Bill Gates is walking through the desert carrying a bottle of water. He passes a man who is half dead of thirst. Should he offer the man a drink? Should the law require him to?
We’ve been talking about economic efficiency and why it’s a good thing to care about. Today I want to look at this hardest of cases through the efficiency lens.
Let’s suppose Bill’s water is worth, say, $10,000 to him. He’d be willing to pay that much for it, and he wouldn’t cheerfully sell it for less. Why such a high number? It’s not because Bill enjoys his water any more than you or I do — it’s just because Bill happens to be filthy rich.
And the dying fellow? He’s willing to pay up to $100 for that water. He’d pay more if he had it, but $100 happens to be all he has in the world.
Should the law require Bill to give up his water? And regardless of the law, what’s his moral obligation?
A few observations:
First, there are multiple versions of the efficiency criterion, and they usually all give the same answer — but not always. So we have to specify which version of the efficiency criterion we’re talking about. I’ll stick with the simple version that says $10,000 beats $100, so Bill gets to keep the water.
But that’s not the end of the story. Suppose our dying man (call him “Fred”), who slept through his economics class and never learned about the efficiency criterion, manages forcibly to snatch the bottle out of Bill’s hand. Now that he’s got the bottle, he wouldn’t sell it for anything less than $50,000. Now $50,000 beats $10,000 so Fred gets to keep the water.
So according to the efficiency criterion, the water is rightfully Bill’s — unless Fred manages to steal it, at which point it becomes rightfully Fred’s. Unless of course Bill manages to steal it back again, in which case it’s rightfully Bill’s. Here the efficiency criterion flirts with incoherence, and we have good cause to mistrust it.
Second, where’s the incoherence coming from? Answer: it comes entirely from the difference between Fred’s Willingness to Pay, which is constrained by his bank balance, and in this case is only $100, and his Willingness to Accept, which is $50,000. In informal accounts of the efficiency criterion, we (or at least I) sometimes talk about “what the water is worth to Bill” versus “what the water is worth to Fred”. But “what the water is worth to Fred” is an ambiguous phrase. Does it mean Willingness to Pay or does it mean Willingness to Accept? In this example, the answer matters. A lot.
Third: We rarely have to worry about such discrepancies. That’s because Willingness to Pay and Willingness to Accept are in most cases nearly equal. They are nearly equal whenever the stakes are small compared to people’s incomes — which is most of the time. (In our example, the stakes are high relative to Fred’s income, which is why the two Willingnesses can differ so drastically.)
Why do I say that Willingness to Pay and Willingness to Accept are in most cases nearly equal? Because I know how to prove it. I prove it every year to my “Topics in Microeconomics” students, using about two hours of classroom time.
I can’t give that proof in a blog post, but take my word for it — when the stakes are small compared to your income, your WTP and WTA will be nearly equal. And most of the things you care about, most of the time, represent pretty small fractions of your income. So most of the time, the efficiency criterion is a whole lot more coherent than in the case of Bill and Fred.
Fourth, economists are therefore most comfortable using the efficiency criterion when the stakes are small. We recognize that the criterion becomes a lot harder to swallow when the stakes are large, and we have a good theory of why that’s so.
Fifth, in matters of economic policy, the stakes are usually small, even when they involve human lives. For example: Should we spend $10,000,000 to build a guard rail that we are (somehow) certain will save exactly one life? If there are a million people affected, and you are the average person among them, then your share of the cost is $10, and your share of the benefit is a one-in-a-million chance that your life will be saved. That one-in-a-million chance is a small thing, so your Willingness to Pay and your Willingness to Accept are nearly equal. If that common value is $5, you’ll consider the guard rail an extravagance; if it’s $15, you’ll consider it a wise investment. Here the efficiency criterion can be an excellent guide to giving the people what they want.
