The Marginal Utility of Bill Gates

John T. Kennedy poses a question to consequentialists:

At the margin $1000 is of negligible value to Bill Gates. If he found it lying on the sidewalk he might not bother to pick it up. The same $1000 could be a small fortune to a poor man. So if we force Gates to hand over $1000 to the poor man the benefit to the poor man is far greater than the harm to Gates.

Is there any reason why we shouldn't consider this a good consequence?

Here is my answer to a similar topic from the past:

There is simply no proof that the pauper values the $100 more than Bill Gates does. I have known many poor people who valued their marginal dollar little more than as an ass-wiping apparatus; I have known many rich people who valued their marginal dollar like their lives depended on it. There is no way to compare the utility of the $100 for Bill Gates and the pauper. There is no way to add, subtract, multiply, divide, transform, factorialize, or take the square root of utilities of different individuals.

Goods such as money are valued by what ends they help achieve, and those ends are subjective to the individual. Action is taken to pursue by the individual those ends to attempt to reach higher states of satisfactions. A second unit of the same good does hold a lower marginal utility than the first unit, as it is used to pursue less desired ends. However, this comparison between different units of the same good can only be made within the individual. The Law of Dimishing Marginal Utility is only valid when referring to a single individual. This Law does not hold for interpersonal comparisons. Bill Gates might well be happier with his billionth $100 than the menial laborer is with his hundredth. There is simply no way to know.

A truer standard of "fairness" is consent. If we really want to "maximize utility", the best thing to do is allow voluntary exchanges, not coercion. Coercion destroys utility.


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At the law firm where I

At the law firm where I work, one of the "attorneys emeritus" (that is to say retired) still comes to work everyday. He still keeps track of all the business news in the WSJ, still watches the stock prices of all his investments, still keeps a tight watch on his money. I know for a fact that this man is worth many millions of dollars.

Oh, yeah, and he's 90 years old.

Marginal dollars mean everything to him. If they didn't he would have stopped coming to work long ago and cancelled his WSJ subscription. The only reason he's worth as much as he is is because of all those marginal dollars.

Micha, Doesn't every

Micha,

Doesn't every voluntary transaction provide some evidence of personal utility for each party to the transaction? Doesn't money provide a standard by which to compare such utility?

Let's say you offer a poor man $1000 to dig a ditch and he jumps at the offer. Now try making the same offer to Bill Gates. He won't dig a ditch for you for $1000.

Why can't we conclude that the poor man who accepts your offer values your $1000 more than Gates does?

John, Because another

John,

Because another explanation might be that the poor man really enjoys digging ditches, while Gates may have a psychological aversion to it because a childhood friend died in a ditch.

That said, I'm not a utilitarianist. The reason we shouldn't force Gates to hand over his money is because that violates his rights. Even if we *could* make interpersonal utility comparisons accurately, it would *still* be wrong.

Cap, Make the offer for

Cap,

Make the offer for something that you know Gates doesn't have a phobia about and the poor man doesn't have any special desire for.

You offer them each $1000 to watch cartoons for 8 hours. You happen to know Gates enjoys watching cartoons. You know the poor guy could watch cartoons in his leisure time, but chooses not to.

The poor man is pleased to take the easy money. Gates says no, he'll just watch cartoons when he feels like it, thanks anyway. ("And don't bother making me any more $1000 offers, okay?")

Why can't we conclude the poor man values your $1000 more than Gates does.

Sorry Jonathan, for calling

Sorry Jonathan, for calling you Micha in my first comment. (Not that there's anything wrong with being called Micha.)

If you freely trade Micha an orange for an apple then can't I safely conclude that (in context) you prefer the apple to the orange and Micha prefers the orange to the apple?

Seems like at least some basis for comparison of interpersonal utility to me.

When Bill Gates declines to

When Bill Gates declines to dig a ditch for $1,000, he is quite properly concluding that he can make more than $1,000 during the time it would take him to dig a ditch by just doing what Bill Gates normally does every day of the week, or that he values that amount of leisure time --- a scarce good for Bill Gates --- more than he values another $1,000. The poor man has no such more lucrative alternative use of his time, but he does have a lot of excess leisure time, so he jumps in and digs the ditch.

