency, it hardly seems worth asking whether it is desirable. Such terms, however, have a precise positive meaning, and it is quite easy to think of reasons why efficiency in the economist's sense might not always be desirable.

My own interpretation of why we use such terms is as follows. People keep coming to economists and asking them what to do. "Should we have a tariff?" "Should we expand the money supply?" The economist answers, "Should? I don't know anything about 'should.' If you have a tariff, such and such will happen; if you expand the money supply, . . ." The people who ask the questions say, "We don't want to know all that. On net, are the results good or bad?" The economist finally answers as follows:

As an economist, I have no expertise in good and bad. I can, however, set up a "criterion of goodness" called efficiency, that has the following characteristics. First, it has a fairly close resemblance to what I suspect you mean by "good." Second, it is so designed that in many cases I can figure out, by economics, whether some particular proposal (such as a tariff) is an improvement in terms of my criterion. Third, I cannot think of any alternative criterion closer to what I suspect you mean that also has the second characteristic.

One could object that the economist, defining efficiency according to what questions he can answer rather than what questions he is being asked, is like the drunk looking for his wallet under the street light because the light is better there than where he lost it. The reply is that an imperfect criterion of desirability is better than none.

The point of this story is to show how it is that economists claim to be positive scientists yet frequently use normative-sounding words. Three of these words are "improvement," "superior," and "efficient." They are used in a number of different ways in economics, and it is easy to confuse them.

While the terms "improvement," "superior," and "efficient" are used in a number of different ways in different contexts--we shall discuss five in this chapter--the three words always have the same relation to each other. An improvement is a change--in what is being produced, in how it is produced, in who gets it, or whatever--that is in some way desirable. Situation B is superior to situation A if going from A to B is an improvement. A situation is efficient (in some particular respect) if it cannot be improved--if, in other words, there is no possible situation that is superior to it.

We will start by explaining what it means to produce one good efficiently. The next step is to apply the concept to two goods produced for one individual, seeing in what sense producing more of one and less of the other might be a net improvement. The final and most difficult step is to apply the idea of efficiency to something that affects two or more people.

We start with production efficiency. An improvement in production means using the same inputs to produce more of one output without producing less of another (output improvement), or producing the same outputs using less of one input and no more of any other (input improvement). As long as both inputs and outputs are goods, an improvement in this sense is obviously desirable; it means you have more of one desirable thing without giving up anything else. An output process is production efficient (sometimes called X-efficient) if there is no way of changing it that produces an output or input improvement. Production improvements and production efficiency provide a way of evaluating different outcomes that does not depend on our knowing the relative value of the different goods to the consumer. As long as both are goods, a change that gives more of one without less of the other is an improvement.

Figure 15-la shows a production possibility set for producing two goods, X and Y, using a fixed quantity of inputs; every point in the shaded region represents a possible output bundle. The curve F is the frontier of the set; for any point in the set that is not on F (such as A), there is some point on the frontier (B) that represents an improvement; in the case illustrated, B contains more of both X and Y than A. The points on the frontier are all output efficient; starting at B, the only way to produce more X is by producing less Y, as at C, and the only way to produce more Y is by producing less X, as at D.

This is the first time I have talked about the idea of production efficiency, but not the first time I have used it. From Chapter 3 on, I have been drawing figures with possibility sets and frontiers. A budget line, for example, is the frontier of a possibility set--the set of bundles it is possible to purchase with a given income. In indifference curve analysis, we only consider points on the budget line, not points below it, even though points below it are also possible--we could always throw away part of our income. Figure 15-1b shows this. The shaded area is the consumption possibility set. The line B is the consumption possibility frontier, alias the budget line.

Possibility sets and frontiers. Figure 15-la shows a production possibility set; F is its frontier. Figure 15-1b shows the set of alternative bundles available to a consumer; the budget line B is its frontier.

But since insatiability implies that there is always something we want more of, we would never choose to throw away part of our income. Any point in the interior of the possibility set is dominated by a point on the frontier representing a bundle with more of both goods. Point K on Figure 15-1b is dominated by point L, just as A is dominated by B on Figure 15-1a. So if we are looking for the best bundle, we need only consider points on the frontier.

Similar considerations explain why, in diagrams such as Figures 5-9a and 5-9b of Chapter 5, we only considered output bundles on the frontier of the production possibility set (the number of lawns that could be mowed and meals cooked or ditches dug and sonnets composed with a given amount of labor). If you are going to work that number of hours, you might as well get as much output as possible, not spend some of the time walking around in circles instead of either mowing lawns or cooking meals.

Utility Efficiency

So long as we only consider output efficiency, there is no way of choosing between points B, C, and D on Figure 15-la, all of which are output efficient. To do that, we must introduce preferences. Figure 15-2a is Figure 15-la with the addition of a set of indifference curves. If I am producing X and Y for my own consumption, I can use my indifference curves to compare different efficient points. Point D, for example, is on a higher indifference curve than point C; I would rather consume 5 units of Y and 2 of X (point D) than 3 units of Y and 4 of X (point C).