Sixth, it’s important to distinguish between policy recommendations and moral stances. The efficiency criterion is a guide to policy. In The Big Questions, I introduced the Economist’s Golden Rule, which is a guide to personal morality, using the same calculations that go into the efficiency criterion. Like the efficiency criterion, the EGR flirts with incoherence when the stakes are large but not when they’re small.
Seventh, I have one more thing to say about this example but I think it’s worth saving for a separate blog post, later in the week.
I’m not sure how the efficiency criterion is supposed to assist in answering the question of whether the law should require Bill to give up his water. If Fred’s willingness to pay and Bill’s willingness to accept did overlap, they would not be required by law to complete the transaction—they just would because of rational self-interest, law or no law—right? Rational self-interest hardly needs to be enforced by law. Any law that would require Bill to give up his water would, by virtue of the fact that someone decided it was necessary, contradict efficiency, because if it was efficient for Bill to give up his water, he happily would.
Right? Or am I missing something?
Can you point us to the proof that you mentioned?
I agree with Colin.
Also, efficiency can only be gauged in the context of a functional marketplace. It doesn’t make sense otherwise. Put it another way, imagine Fred manages to kill Bill, steal his identity, and then double Bill’s former net worth. The efficiency criterion says that this works out best for everyone.
But the main problem here is that it obliterates the system in which it is defined to operate. You can consider it a fancy version of the Liar’s Paradox. No really – The sentences, “All liars are truth-tellers” and “Markets absent of private property can be efficient” are entirely equivalent to me. Unless, of course, you’re prepared to say that “efficiency” in a command economy is in any way comparable to efficiency in a market economy… I guess it depends on how far you’re willing to go, but at the bare minimum I would argue that “efficiency” means two different things in command vs. market economies. (Cf. the Socialist Calculation Debates)
Colin:
I’m not sure how the efficiency criterion is supposed to assist in answering the question of whether the law should require Bill to give up his water.
I’m not sure it does. It might, however, assist us in answering the question of whether to put up a guard rail, which is a case where it’s difficult to conduct market transactions on the spot.
Thanks, this is a crucial distinction. It seems very reasonable that WTP and WTA are almost the same for small things. We should be very cautious of efficiency arguments when the stakes are high for at least one group that is sharing the expense. This could be an individual (Fred), or a group (Bangladeshis or Maldives Islanders regarding rising sea levels).
I would like to explore the guard-rail thing a bit, to see where it takes us. Lets say we had a canyon with side A and side B. We could put it on side A of the canyon, where it will save exactly 1 life from population A, or on side B, where it will save one B resident. Or we could build both.
“A” side canyoners are richer than B siders, and we know (from their insurance and similar) that they are willing to pay $15 for a 1 in a million reduction in risk. “B” siders are poorer and would only pay $5. Efficiency arguments suggest that we build the rail on side A, but not side B. This makes perfect sense, because we can then use the $10,000,000 saved on the “B” side and spend it to obtain greater benefit, i.e. spend it on things B siders would prefer. A siders would rather have the rail than, say, a new bus terminus. B siders the opposite. If this is done comprehensively everyone is better off.
Politically, you can see why things do not go quite so smoothly. When the B sider drops off the cliff, he suddenly becomes “Little Johnny” (for it is he). The calculation is then put in terms of the “willingness to accept” by little Johnny and his family, rather than the more correct “willingness to pay” by the population as a whole. This is why named lives are valued higher than statistical lives, so suddenly the efficiency argument becomes incoherent. The re-election chances of the Mayor of B town do not look good, despite the brand new bus station.
Perhaps the politically most difficult is ensuring that the $10,000,000 actually gets spent in B town on the new bus station. Say B town residents would each pay $11 for a new bus station costing $10,000,000. They get better value than building the handrail, so build the bus station. But what if A towners would pay $12 for a new opera house (costing the same)? Efficiency arguments suggest we build both, so there is no problem with the theory. If there were constraints on expenditure or building supplies, then the opera house should be built rather than the bus station as it provides higher returns. Here is where politics comes into it. In the real world, it is possible that B town gets neither the guard rail or the bus station.