There is simply no way to conclude from this that Bill Gates values $1,000 less than does a poor man. A Nobel prize is on hold for the first person to do so, and Heaven help the rest of us if anyone ever does.

The usual diminishing marginal utility for money argument for wealth transfers is on even weaker grounds. It more typically would call for Bill Gates to give up $1,000,000,000 in order that 1,000,000 poor people might have an additional $1,000. Good luck proving that one is welfare enhancing. Again, Nobel prizes are at the ready.

At family dinner last

At family dinner last sunday, I got into an argument with some liberal (hippie, really) family and friends about value theory (no, seriously).

The best argument I was able to come up with revolved around differentiating between /value/ and the /expression/ of value. Your value of something exists only in your mind, and cannot be compared to anyone else's because it cannot be quantified in terms of a unit. Your expression of value, that is your demand, can be so compared because it is an objective, physical phenomenon. That is, if I put $1 in a vending machine, I've expressed in a very real manner that I value that 20oz Pepsi more than $1 (or properly, any known available alternative use of that $1).

In the abstract, it would be nice if we could direct resources to their highest-valued uses, in terms of individuals' actual values. But we cant, because those values can't be communicated. The best we can do is direct resources to the highest expressed values, which is what the market does. Yes, that means that people who command more resources (wealth) are able to make their values count more, but that's the best we can do. Moreover, if you think your values are more important, get rich (and don't dare tell me it's "not that simple"!) and express those values.

I also had an exchange with Walter Block and Roy Cordato at ASC, at the session on Coase. Discussing the problems of Coasian social cost theory in terms of interpersonal utility comparisons and the non-additivity of utility across individuals made it clear to me that the Neoclassical idea, particularly vital to Law & Economics, of social optimality simply isn't valid, to which Walter and Roy seemed to agree. And if you invalidate social optimality, it seems to me utilitarianism almost in its entirety goes right out the window.

That's sort of a scary implication to me, in its magnitude if nothing else. Can anyone find a flaw in that reasoning that can "rescue" social optimality?

JTK, "If you freely trade

JTK,

"If you freely trade Micha an orange for an apple then can?t I safely conclude that (in context) you prefer the apple to the orange and Micha prefers the orange to the apple?"

The valid conclusion is that those relative preferences existed at the instant before the exchange took place. Every exchange action can be expected to produce major re-arrangements in an individual's subjective rankings on his single scale of values.

If you chose to purchase one slightly redder apple over another one, the ranking of the second apple is likely to fall significantly as a result of the fact that the satisfaction expected to be provided by an apple has now been translated into action.

Regards, Don

JTK, “If you freely trade

JTK,

“If you freely trade Micha an orange for an apple then can’t I safely conclude that (in context) you prefer the apple to the orange and Micha prefers the orange to the apple?”

This isn't an "interpersonal comparison," is it? It is simply two statements of personal preferences.

If you said that you prefer the apple to the orange _more_ than Micha preferred the orange to the apple, then you would be making an interpersonal comparison; however, the fact of the free trade doesn't give you that info.

Bill, If Jonathan will pay

Bill,

If Jonathan will pay $10 for a pear but Micha will pay no more than $9 for it, and Jonathan and Micha are indifferent to trading dollars with each other on a one-for-one basis, then can't we safely conclude that Jonathan values the pear more than Micha does?

JTK, "If Jonathan will pay

JTK,

"If Jonathan will pay $10 for a pear but Micha will pay no more than $9 for it, and Jonathan and Micha are indifferent to trading dollars with each other on a one-for-one basis, then can?t we safely conclude that Jonathan values the pear more than Micha does?"

Trading dollars is a sham exchange and has no evidenciary significance. The spending of dollars is only significant of value preferences when they are being spent for use-valued goods. The value of dollars, and other exchange-valued goods, comes from their future purchasing power and the flexibility to respond to the fundamental uncertainty of the future as both subjective values and the supply and variety of available goods change.

Regards, Don

Don, "The valid conclusion

Don,

"The valid conclusion is that those relative preferences existed at the instant before the exchange took place."

Then we have a data point. And the universe of voluntary transactions provides us with an arbitrary number of data points. Seems to me that could provide a basis for drawing some reasonable inferences about interpersonal values.