A utility improvement is a change that increases my utility--moves me to a higher indifference curve. A situation is utility efficient if no further such improvements are possible. On the diagram, point E is the only point in the production possibility set that is utility efficient.

The fact that one point is output efficient and another is not does not mean that the first point is either output or utility superior to the second. On the diagram, point C is output efficient and point A is not--but A is on a higher indifference curve than C! A is inefficient because B is superior to it (more of both X and Y). B is also on a higher utility curve than A; it must be, since X and Y are both goods. C is efficient not because it is output superior to A (it is not--C has more X but less Y, so neither is output superior to the other) but because nothing is output superior to it. Since C is not output superior to A, there is no reason why it cannot be utility inferior to it--and in fact it is. If someone argued that "You should produce at C instead of at A, since C is efficient and A is not," his argument would sound plausible but be wrong.

On first reading, the previous paragraph may seem both confusing and irrelevant. It is there because the same point will be crucial to understanding the use (and misuse) of another and very important form of improvement and efficiency--Pareto efficiency--which I shall describe later in the chapter. The relevant concept--that the fact that A is not efficient and C is does not imply that C is an improvement on A--is easier to understand in the context of output efficiency than in the context of Pareto efficiency, so I advise you to try to understand it at this point.

Efficient and inefficient outcomes. On Figure 15-2a, the alternatives are different output bundles to be consumed by an individual whose tastes are shown by the indifference curves; on Figure 15-2b, they are different allocations of goods (and hence utility) to two individuals. In each case, points on the frontier are efficient and points not on the frontier are not, but the former are not necessarily superior to the latter.

So far, we have been considering changes that affect only one person. The fundamental problem in defining what economic changes are, on net, improvements is the problem of comparing the welfare of different people. If some change results in my having two more chocolate chip cookies and one less glass of Diet Coke, there is a straightforward sense in which that is or is not an improvement; I do or do not prefer the new set of goods to the old (utility improvement). But what if the change results in my having two more cookies and your having one less glass of Diet Coke? It is an improvement from my standpoint, but not from yours.

The usual solution to this problem is to base the definition of efficiency on the idea of a Pareto improvement (named after the Italian economist Vilfredo Pareto)--defined as a change that benefits one person and injures nobody. A system is then defined as Pareto efficient if there is no way it can be changed that is a Pareto improvement. The problem with this approach is that it leaves you with no way of evaluating changes that are not Pareto improvements; the attempt to get around that problem while retaining the Paretian approach leads to serious problems, which I will discuss later.

One reason so many examples in earlier chapters involved identical producers and identical consumers was that I wanted to avoid the problem of balancing a loss to one person against a gain to another. If everyone is identical, any change that is in any sense an improvement must be a Pareto improvement: if it benefits anyone, it must benefit everyone. Early in the book, with the discussion of efficiency still many chapters in the future, that was very convenient.

Output efficiency is analogous to Pareto efficiency, with different people's utilities in the latter case corresponding to outputs of different goods in the former. A situation is Pareto efficient if there is no way of changing it that benefits one person and harms nobody--increases someone's utility without decreasing anyone else's. A situation is output efficient if there is no way of changing it that increases one output without decreasing some other output. Figure 15-2b shows the similarity; the axes are my utility and your utility, the region R consists of all possible combinations (the utility possibility set), and the frontier of that region, the curve F, consists of all the Pareto-efficient combinations.

In the case of output, we have a common measure by which to compare various points on the boundary: the utility of the individual consuming the output. This lets us compare two alternative output bundles, one of which contains more of one output and less of another. The important difference between Figure 15-2b and Figure 15-2a is the absence of indifference curves on 15-2b. The problem in comparing outcomes that affect several people is that there is no obvious way of comparing two different outcomes, one of which produces more utility for me and less for you than the other.

Some economists have tried to deal with such problems by imagining a social equivalent of the individual utility function (called a social welfare function). A social welfare function would give the welfare of the whole society as a function of the utilities of individuals, just as the utility function gives the welfare of the individual as a function of the quantities of goods he consumes. If we knew the social welfare function for the two-person society shown on Figure 15-2b, we could draw a set of social indifference curves on Figure 15-2b, just as we drew individual indifference curves on Figure 15-2a.

If we assume there is a social welfare function, we can try to analyze the outcome of different economic arrangements in terms of social preferences without actually knowing what the social preferences are--just as we have analyzed situations involving individual preferences without knowing what any particular real-world individual's preferences actually are. Some of the difficulties with this approach are discussed in the optional section of this chapter.