There is also the separation of A and B town. If we treat them as one population, we get a balanced efficiency argument, the cost of the reduction in risk of 2 handrails is the same as the benefits overall.
Ryan:
Put it another way, imagine Fred manages to kill Bill, steal his identity, and then double Bill’s former net worth. The efficiency criterion says that this works out best for everyone.
Of course the efficiency criterion says no such thing, and for several reasons. First, it would be *false*. What you’ve described obviously does not work out best for Bill. Second, the efficiency criterion would not in fact recommend this outcome. Third, even if it *did* recommend this outcome, it would not follow that it labels the outcome “best for everyone”; it never labels any outcome “best for everyone”. All it does is choose among outcomes.
Harold:
Efficiency arguments suggest that we build the rail on side A, but not side B. This makes perfect sense, because we can then use the $10,000,000 saved on the “B” side and spend it to obtain greater benefit, i.e. spend it on things B siders would prefer. A siders would rather have the rail than, say, a new bus terminus. B siders the opposite. If this is done comprehensively everyone is better off.
This is particularly well put.
Politically, you can see why things do not go quite so smoothly. When the B sider drops off the cliff, he suddenly becomes “Little Johnny” (for it is he). The calculation is then put in terms of the “willingness to accept” by little Johnny and his family, rather than the more correct “willingness to pay” by the population as a whole.
Yes, this is very much a problem, and (perhaps paradoxically) it suggests that everyone would prefer to live in a world where we could commit in advance to abandoning Little Johnny (before we know who he is).
Isn’t Fred’s WTP at that point approaching something like $50,000 in this case? Saying he only has $100 assumes that his current bank balance is all that he has of value to offer Bill.
I would think if he is on the verge of dying, a lifetime of servitude in the Gates household, even under extremely harsh conditions, would be something he would be willing to offer.
He would probably be willing to offer to sabotage the next iPod launch as well.
His WTA $50,000 I assume means he is willing to die for that amount of money, presumably to bequeath to his heirs (otherwise what good does the money do to him?).
So isn’t $50,000 his and his family’s indifference point between his life as a slave/sabotaguer and his death?
Steve – you say you can prove that Willingness to Pay and Willingness to Accept are roughly similar when the amounts concerned are not large compared to individual incomes – but isn’t there an awful lot of stuff in the behavioural economics literature which says that there is a fairly substantial WTP/WTA gap even for things like mugs and lottery tickets? In fact, isn’t that pretty much what Prospect Theory was invented to explain?
John Faben: Yes, the proof assumes stable preferences, which is an assumption that Prospect Theory disputes. I am inclined to believe that the stable-preference assumption is a good one for issues that actually matter (as opposed to issues like choosing a flavor of jam) but one might reasonably argue otherwise.
Of course, if preferences are *not* stable, then it becomes almost impossible to say what counts as an improvement. (If you sometimes prefer A to B and other times prefer B to A, is it better to give you A or B?). So without stable preferences, it’s not just the efficiency criterion that goes out the window, it’s almost all of normative economics.
As to morality, yes, Bill should give up his water (according to the amnesiac criterion.)
As to the law, let us hope that this example is sufficiently rare that there is no need for Congress to write such a law. The bill would be a thousand pages long, require watering stations in every desert state, and involve an army of lawyers in interpreting it.
If I remember correctly, the proof you’re referring to is the class on Equivalent Variation and Compensating Variation, is it not? I still remember the intution and could quickly sketch out the utility function/budget line moves, but I never did learn to remember which was EV and which was CV.
My best guess is that CV is the amount by which I would need to pay you to exactly compensate you for an increase in the price of some good (hold the indifference curve constant, rotate the budget line in, shift the new steeper line up until it hits the indifference curve, and the vertical shift = CV).
Then EV is the amount which you would pay to avoid a price increase of that good, leaving you exactly as poorly off as if the price had been increased. (Draw the indifference curve tangent to the ‘new price’ budget line, then shift the original budget line down until it is tangent to the new indifference curve, and the vertical shift = EV).