JTK, If Jonathan will pay

JTK,

If Jonathan will pay $10 for a pear but Micha will pay no more than $9 for it, and Jonathan and Micha are indifferent to trading dollars with each other on a one-for-one basis, then can?t we safely conclude that Jonathan values the pear more than Micha does?

No. You are assuming that a dollar is an objective measure of value.

A dollar is a scarce economic good just like a pear, a widget, or a piano lesson is. Both Jonathan and Micha value the dollar differently, many times vastly differently depending on many factors, including religious beliefs, goals in life, uncertainties of the future, immediate pressing concerns, and more.

Jonathan values the pear

Jonathan values the pear more than Micha does with respect to consuming other goods. So if Micha has the pear Jonathan could pay somewhere between $9 and $10 for the thing (call it p), and Micha would benefit (p-$9>0). So would Jonathan ($10-p>0). Jonathan should get the pear, and in a market situation he would.

If you're talking about money, things are different. We all value $1 at $1, so trading money for money doesn't make anyone better off. All we can say is that all else equal, we'd expect people to prefer more income to less. Utility only makes sense when we're talking about a tradeoff between two or more goods--apples and oranges, or pears and other stuff.

Talk about tradeoffs between income and leisure, and now you're getting somewhere. Welcome to the field of labor economics.

More formally, the level of utility doesn't matter; what matters is the shape of the tradeoffs between different things that people are willing to tolerate. Utility is normally an ordinal concept, not a cardinal one, used for analytical convenience. Mathematically, this is the difference between assuming concavity or quasiconcavity; the latter is a fancy way of saying that people seem to like variety but don't like risk.

I think that a lot of the confusion comes from the fact that the word "utility" means at least three different things in economics (all mathematical objects), and none of these is the same as what ordinary people think of as utility (something similar to happiness). I really wish that we'd use different words to describe these things because it confuses the heck out of people.

Don, Is it a sham exchange

Don,

Is it a sham exchange of present and future dollars if M borrows $1000 from J at a certain rate of interest?

Jonathan, A dollar is a

Jonathan,

A dollar is a scarce economic good just like a pear, a widget, or a piano lesson is. Both Jonathan and Micha value the dollar differently, many times vastly differently depending on many factors, including religious beliefs, goals in life, uncertainties of the future, immediate pressing concerns, and more.

In a given context how could you know M values the dollar differently than you? Wouldn't any evidence for that be evidence of his personal values?

JTK, In a given context how

JTK,

In a given context how could you know M values the dollar differently than you? Wouldn?t any evidence for that be evidence of his personal values?

No. I come to the conclusion that Jonathan and Micha value the dollar differently from the general observation that all scarce resources are valued subjectively by individuals based on what ends they are pursuing. Just as Jonathan and Micha value pears, widgets, and piano lessons differently based on their individually unique ends, they also value dollars differently.

Just because dollars are used as the medium of exchange does not mean that they somehow take on objective value. They have an objective purchasing power at any given time as defined by the array of prices of goods available for exchange at a market rate, but purchasing power is not utility.

No. I come to the conclusion

No. I come to the conclusion that Jonathan and Micha value the dollar differently from the general observation that all scarce resources are valued subjectively by individuals based on what ends they are pursuing.

I don't know how you observe this without observing evidence of their values.

I don?t know how you observe

I don?t know how you observe this without observing evidence of their values.

The fact that I observe that people value goods based on their own subjectively defined ends does not imply that there is an objective standard by which I can measure how much different people value those goods. In fact, it implies that I cannot.

Noah, I believe your

Noah,

I believe your reasoning is perfectly sound. I've kept an interested eye out, literally for nearly 30 years now, for someone who could either compare or add interpersonal utility and rescue welfare economics and the notion of social optimality. Not that I hope someone could do so, because the political consequences would be horrendous to my way of thinking. Anyway, so far, nobody's done it. Typically, there's a nod to the fact that it's impossible, but then it's assumed possible for reasons of mathematical tractability and to simply see what conclusions can be obtained.

"Let?s say you offer a poor

"Let?s say you offer a poor man $1000 to dig a ditch and he jumps at the offer. Now try making the same offer to Bill Gates. He won?t dig a ditch for you for $1000.