Another way of approaching the problem is to claim that although we have no way of deciding which of two Pareto-efficient outcomes is preferable, at least we should prefer efficient outcomes to inefficient ones. This argument is often made and sounds reasonable enough, but it runs into the difficulty that I discussed earlier in the context of output efficiency. While we may all agree that a Pareto improvement is an unambiguously good thing, it does not follow that a situation that is Pareto efficient is superior to one that is not.

Consider a world of two people, you and me, and two goods, cookies and Diet Cokes (20 of each). The situation is shown on Figure 15-2b; the axes are not Diet Cokes and cookies but my utility (which depends on how many of the Diet Cokes and cookies I have) and your utility (which depends on how many you have). One possible situation (A on Figure 15-2b) is for you to have all the cookies and all the Diet Cokes. That is Pareto efficient; the only way to change it is to give me some of what you have, which makes you worse off and so is not a Pareto improvement. Another possible situation (B) is for each of us to have 10 cookies and 10 Diet Cokes. That may be inefficient; if I like cookies more, relative to Diet Cokes, than you do, trading one of my Diet Cokes for one of your cookies might make us both better off (move us to C). The first situation is (Pareto) efficient and the second is not, yet it seems odd for you to say that the first situation is better than the second and expect me to agree with you.

The problem is that situation B is inefficient not because changing from B to A is a Pareto improvement (it is not) but because changing from B to C (I have nine Diet Cokes and eleven cookies, you have eleven Diet Cokes and nine cookies) is; it is hard to see what that has to do with A being better than B.

As this suggests, there are serious difficulties with the Paretian solution to the problem of evaluating different outcomes. They are sufficiently serious to make me prefer a different solution, proposed by the British economist Alfred Marshall; while he did not use the term "efficiency," his way of defining an improvement is an alternative to Pareto's, and I shall use the same terms for both. In most practical applications, the two definitions turn out to be equivalent, for reasons that I shall explain in the next section; but Marshall's definition makes it clearer what "improvement" means and in what ways it is only an approximate representation of what most of us mean by describing some economic change as "a good thing," "desirable," or the like. I have introduced the Paretian definition here because it is what most economics textbooks use; you will certainly encounter it if you study more economics.

To understand Marshall's definition of an improvement, we consider a change (the abolition of tariffs, a new tax, rent control, . . .) that affects many people, making some worse off and others better off. In principle we could price all of the gains and losses. We could ask each person who was against the change how much money he would have to be given so that on net the money plus the (undesirable) effect of the change would leave him exactly as well off as before. Similarly we could ask each gainer what would be the largest amount he would pay to get that gain, if he had to. We could, assuming everyone was telling us the truth, sum all of the gains and losses, reduced in this way to a common measure. If the sum was a net gain, we would say that the change was a Marshall improvement. If we had a situation where no further (Marshall) improvement was possible, we would describe it as efficient.

This definition does not correspond perfectly to our intuition about when a change is good (or makes people "on average, happier") for at least two reasons. First, we are accepting each person's evaluation of how much something is worth to him; the value of heroin to the addict has the same status as the value of insulin to the diabetic. Second, by comparing values according to their money equivalent, we ignore differences in the utility of money to different people. If you were told that a certain change benefited a millionaire by an amount equivalent for him to $10 and injured a poor man by an amount equivalent for him to $9, you would suspect that in some meaningful sense $10 was worth less to the millionaire than $9 to the poor man and therefore that "net human happiness" had gone down rather than up. The concept of efficiency is intended as a workable approximation of our intuitions about what is good; even if we could make the intuitions clear enough to construct a better approximation, it would still be less useful unless we had some way of figuring out what changes increased or decreased it.

How do we find out what changes produce net benefits in Marshall's sense? The answer is that we have been doing it, without saying so, through most of the book. Consumer (or producer) surplus is the benefit to a consumer (or producer) of a particular economic arrangement (one in which he can buy or sell at a particular price) measured in dollars according to his own values.

Several chapters back, I showed that the area under a summed demand curve was equal to the sum of the areas under the individual demand curves. So when we measure consumer surplus as the area under a demand curve representing the summed demands of many consumers, we are summing benefits--measured in dollars--to many different people. If we argue that some change in economic arrangements results in an increase in the sum of consumer and producer surplus, as we shall be doing repeatedly in the next few chapters, we are arguing that it is an improvement in the Marshallian sense.

The essential problem we face is how to add different people's utilities together in order to decide whether an increase in utility to one person does or does not compensate for a decrease to another. Marshall's solution is to add utilities as if everyone got the same utility from a dollar. The advantage of that way of doing it is that since we commonly observe people's values by seeing how much they are willing to pay for something, a definition that measures values in money terms is more easily applied in practice than would be some other definition.

Alfred Marshall was aware of the obvious argument against treating people as if they all had the same utility for a dollar: the fact that they do not. His reply was that while that was a legitimate objection if we were considering a change that benefited one rich man and injured one poor man, it was less relevant to the usual case of a change that benefited and injured large and diverse groups of people: all consumers of shoes and all producers of shoes, all the inhabitants of London and all the inhabitants of Birmingham, or the like. In such cases, individual differences could be expected to cancel out, so that the change that improved matters in Marshall's terms probably also "made things better" in some more general sense.