After drawing both of them on the same utility plot, you can then demonstrate that it must be an inferior good and/or there must be significant income effects in order for EV and CV to significantly deviate.
The problem I’m having now is relating the EV/CV lecture to the Bill/Fred problem. I think the connection is that once Fred has the water, Bill would need to pay him a lot to get him to release it (high WTA/high CV), but he would not be willing to pay very much to keep it (low WTP/low EV). It’s possible I have this exactly backwards, but some combination of what I wrote and a mirror-image of it should make perfect sense. I believe the example you gave in class was on the difference between how much someone would pay me not to club a baby seal vs. how much I would need to pay them in order for them to allow me to club it.
“So without stable preferences, it’s not just the efficiency criterion that goes out the window, it’s almost all of normative economics.”
How about not stable, but varying in some predictable way? Our preference for healthcare over jelly beans is likely to increase as we get older.
I have a feeling that cosiderations such as these effectively increase the “error bar”, or decreases the confidence, on economic conclusions. Policy A may appear more efficient, but if all the uncertainties on the assumptions were included, it would be very helpful in assesing how much confidence we should have in the conclusion. I presume this sort of estimate has been attempted?
Steve –
Okay, I take your point, very fair. But, I think you may have side-stepped the market definition issue I was really driving at. If we allow Fred to steal Bill’s water, then we can just as easily allow Bill to steal it back. This can go on for several iterations until either Bill or Fred figures out that the only way to keep the water is to defend it with their lives. (Here I’m assuming that if one of them drinks the water immediately after it’s stolen, then the other person dies.)
Obviously, this is state-of-nature stuff. There’s no market involved here. What I’m really arguing is that as soon as we allow a disregard for private propoerty to enter into the equation, then the market ceases to exist, and therefore the efficiency principle no longer offers any useful insight into the situation. Efficiency as economists use the term only really applies to markets. No property = no market, that’s my position, anyway.
To further speak to your point, I’d go so far as to suggest any law passed to redistribute water would necessarily involve a state-mandated disregard for original ownership.
At this point we have to make a choice between Rule of Law and the efficiency principle. I’m choosing the former because I see it as being a necessary condition for the latter.
Neil’s right, but I think he understates the difficulty. If you start holding people liable for failing to prevent some harm, when they “reasonably” ought to have prevented it, you will have created a situation in which everybody in the vicinity of an accident becomes a potential defendant. The legal system already has too many potential defendants. Some years ago, one of those fire-in-a-dance-hall cases had several thousand defendants. Not just the morons who let in too many people and locked the emergency exists, but the people who made each item of furniture, the people who made or sold the paint used on that furniture, and so on. Add liability for failure to prevent harm, and you’ve multiplied the number of defendants enormously. Somebody steps into the road and gets hit by a car, and you can sue anybody on the sidewalk, who might have noticed (or “ought to have noticed, but didn’t”) the victim stepping off and stopped him. And then a group of people whom you wouldn’t dream of asking for advice about any important matter gets to sort all this out. You might as well pass a law that says “the wealthiest person within 1000 yards of an injury has to pay.” That probably wouldn’t pass anybody’s efficiency test.
The difficulty here is that you can’t make a rule for the Bill Gates in the desert case that doesn’t mess up thousands of other cases. Even if (some version of) efficiency is the right goal to look for, it wouldn’t make sense to ask what would be efficient for this particular case if you can’t make a rule for just that particular case.
In France it is a legal requirement to help somone who is injured. I do not know if dying of thirst counts as injured.
I punted on the legal issue and addressed only the easier moral issue in this example. But I’ll come clean–I would oppose any law that would require me (or you), as an individual, to come to someone’s aid. Not giving my bottle of water to a man dying of thirst may make me the world’s biggest jerk, but in a free society I have the right to be a jerk.