Why can?t we conclude that the poor man who accepts your offer values your $1000 more than Gates does?" (Posted by John T. Kennedy at April 8, 2004 09:19 AM)

Gates and the poor man value "Dig the ditch", not "$1000". I agree with Noah Yetter, in this case, $1000 is an "expression of value". And this number is assigned by someone else, not the real value from the individual's preference. If $1000 is not attached to anything else and treated as "apple" or "orange", in other words, as A THING, Gates and the poor man might value $1000 as the same. I think that is Jonathan's point.

"You offer them each $1000 to watch cartoons for 8 hours. You happen to know Gates enjoys watching cartoons. You know the poor guy could watch cartoons in his leisure time, but chooses not to.

The poor man is pleased to take the easy money. Gates says no, he?ll just watch cartoons when he feels like it, thanks anyway. (?And don?t bother making me any more $1000 offers, okay??)

Why can?t we conclude the poor man values your $1000 more than Gates does." (Posted by John T. Kennedy at April 8, 2004 10:13 AM)

Value doesn't necessarily use the monetary number to measure. Gates might value watching cartoon more. But when they decide whether to take $1000 bill, they face different evaluation question: whether it is OK to take this money. Not the question whether and how much they value watching cartoons.

JTK: ?If you freely trade

JTK: ?If you freely trade Micha an orange for an apple then can?t I safely conclude that (in context) you prefer the apple to the orange and Micha prefers the orange to the apple??

Bill hit the nail on the head: 'This isn?t an ?interpersonal comparison,? is it? It is simply two statements of personal preferences.'

It may be the case that Jonathon values an apple more than Micha and that Micha values an orange more than Jonathon. But it may also be the case that they both value apples equally -- only Micha values oranges more than this amount, and Jonathon values oranges less. Or similarly they may both value oranges equally, with differing valuations of apples.

Indeed, it may also be the case that Micha values both apples and oranges extremely highly (oranges slightly more) and Jonathon places extremely little value on either (least of all oranges). Or the reverse.

Similarly, the even exchange of dollars for dollars tells us nothing. It says that Micha is indifferent between one dollar and another similar dollar, and Jonathon is likewise. But it gives us no basis for comparing Jonathon's preference for dollars to Micha's.

Consider again the fruit scenario. We know that Jonathon prefers apples to oranges, and Micha prefers the opposite. However, it would be perfectly reasonable to expect that *both* Jonathon and Micha would be indifferent to trading an apple for a similar apple *or* an orange for a similar orange. If the one to one trade really gave us any basis for interpersonal comparison, this would be paradoxical.

The same principle holds between Bill Gates and the poor man. We can conclude that Gates values another use of his time more than $1000, and the poor man has a different ordering of preferences, but we have no basis of comparison between them. You can try to get around this by specifying, for example, that Gates enjoys watching cartoons, and the poor man doesn't -- but this leaves out the crucial element: compared to what?

Let's break it down. Suppose we call C1 the utility to Gates of watching cartoons and C2 is the utility of cartoons to the poor man. We know that C1 is positive (Gates likes cartoons) and C2 is negative (the poor man doesn't). M1 and M2 represent the utility of the money to each of them. These are our unknowns. The poor man accepts the option of C2 + M2, while Gates rejects C1 + M1. You seem to be concluding that this means C2 + M2 > C1 + M1, and given that M1 is positive, while C2 is negative, M2 is clearly greater than M1.

But this leaves out the crucial variables X1 and X2, representing the utility of whatever the two men would otherwise have done with their time. What we have really established is that C2 + M2 > X2 and X1 > C1 + M1. Unless we assume that X2 = X1, your conclusion doesn't hold, and we have no good reason to assume that. In fact it's very easy to imagine that Gates has an alternate use of his time with a much higher utility than that of the poor man's alternate activity, in which case we can conclude nothing about the relation between M1 and M2.

More generally, if we have two people for whom we have ranked a large number of experiences according to their respective preferences, it's perfectly possible that the highest ranked preference on one list has less utility than the lowest on the other.

Furthermore, we can't determine anything about the difference in utility between two different preferences for one person. A change from one person's 11th ranked to 10th ranked preference may be only a very marginal increase in utility, while for another person that same change may be a huge increase.