There is another respect in which Marshall's definition of improvement is useful, although it is one that might not have appealed to Marshall. If a situation is inefficient, that means that there is some possible change in it that produces net (dollar) benefits. If so, a sufficiently ingenious entrepreneur might be able to organize that change, paying those who lose by it for their cooperation, being paid by those who gain, and pocketing the difference. If, to take a trivial example, you conclude that there would be a net improvement from converting the empty lot on the corner into a McDonald's restaurant, one conclusion you may reach is that the present situation is inefficient. Another is that you could make money by buying the lot, buying a McDonald's franchise, and building a restaurant.

There are several ways in which it is easy to misinterpret the idea of a Marshall improvement. One is by concluding that since net benefits are in dollars, "Economics really is just about money." Dollars are not what the improvement is but only what it is measured in. If the price of apples falls from $10 apiece to $0.10 apiece and your consumption rises from zero to 10/week, you have $1/week less money to spend on other things, but you are better off by the consumer surplus on 10 apples per week--the difference between what they cost and what they are worth to you. Money is a convenient common unit for measuring value; that does not mean that money itself is the only, or even the most important, thing valued. The definition of a Marshall improvement does not even require that money exist; all values could have been stated in apples, water, or any other tradable commodity. As long as the price of apples is the same for all consumers, anything that is a net improvement measured in apples must also be a net improvement measured in money. If, for instance, apples cost $0.50, a gain measured in apples is simply twice as large a number as the same gain measured in dollars, just as a distance measured in feet is three times the same distance measured in yards.

A second mistake is to take too literally the idea of "asking" everyone affected how much he has gained or lost. Basing our judgments on people's statements would violate the principle of revealed preference, which tells us that values are measured by actions, not words. That is how we measure them when analyzing what is or is not a Marshall improvement. Consumer surplus, for example, is calculated from a demand curve, which is a graph of how much people do buy at any price, not how much they say they think they should buy.

If we decided on economic policy by asking people how much they valued things, and if their answers affected what happened, they would have an incentive to lie. If I really value a change (say, the imposition of a tariff) at $100, I might as well claim to value it at $1,000. That will increase the chance that the change will occur, and in any case I do not actually have to pay anything for it. That is why, in defining a Marshall improvement, I added the phrase "assuming everyone was telling us the truth." What they were supposed to be telling the truth about was what they would do--how much they would give, if necessary, in order to get the result they preferred.

The conventional approach to economic efficiency defines a situation as (Pareto) efficient if no Pareto improvements are possible in it. At first glance, that definition appears very different from the one I have borrowed from Marshall, which compares losses and benefits measured in dollars and defines a situation as efficient if no net improvement can be made in it. The Paretian approach appears to avoid any such comparison by restricting itself to the unobjectionable statement that a change that confers only benefits and no injuries is an improvement. The problem comes when one tries to apply this definition of efficiency to judging real-world alternatives.

Consider the example of tariffs. The abolition of tariffs on automobiles would make American auto workers and stockholders in American car companies worse off. Buyers of cars and producers of export goods would be better off. It can be shown that under plausible simplifying assumptions, there exists a set of payments from the second group to the first that, combined with the abolition of tariffs, would leave everyone better off. The payments by members of the second group would be less than their gain from the abolition; the receipts by members of the first group would be more than their losses from abolition.

This is equivalent to showing, as I shall do in Chapter 19, that the dollar gains to the members of the second group total more than the dollar losses to the members of the first group--that the abolition of tariffs is an improvement in Marshall's sense of the term. If I gain by $20 and you lose by $10, it follows both that there is a net (Marshall) improvement and that if I paid you $15 the payment plus the change would leave us both better off (by $5 each), making it a Pareto improvement. So a Marshall improvement plus an appropriate set of transfers is a Pareto improvement; and any change that, with appropriate transfers, can be converted into a Pareto improvement must be a Marshall improvement.

The abolition of auto tariffs by itself, however, is not a Pareto improvement: auto workers and stockholders are worse off. How then can Pareto efficiency be used to judge whether the abolition of tariffs would be a good thing? By the following magic trick.

The abolition of tariffs plus appropriate payments from the gainers to the losers would be a Pareto improvement. Since the situation with tariffs could be Pareto improved (by abolition plus compensation), it is not efficient. The situation without tariffs cannot be Pareto improved (I have not proved this; assume it is true). Hence abolition of tariffs moves us from an inefficient to an efficient situation. Hence it is an improvement.

If you believe that, I have done a bad job of explaining, earlier in this chapter, why a movement from an inefficient to an efficient situation need not be an improvement--a point made once in the context of output efficiency and again in the context of Pareto efficiency. A world without tariffs (and without compensation) is efficient, and a world with tariffs is not; but it does not follow that going from the latter to the former is an improvement. The situation with the tariff is being condemned not because it is Pareto inferior to the situation without the tariff but because it is Pareto inferior to yet a third situation: abolition of the tariff plus compensating payments.