Paradoxical as it sounds, that does not mean that I would necessarily oppose a tax financed program that helps people in dire circumstances get access to goods and services they desperately need (translation of “desperately need”–they would pay a lot to get it if only they had the ability to pay) but cannot afford, for example emergency health care. Moreover, I would prefer an “in kind” program in such circumstances rather than a supposedly more efficient cash program, because if they truly desperately need this good they would spend all of any additional cash on it anyway.
You say, “…Bill’s water is worth, say, $10,000 to him… Why such a high number? It’s not because Bill enjoys his water any more than you or I do — it’s just because Bill happens to be filthy rich.”
And you are right but I think you are presenting it in the wrong terms.
A things worth is the monetary value attached by a person or organization to a thing or service. As you pointed out, the bottle of water has the same intrinsic value to Bill as it does to the dying man. But it is worth more, as you say, because Bill is filthy rich.
The implication is there but you left it unsaid. The bottle of water is worth MORE to Bill because dollar bills are worth LESS. They are worth less because he has so many of them. I bring this up because this is a great example of what can happen when wealth and capital are consolidated into a small number of holders. Some of them become philanthropists like Gates, but most do not.
For those that do not, to get any value out of their increasingly worthless bank accounts they have to invest it in increasingly risky ventures like credit-default swaps against sub-prime interest loans. And to find a place to put that investment, incentives for bad behavior (like taking out a home loan when you don’t have a job) are put in. It wouldn’t bother Bill Gates if he invested $30 billion in a Thailand factory and it flopped, that’s pocket change. But the destructive nature of that kind of speculation is devastating.
Switching gears… I think Kant said all there needs to be said on the subject of morality. If Bill would wish that every individual person in his place would keep the water or extort an unreasonable fee for it from a dying man then he should be able to sleep well at night.
I’m not sure it does.
So, why are we talking about Fred and Bill then? Are you trying to demonstrate that the efficiency criterion can fly in the face of moral intuition? I think it does that spectacularly.
Although, I don’t think that we are taking Bill’s tastes fully under consideration either. Sure, he values his water at $10,000, but if that is the case, I (and I think society) believe that he should value people not dying in front of him at at least $10,000.01. My willingness to pay in order to not have people die in front of me on the street is certainly higher than my willingness to accept for a bottle of water, and I think most people would be the same. In essence, what I’m doing if I’m giving Fred water is reallocating my water from its previous task of providing me with personal-enjoyment into a new task of stranger-death-prevention – a place where, according to my personal tastes (and the stranger’s), it is more efficient. In fact, I believe that that is the basis for a law requiring Bill to give up his water: society’s willingness to pay in order to prevent people from dying of thirst on the street in the presence of water bottles is at least as high as the enforcement costs of the law.
Colin: I feel quite sure that Bill would actually give Fred some water, so in some way this must be more efficient, by definition. You explain how this can be. However, I think the point is that efficiency arguments become less useful the difference between WTA and WTP increase. We can introduce stranger death prevention terms into the calculation, but it becomes hard to put values on them. If we extend this to the canyon example, we should include how much city A people are prepared to pay to reduce the risk of residents from city B falling off a cliff. They are prepared to pay $15 to reduce their own risk, they would surely pay something to reduce a stranger’s risk. However, I am not sure how to measure it.
Harold – I myself am getting stuck on the concept of “Willingness to Accept.” Isn’t everyone’s WTA always an arbitrarily high number? Aren’t we all more willing to accept $2 for something that we are also willing to accept $1 for?
I guess the idea is not WTA, but MINIMUM WTA. Here again, in this example, I am struck by the fact that a dying man would accept any quantity of money for a life-saving drink of water in the middle of the desert. (Good luck spending $50,000 dollars in the desert, while dead.) That Fred would be willing to engage in any such trade thwarts every notion of common sense we have. This is doubly true if Bill also needs the water to finish crossing the desert.