We may be able to subjectively estimate some of these comparisons (for example, by observing how much happier or sadder certain events make one person than another), but this is subjective, and it's nothing that economics tells us.

-Mike

What's all this great mess

What's all this great mess about proving things that have to do with ethics? Seems like we're pretty far away from such proofs. We barely scratch the surface of ethical generalizations.

I think Nozick, in his (in)famous Wilt Chamberlain argument acknowleged that the intuition toward redistribution of wealth to help those in need is one of our strongest moral impulses. That seems to me fundamentally correct, and I've yet to see a good argument against the intuition.

Let's run a little Turing Test on this interpersonal comparisons of utility argument. Suppose you are distributing water on a hot day to thirsty kids. They wear a sign around their neck that can be faced a certain way to indicate that they want water, and another to indicate that they don't. Suppose you give Kid A (rather than "Ok Computer" or "Hail to the Thief") the first bottle of water (which, we'll assume, is relatively scarce.) Kid A keeps his sign turned toward wanting water, because it's a damn hot day. Can we not conclude that it's very likely that other Kids are more in need (or "want" if you prefer) than Kid A? I think it's safe to say that we can. Giving Kid A water because he still wants it as the other kids pass out around him seems ridiculous. so, there is an interpersonal comparison of diminishing marginal utility. Mouthful.

I wasn't trying to prove

I wasn't trying to prove that the marginal utility of a dollar to a rich person is not less than the marginal utility to a poor person (I'll discuss that more in a moment) -- I was only showing that an argument purporting to prove otherwise doesn't hold up.

But first let's take a look at your example with the water bottles. Anyone who has spent time on athletic teams, both with coaches who allow very liberal consumption of water and coaches who give water breaks only sparingly, knows that thirst varies enormously from person to person. It is extremely easy to imagine one kid who is still more thirsty after having one bottle of water than another kid who hasn't had any (assuming for the sake of the argument that thirst is a good proxy for utility of water).

But on average, yes, it's reasonable to assume that the marginal utility of a bottle of water is greater to those kids who haven't had any than to those who have already had a bottle *on average*. But only on average.

But here's the major flaw in your example -- it assumes that the utility of water and amount of water consumed by an individual is independent. Consider this alternate scenario:

Imagine you ask who is thirsty, and some number of kids raise their hands. You give water to those kids, but not to the others. Then, a little later, you again ask who is thirsty. It would not be surprising to find a large overlap between the hands raised the first and second time. In other words, the kids who had already consumed water were more likely to be thirsty again than those who hadn't, showing that water still has a higher utility for them.

In fact, the only way this would not be the case is if there were absolutely no connection between an individual's propensity to be thirsty (and thus the utility of water to that individual) and that individual's efforts to obtain water.

The result is similar if we turn to money. We would fully expect that an individual for whom money has a higher marginal utility would be more likely to attempt to earn, save, invest, and otherwise take actions that would cause him to have more money. In other words, one of the factors that influences whether a person becomes wealthy is the marginal utility of money to that person.

So just assuming that money must have a lower marginal utility for someone who is richer is a very questionable assumption.

-Mike

Matt, I haven't read Nozick

Matt,

I haven't read Nozick in a while. How does his Wilt Chamberlain example demonstrate that redistribution of wealth is a strong intuition? Isn't the whole point of the example to show why redistribution does not coincide with our intuitions?

Michael,

Once you accept that interpersonal comparisons are valid on average, even though they may not be valid in specific cases, you are in agreement with neoclassical economists on the issue.

I find Jonathan's argument

I find Jonathan's argument that Bill Gates might value his marginal $1000 as much as a pauper rather unconvincing. Suppose there is someone out there for whom that $1000 makes the difference between life and death. In order for the argument to be correct, for every single grand that Bill Gates earns, he must experience an increased happiness equal to the difference between life and death for that individual. Bill does have a goofy smile sometimes, but if this were true he'd be incandescent with joy, beaming like a million blissed-out ravers. I simply don't believe that such a range of human happiness exists, not only due to my personal experience but also the neurochemical factors related to happiness.

I totally agree that one reason that some people have more money is that they value it more and choose to work for it. But in such extreme comparisons, using this to rule out comparisons seems ludicrous. For example, Bill Gates does not have the most money because he values money more than anyone else in the country and has worked the hardest for it. I still believe this if you only consider those of equal talent. The simple truth is that there are many very talented, driven individuals, and they still earn vastly different amounts of money due to pure luck. Thus there is plenty of noise along with the money-preference signal, which weakens the strength of this effect.