Half of the trick is in confusing "going from a Pareto-inefficient to a Pareto-efficient outcome" with "making a Pareto improvement." The other half is in the word "possible." Arranging the compensating payments necessary to make the abolition of tariffs into a Pareto improvement may well be impossible (or costly enough to wipe out the net gain), since there is no easy way of discovering exactly who gains or loses by how much. If so, then the Pareto improvement is really not possible, so the initial situation is not really Pareto inefficient. The concept of Pareto improvement, and the associated definition of efficiency, can be applied to judge many real-world situations inefficient if you assume that compensating payments can be made costlessly (i.e., with no cost other than the payments themselves). Without this assumption, which is usually not made explicit, the Paretian approach is of much more limited usefulness.

One way to get out of this trap while retaining the trappings of the Paretian approach is to describe the abolition of the automobile tariff (without compensation) as a potential Pareto improvement or Kaldor improvement, meaning that it has the potential to be a Pareto improvement if combined with appropriate transfers (the compensation principle--it is an improvement if the gainers could compensate the losers, even though they don't). This, as I pointed out above, is equivalent to saying that it is an improvement in Marshall's sense.

I prefer to use the Marshallian approach, which makes the interpersonal comparison explicit, instead of hiding it in the "could be made but isn't" compensating payment. To go back to the example given earlier, a change that benefits a millionaire by $10 and costs a pauper $9 is a potential Pareto improvement, since if combined with a payment of $9.50 from the millionaire to the pauper it would benefit both. If the payment is not made, however, the change is not an actual Pareto improvement. The "potential Paretian" approach reaches the same conclusion as the Marshallian approach and has the same faults; it simply hides them better. That is why I prefer Marshall. From here on, whenever I describe something as an improvement or an economic improvement, I am using the term in Marshall's sense unless I specifically say that I am not.

It is worth noting that although a Marshall improvement is usually not a Pareto improvement, the adoption of a general policy of "Wherever possible, make Marshall improvements" may come very close to being a Pareto improvement. In one case, the Marshall improvement benefits me by $3 and hurts you by $2; in another it helps you by $6 and hurts me by $4; in another . . . Add up all the effects and, unless one individual or group is consistently on the losing side, everyone, or almost everyone, is likely to benefit. That is one of the arguments for such a policy and one of the reasons to believe that economic arrangements that are Marshall efficient are desirable.

In describing some economic arrangement as efficient or inefficient, we are comparing it to possible alternatives. This raises a difficult question: What does "possible" mean? One could argue that only that which exists is possible. In order to get anything else, some part of reality must be different from what it is.

But one purpose of the concept of efficiency is to help us decide how to act--how to change reality to something different than it now is. So any practical application of the idea of efficiency must focus on some particular sorts of changes. What sorts of changes are and should be implicit in the way we use the term?

One could argue that however well organized the economy may be, it is still inefficient. A change such as the invention of cheap thermonuclear power or a medical treatment to prevent aging would be an unambiguous improvement--and surely some such change is possible. That might be a relevant observation--if this were a book on medicine or nuclear physics. Since it is a book on economics, the sorts of changes we are concerned with involve using the present state of knowledge (embodied for our purposes in production functions, ways of converting inputs to outputs) but changing what is produced and consumed by whom.

One way of putting this that I have found useful is in terms of a bureaucrat-god. A bureaucrat-god has all of the knowledge and power that anyone in the society has. He knows everyone's preferences and production functions and has unlimited power to tell people what to do. He does not have the power to make gold out of lead or produce new inventions. He is benevolent; his sole aim is to maximize welfare in Marshall's sense.

An economic arrangement is efficient if it cannot be improved by a bureaucrat-god. The reason we care whether an arrangement is efficient is that if it is, there is no point in trying to improve it. If it is not efficient, there still may be no practical way of improving it--since we do not actually have any bureaucrat-gods available--but it is at least worth looking.

At this point, it may occur to you that while efficiency as I have defined it is an upper bound on how well an economy can be organized, it is not a very useful benchmark for evaluating real societies. Real societies are run not by omniscient and benevolent gods but by humans; however rational they may be, both their knowledge and their objectives are mostly limited to things and people that directly concern them. How can we hope, out of such components, to assemble a system that works as well as it would if it were run by a bureaucrat-god? Is it not as inappropriate to use "efficiency" in judging the performance of human institutions as it would be to judge the performance of race cars by comparing their speed to its theoretical upper bound--the speed of light?

The surprising answer is no. As we will see in Chapter 16, it is possible for institutions that we have already described, institutions not too different from those around us in the real world, to produce an efficient outcome. That is one of the most surprising--and useful--implications of economic theory.