There’s a dual problem here with respect to WTP. This, too, is an arbitrarily big number. The amount we’re all REALLY willing to pay to save our own lives is not $100 or $10,000 but rather “everything.” Just because Fred only happens to have $100 doesn’t mean the water is only of $100 value to him. It just means he can’t afford the asking price, no matter what valuation he places on the water.
So I think these concepts are obscuring the true nature of the problem. Poor people don’t value everything less just because they’re poor and have lower WTPs. WTP is a function of money income. Value is a function of personal taste.
I value my car for the $20,000 it’s worth, even though I bought it on financing and only pay a monthly partial payment. First I have to generate money income before I can apply that income to what I value. I hope we can all see that WTP /= Value. As Benkyou Burito noted above, $10,000 for a bottle of water is more a function of Bill’s relatively worthless dollars than it is a function of his preference for water (I’ll stop short of endorsing the rest of his comments, though).
I was teaching Intermediate Micro when Prospect Theory began to emerge. This made for some pretty interesting discussions re the meaning of the indifference curve, etc. The experimental and behavioral economics literature that attributes WTA>WTP to an “endowment effect” also spawns some lively in-class exchanges.
“…it comes entirely from the difference between Fred’s Willingness to Pay, which is constrained by his bank balance, and in this case is only $100, and his Willingness to Accept, which is $50,000”
It seems like the only thing constrained by Fred’s bank balance is his ability to pay, not his willingness to pay. It would be plausible to me that Fred would be willing to pay $50,000 in this scenario, which would mean his WTP and WTA are equal.
His ability to pay is constrained by his bank balance and Bill’s willingness to extend credit.
Efficiency implies nothing whatsoever about what laws to impose or whether or not guardrails should be constructed. If people value the dying guy getting the water more than Bill Gates, they’ll pass a law saying Bill should give up the water, and that will be efficient. If they don’t, they won’t pass such a law, and that will be efficient, too. Same goes for the guardrail.
Moral preferences are included in utility functions. Asking whether or not the efficiency criterion is morally relevant is as nonsensical as asking whether or not we should value values.
Perhaps you can post some additional information on why you are “inclined to believe that the stable-preference assumption is a good one for issues that actually matter (as opposed to issues like choosing a flavor of jam.)”
Prospect theory and loss aversion aren’t exactly new or controversial topics, and the field of marketing is all about driving imperfectly rational human behavior.
The comment, “it’s not just the efficiency criterion that goes out the window, it’s almost all of normative economics” seems like saying that Einstein sent all of Newtonian physics out the window.
Ryan: I think the important thing is to ask the right question. In the Bill and Fred case, the efficiency argument becomes nonesensical, because of the difference between WTP and WTA. If we assume they are both about the same, then we can talk efficiency. Take the canyon example. We are not asking “Is a life from A town worth more than a life from B town?”, although it might look like that. I think the question is “A guard rail will cost $10,000,000, should we build it, or use the resources for something else?”
From the analysis, the answer for A town is “Yes”, probably because they have all the basic necessities already. For “B” town, the answer is “No”, because they lack some of the basic necessities. B towners would prefer the money to be spent on other things before building a guard-rail. If we were to take an extreme example, and say B towners had no food, then we would be very foolish to build a guard-rail whilst the population starved.
I have reservations about this for 2 reasons. I have a feeling that in the real world, what tends to happen is that A town gets its guard-rail and B town gets nothing. This is due to incomplete application of the theory above. I think that in an economist’s ideal world every project that was efficient would get done. This is possible because the “willingness to pay” is limited by the “ability to pay”, as in the Fred case. In the real world, we tend to start from “We have so much money, what shall we spend it on?” If A and B town had $20 million to spend between them, then the two projects that would provide greatest “gains” in $ terms would be A town guard-rail and A town opera house. This occurs because it uses efficiency arguments to answer the wrong question. The minute we start comparing different projects to see which provides the greatest gain, then we are putting a value on the $ of different people. As Benkyou Burito pointed out, $’s can be of very different value to different people.