As for Jason's case, rather than believing that someone who fights to earn dollar 1,000,001 as much as dollar 1,001 values them the same, it seems more reasonable to me to say that he values fighting for every dollar. So its not that he values $10M as much as $5M, if he worked his hardest and got $10M, he might be just as happy as if he worked his hardest and got $5M.

I've known plenty of rich people who haggled over and worked for every dollar. I still think they get more value from the dollars that pay for their food than for those they use to buy knick-knacks on eBay. Nor do they seem twice as happy if they work their hardest and earn $2M than if they work their hardest and earn $1M.

I agree there are serious problems with interpersonal utility comparisons, I just think that when you make the cases really extreme, such comparisons become valid.

Don't let any of this imply that I believe in redistribution, despite being a consequentalist. The benefits are very short-term and ignore incentive effects, long-term effects, and some nasty slippery slopes. I think that a libertarian society would result in such a mammothly bigger pie that even the paupers will get much bigger slices. But I do think there are immediate, short-term benefits in total societal utility to transferring wealth from the richest to the poorest.

Mike- that's an interesting

Mike-
that's an interesting point you raise. With the exception of one basic point, it actually seems to support an argument made by a guy named Abba Lerner. The exceptional point is simply that the "opportunity cost" (using this term seems odd here, but anyway) for attaining wealth is not equal for all people, so poor person A may value money more than rich person B, but it "costs" him more to get and so doesn't. There's also the question of extravagent wealth, which is much more relevant to questions of distribution as far as I'm concerned, which seem to be produced by a combination of desire and incredible luck. Anyway though, Lerner says that interpersonal comparisons of utility exist, but there's no good way of figuring out what they are. So he says to suppose that they are randomly distributed throughout society, and thus an equal distribution of wealth is rockin'.

How does his Wilt Chamberlain example demonstrate that redistribution of wealth is a strong intuition? Isn?t the whole point of the example to show why redistribution does not coincide with our intuitions?
absolutely Micha. I wasn't saying that the example demonstrated it, rather that in Nozick's discussion of the argument he acknowledges the fact of intuition (then proceeds to argue against it.)

Patri,
I tend to agree with you. I think the Rich person's drive for a dollar has more to do with competiveness than with the actual value of the dollar (as per your 1 mil vs. 2 mil example.)
-Matt

It is my understanding that

It is my understanding that the philosophical problems with utilitarianism are well known, at least in philosophy. The measurement problem (and happiness is not neurochemical), even if it could be overcome, still does not make possible any decision method, and ultimately the inability to predict invention and discovery is not going away either. Furthermore, utilitarianism in itself does not provide any reason to accept utilitarianism.

Then there are the problems raised by the question of whether everyone ought to adopt a utilitarian ethic. On the one hand, if the utilitarian ethic were right, then surely everyone ought to adopt it; but on the other hand, if everyone does and thereby makes it his end to, say, optimize total utility, a conundrum results in which no one can know what he really wants: an individual would have to check with everyone else first, but everyone else has to check with the first individual, who can't know what to want until he knows what everyone else wants, but no one else can know what to want without knowing what the first individual wants.

Still, utilitarian theories are fun to construct and criticize, and philosophers like that sort of thing. Usually, a bit of hand-waving occurs as to how everyone knows this is all impossible, but then they all assume some sort of argument from desire to the effect that, since we want to do some ethical theorizing here, let's assume it works. (Of course there are some people who insist on exclusively employing utilitarian arguments in practical ethics. It is not clear whether they are philosophically ignorant or intellectually dishonest in that they ignore the philosophical implications and assumptions of their views.)

Redistribution requires a real political process to occur, and the devil is in the details. The devil has much to work with in those details. Nozick was arguing that freedom and equality are inevitably in conflict. However, his argument makes many assumptions, for example that Wilt Chamberlain doesn't decide to work for free or give of his plenty to charity.

i just would like to know

i just would like to know what is bill gates religion i have been looking and can't find anything. why i want to know you may ask well is a class related. thanks Margarita