While the way in which this textbook teaches economics is somewhat unconventional, the contents--what is taught--are not very different from what many other economists believe and teach. This chapter is the major exception. While Alfred Marshall was, in other respects, a much more important figure in the history of economics than Vilfredo Pareto, Marshall's solution to the problem of deciding what is or is not an improvement has largely disappeared from modern economics; virtually all elementary texts teach the Paretian approach. Both the Marshallian approach and the Paretian, as it is commonly applied, have, under most circumstances, the same implications for what is or is not efficient. What differs is the justification given for the conclusions that both imply.

I am by no means the only contemporary economist who feels uncomfortable with the Paretian approach, but I may be the first to put that discomfort, and the Marshallian solution, into a textbook. In that respect, this chapter is either "on the frontier" or "out of the mainstream," according to whether one does or does not agree with it.

OPTIONAL SECTION

SOCIAL WELFARE AND THE

ARROW IMPOSSIBILITY THEOREM

Earlier in this chapter, I mentioned that one "solution" to the problem of evaluating outcomes that affect different people is to assume that there exists a social welfare function--a procedure for ranking such outcomes--without actually specifying what it is. This is somewhat like the way we handle individual preferences; we assume a utility function that allows the individual to rank alternatives that affect him, although we have no way of knowing exactly what that function is.

But in the case of the utility function, although we cannot predict it, we can observe it by observing what choices the individual actually makes. There seems to be no equivalent way to observe the social welfare function, since there is no obvious sense in which societies make choices. We could try to describe a particular set of political institutions in this way, substituting "the outcome of the political process" for "what the individual chooses." But while this might be a useful way of analyzing what those institutions will do, it tells us nothing about what they should do--unless we are willing to assume that the two are identical. This leaves the social welfare function as an abstract way of thinking about the question, with no way of either deducing what it should be or observing what it is.

Even as an abstract way of thinking about the problem, the social welfare function has problems; not only is it an unobservable abstraction, it may well be a logically inconsistent one. To explain what I mean by that, I will start by showing how we can eliminate a particular candidate for a social welfare function--majority rule. I shall then tell you about a similar and much stronger result that eliminates a broad range of possible social welfare functions.

A social welfare function is supposed to be a way of ranking outcomes that affect more than one person; it is intended to be the equivalent, for a group, of an individual's utility function. There are two different ways in which one could imagine constructing a social welfare function. One is to base social preferences on individual preferences, so that what the society prefers depends, perhaps in some complicated way, on what all of the individuals prefer. The other is to have some external standard: what is good according to correct philosophy, in the mind of God, or the like. Economists, knowing very little about either the mind of God or correct philosophy, are reluctant to try the second alternative, so they have usually assumed that social preferences are built on individual preferences.

One advantage to defining social preferences in terms of individual preferences is that individual preferences express themselves in individual actions. Perhaps if we could set up the right set of social institutions, the choices made by all the individual members of society would somehow combine to produce the "socially preferred" outcome for the society. That, in a way, is the idea of democracy: Let each individual vote for what he prefers and hope that the outcome will be good for the society. Seen in this way, majority rule is a possible social welfare function. For each pair of alternatives, find out which one more people like and label that the socially preferred choice.

One problem with this was pointed out several centuries ago by Condorcet, a French mathematician. Majority vote does not produce a consistent set of preferences. Consider Table 15-1, which shows the preferences of three individuals among three outcomes. Individual 1 prefers outcome A to outcome B and outcome B to outcome C; Individual 2 prefers B to C and C to A; Individual 3 prefers C to A and A to B. Suppose we consider a society made up of only these three people and try to decide which outcome is preferred under majority rule. In a vote between A and B, A wins two to one, since Individuals 1 and 3 prefer it. In a vote between B and C, B wins two to one, since 1 and 2 prefer it. It appears that we have a social ranking; A is preferred to B and B to C.

If A is preferred to B and B to C, then A must also be preferred to C. But it is not. If we take a vote between A and C, Individual 1 votes for A but both 2 and 3 vote for C--so C wins. We have a system of social preferences in which A is preferred to B, B to C, and C to A! This is what mathematicians call an intransitive ordering; obviously it does not produce a consistent definition of what is socially preferred.

This Condorcet Voting Paradox eliminates majority rule as a possible definition of social welfare. A similar and much more general result proved by Kenneth Arrow, called the Arrow Impossibility Theorem, eliminates practically everything else. Arrow made a few plausible assumptions about what a social welfare function must be like and then proved that no possible procedure for going from individual preferences to social preferences could satisfy all of them.