I also think it very difficult to assign the value on reducing risk. Society and individuals seems willing to pay very different amounts in different circumstances for the same risk reduction. Smokers assign a low cost, but if there is a train crash, then billions are spent for very little risk reduction. People sometimes act in contradictory ways, such as avoiding freeways because they have heard about multiple pile-ups, thus using more dangerous minor roads. This suggests unstable preferences, and as Steve said, “without stable preferences, it’s not just the efficiency criterion that goes out the window, it’s almost all of normative economics”
Just a correction to above: I said things go wrong when we compare different projects to see which gets done. I think that should be when we compare different populations.
Harold, good points all around.
I have to ask this question, even if it’s mildly annoying! :) What is a collective preference for a guardrail?
Surely there are citizens of Town A that cannot afford their share of the guardrail and would prefer that money be applied elsewhere. Surely there are citizens of Town B that can afford their share of the guardrail and want to see it built. You can’t really “net that out.”
Regardless of preference, the guardrail should not be built unless sufficient funds can be raised voluntarily. When people are compelled to act outside of their preferences, then they experience disutility. Total utility, as Steve’s example points out, is not necessarily democratic, i.e. just because “a majority” of citizens in one town reach a certain resource-allocation conclusion doesn’t mean that the resulting total utility of the town will reflect that conclusion.
I guess I’m getting pretty disjointed here. There is much about this issue that I find objectionable, from assuming WTP = value all the way to assuming majority = unanimity.
But I’m kind of a “crazy Austrian School guy,” so take that for what it’s worth! :p
Ryan- “Regardless of preference, the guardrail should not be built unless sufficient funds can be raised voluntarily. ”
Landsburg had a good traffic or streetlight example refuting this in either More Sex is Safer Sex or TBQ, I can’t remember which. I think your sentence would be correct if you added the caveat that there was no free-rider problem.
Your larger point regarding the difficutly estimating, explaining, understanding, or coherently referring to collective preferences is well taken.
What happens to the value of a $1.00 when you have bought everything you could ever need or want and everything you will likely ever need or want?
At Bill Gates’ garage sale how much would he have to expect to get for that old George Foreman Grill to make it worth his time to drag the card tables up from the basement?
In this case the bottle of water is the currency, it buys sated thirst. Cash, in this case, is behaving more like labor or occupation; what you give up in order to get the currency so you may buy the final product (sated thirst). The water is worth the same to Bill as to anyone in the same position and actually worth more to the dieing man since on the verge of death the same amount of water will buy him the continuation of life where as it only buys bill the same in the probable event that he continues in the desert.
Having amassed so much of it, the actual dollar bills become worth less and less to him because they can no longer be exchanged for the things he needs or wants (because he already has them).
Douglas – Unfortunately I’ve only read “The Big Questions” (so far!). One recurring aspect of that book, however, that I still can’t sign onto is Landsburg’s preference for ethics based on majority outcome. For example, the trolley problem, and Landsburg’s conclusion that it’s better to kill one person to save five (his view) than it is to kill zero people and save zero people (mine). I think he would object to my “deontological” tendencies, which is fair enough.
However, I do believe these basic premises have a great impact on economic models in general. In the modelling process, economists have a tendency to withhold certain considerations and/or add others depending on their own normative values and epistemology. So it may be that Landsburg is correct about his model, but that another could be drawn that I would be correct about. At that point, it’s not a discussion about who’s right, it’s a question of whose model do we “buy-into.” And that, in turn, speaks to our normative values and epistemology (of course).
To cut a long story short, I think you can essentially prove both decisions with economic models, but that it still comes down to an ethical choice about the kind of system you want to live in, and that choice determines which model you prefer. I.e. it looks like economics, but it’s really just ethics.
The different outcomes in the case where Bill or Fred have the water initially can I think also be thought of as wealth distributions being different can they not? The Coase theorem assumes effects from different distributions of wealth that drive the different outcomes here.