What are the assumptions? One is nondictatorship; the social welfare function cannot simply consist of picking one individual and saying that whatever he prefers is socially preferred. Another has the long name independence of irrelevant alternatives. It says that if the social welfare function, applied to individuals with a particular set of individual preferences, leads to the conclusion that alternative A is preferred to alternative B, then a change in preferences that does not affect anyone's preferences between A and B cannot change the social preference between A and B. Another assumption is that social preferences are positively related to individual preferences; if some set of individual preferences lead A to be preferred to B, a change in the preference of one of the individuals from preferring B to preferring A cannot make the social preference change in the other direction. The society cannot switch to preferring B as the result of an individual switching to preferring A. Finally the social welfare function must lead to a consistent set of preferences; if A is preferred to B and B to C, then A must be preferred to C.

What Arrow proved was that no rule for going from individual preferences to group preferences could be consistent with all of those assumptions.

Economics Joke #2: A physicist, a chemist, and an economist were shipwrecked on a desert island. After a while, a case of canned beans drifted to shore; the three began discussing how to open the cans. The chemist (a physical chemist) suggested that if they started a fire and put a can of beans on it, he could calculate at what point the resulting pressure would burst the can. The physicist said that he could then calculate the trajectory the beans would take as they spouted out of the burst can and put a clean palm leaf down for them to land on. "That's too much trouble," the economist said. "Assume we have a can opener." (This is a joke about the social welfare function.)

The Arrow Impossibility Theorem does not quite prove that a social welfare function is logically impossible. For one thing, the theorem only applies to social preferences based on individual preferences; a social welfare function that says, "Socially preferred means what God wants" or "Socially preferred means what a philosopher can prove that we all ought to want," is not eliminated by the theorem. Furthermore it applies to social welfare functions based on preferences but not to those based on utility functions. The only form in which utility functions are observable is as preferences; we can observe that you prefer a cookie to a Diet Coke (because given the choice, you take the cookie), but we cannot observe by how much you prefer it. Even the Von Neumann version of utility discussed in the optional section of Chapter 13, while allowing quantitative statements about my preferences, does not allow quantitative comparisons between my preferences and yours.

If, in deciding what was socially preferred, we could use not only the fact that I preferred A to B but also that I preferred A to B by seven utiles and B to C by two, while you preferred B to A by one utile and C to B by three, the Impossibility Theorem would no longer hold. In this case, the obvious social welfare function would be total utility: Add up everyone's utility for each outcome and use the sum as your social welfare function. This rule for defining what is desirable, called utilitarianism by philosophers, played an important role in the development of economics (and philosophy). Alfred Marshall, for instance, was a utilitarian who proposed what I have called Marshall efficiency as an approximate rule for maximizing the (unobservable) total utility.

For most purposes, improvement in Marshall's sense provides an adequate working rule for applying our rather vague ideas of what is or is not a net improvement, but there are situations in which it can lead to apparently inconsistent results. Imagine a society of two people, you and me. There is one good in this society that is immensely valuable: a life-extension pill that doubles the life expectancy of whichever one of us takes it. There are also other goods. Suppose we want to use Marshall's approach to decide which of us should have the pill.

If I have the pill, there is no sum you could offer me that would make me willing to give it up; the pill plus the goods I already have are worth more to me than all of the other goods (mine plus yours) without the pill. The maximum you would be willing to offer me for the pill is less than all of your goods, since there is no advantage to you in taking the pill and then starving to death. So the dollar value of the pill to me (the amount I would have to be paid to give it up) is greater than its dollar value to you (the amount you would pay to get it). Leaving me with the pill is then, by Marshall's criterion, the preferred outcome; more precisely, taking the pill away from me is not an improvement.

But suppose we start with you having the pill. Following exactly the same argument, we find that leaving you with the pill is the preferred outcome! The problem is that since the pill is immensely valuable to both of us, whoever has it is, in effect, much wealthier than if he did not. He is wealthier not because he has more money but because he already has the most important thing that he would want money to buy. Since he is wealthier, the utility of money to him is less. So the money value of anything to him--what he would be willing to pay to get other goods or what he would have to be paid to give up the pill--is higher than it would be if he did not start out owning the pill. Since we are measuring utility by how much money (or goods) someone is willing to give to get something or willing to accept in exchange for giving something up, we get different results according to who we assume starts off with the pill.

Most applications of Marshall's definition of improvement do not involve this problem. If, for example, we consider the desirability of tariffs, it probably does not matter whether we start by assuming that tariffs exist and ask how people would be affected by abolishing them (measuring the amount of gains and injuries by their dollar equivalents) or start by assuming they do not exist and ask how people would be affected by imposing them. One reason it would not matter is that most of the gains and losses are themselves monetary; the dollar value to you of a $1 increase in your income is the same however rich you are. Another reason is that even if some of the gains and losses were nonmonetary, the abolition (or institution) of tariffs would have a relatively small effect on most people's income, hence a small effect on the monetary equivalent to them of some nonmonetary value.

This sort of problem is not limited to the Marshallian approach. Under the strict Pareto definition (an improvement means a Pareto improvement: someone is benefited and no one is hurt), most alternatives are incomparable; not only is there no way of deciding who should get the life-extension pill, there is no way of deciding whether tariffs should be abolished. As long as the abolition makes one person worse off, it is not a Pareto improvement. Under the "potential Pareto" criterion (a change is an improvement if there is some set of transfers from gainers to losers that, combined with the change, results in a Pareto improvement), one gets exactly the same problems as with Marshall's criterion.

PROBLEMS

1. In Figure 15-3a, the production possibility set for a worker working eight hours per day is shown as the shaded area. Which labeled points are output efficient? Which labeled points are output superior to point A?

Opportunity sets for Problems 1-3.

2. In Figure 15-3b, the shaded area shows possible outcomes in terms of the resulting divisions of income between two people, John and Lisa; nobody else exists. Which labeled points are Pareto efficient? Which are Marshall efficient? Which are Pareto superior to point A? Which are Marshall superior to point A? Which are "potentially Pareto superior" to point A?

3. Figure 15-3c is similar to Figure 15-3b. What do you think is the significance of the difference between the shapes of the shaded areas in Figures 15-3b and 15-3c? (Warning: This question requires original thought.)

4. The shaded area on Figure 15-4a is the possibility set for a worker working eight hours a day cutting down trees and making sawdust. Which labeled points are output efficient? Which are output superior to A? to B? to D? Which labeled points is A superior to? What about D?

Figure 15-4a Figure 15-4b

Figures for problems 4-6.

5. The shaded area on Figure 15-4b shows possible outcomes in terms of their effect on the incomes of two people, Ann and Bill; nobody else exists. Which labeled points are Pareto efficient? Which are Marshall efficient? Which are Pareto superior to point A? Which are Marshall superior to point A? Which are potentially Pareto superior to point A?

6. Draw the Pareto-efficient part of Figure 15-4b.

7. In this chapter, I gave one example of a Marshall improvement that many people would consider undesirable: a change that benefited a rich man by $10 and injured a poor man by $9. Give at least two other examples of Marshall improvements that many people (including well-informed people not themselves affected) would consider undesirable, where the reason for the conflict between the Marshall criterion and desirability does not depend on differences in income or wealth among the people affected.

8. One obvious objection to Marshall's definition of improvement is that we should take into account distributional effects: if a policy is a slight Marshall worsening but helps the poor it might still be desirable from a utilitarian standpoint. In order to take account of such effects, we must know what they are; this is not always easy. For each of the following policies, first describe what you think its distributional effect is (makes incomes more equal or makes incomes less equal) then give at least one reason why it might have the opposite effect.

a. Agricultural price supports.

b. Minimum wage laws.

c. Tax-supported state universities.

9. The government imposes a tax of $0.10/pound on artichokes; the money is used to give everyone $5 for Christmas. Assume that people are not all identical. Is the law a Pareto improvement? A Marshall improvement? Would its abolition be a Pareto improvement? A Marshall improvement? Explain.

10. Do Problem 9 on the assumption that people are all identical.

11. The government imposes a $0.10/pound tax on artichokes; the supply and demand curves are shown in Figure 15-5. The money is used to finance research on thermonuclear power. Each dollar spent on such research produces two dollars worth of benefits. Answer as in Problem 9.

Supply and demand for artichokes-Problem 11.

12. The situation is as in Problem 11, except that you can vary the level of tax. How would you find the (Marshall) efficient level? Approximately what is it? (Warning: This is a hard problem. A verbal explanation requires original thought. A numerical answer may require either more mathematics than some of you have or a good deal of trial and error.)

The ideas I have described as "Marshall improvement" and "Marshall efficiency" are more commonly derived from the idea of a potential Pareto improvement and referred to as the Hicks/Kaldor criterion. For the original, interesting, and readable discussion of those ideas, you may want to look at Alfred Marshall, Principles of Economics, (8th. ed.; London: Macmillan, 1920), Book III Chapter VI.

Some other important papers on the Hicks/Kaldor criterion include: Nicholas Kaldor, "A Note on Tariffs and the Terms of Trade," Economica (November, 1940); John R. Hicks, "The Foundations of Welfare Economics," Economic Journal (December, 1939); and Tibor Scitovsky, "A Note on Welfare Propositions in Economics," Review of Economic Studies (November, 1941).

The Arrow Impossibility Theorem is proved in Kenneth Arrow, Social Choice and Individual Values, (2nd ed.; New Haven, CT: Yale University Press, 1970).

At several points in this chapter, I have asserted that the Marshallian and potential Paretian (Kaldor/Hicks) definitions of efficiency lead to the same conclusion; any situation that is efficient by one definition is efficient by the other. That is not quite true, as I discovered after the first edition of this book was published. For a description of circumstances under which an outcome can be Kaldor efficient but not Marshall efficient, see: David Friedman, "Does Altruism Produce Efficient Outcomes? Marshall vs Kaldor," Journal of Legal Studies Vol. XVII, (January 1988).