On intuitive conceptions of interpersonal utility comparison derivable from introspection and social observations… We certainly ‘can do’ the above qua our faculties as Human beings. But this does not mean we can do so with scientific precision, or with praxeological certainty. When we do the above we engage in psychology and thymology; we are not thinking qua ‘economists’
In short, if one is suitably humble in ones claims and does not confuse the claims with claims vis economics then one can reasonably say things about interpersonal utility. I hope this isn’t too dissapointing for neo-classicals who would want to quantify it and make it a bedrock of economics…
By the way, I want to thank David for having written Machinery of Freedom, one of my favourite works of non-fiction. I have recommended it many times and hope to recommend it many more !
Note that this approach to declining marginal utility assumes that utility is additive–the utility of end 1 plus the utility of end 2 plus … . That isn’t in general true–the utility of achieving 1 and 2 might be more or less than the sum of the utility of each one individually, as in my example of the fourth tire.
Let me see if I can state the ordinal version of declining marginal utility to see what its limitations are:
I value having six sacks of wheat instead of five less than I value five instead of four.
What choice I could make would demonstrate that? In a world with uncertainty, it could be put in terms of gambles–but that leads us to Von Neuman and cardinal utility. People defending the ordinal version here don’t want to include choices among lotteries in their argument. But in choosing among certainties, I don’t get to choose between 6 instead of 5 and 5 instead of 4. I might choose which to have for two different time periods–but there is no guarantee that my utility function hasn’t changed from one year to the another.
How about comparing both to a third? I would be willing to give up an hour of my leisure in order to have 5 instead of 4, but not in order to have 6 instead of 5.
But that assumes that utilities are independent–that the value to me of my leisure doesn’t depend on how many sacks of wheat I have.
Would anyone here like to propose a clearer way of establishing declining marginal utility (of anything) by observing choices, assuming that all choices are among certain outcomes and that utility is ordinal, not cardinal?
I value having six sacks of wheat instead of five less than I value five instead of four.
The question is why you value sacks of wheat at all. They are economic good to you because they are means to achieving your ends. If you can accept that you can have various ends, and that the ends are rank ordered, and that the homogenous goods are allocated over them, then you see that economic allocation is such as that the 6th sack is achieving an end which was not so important as the 4th sack.
I understand that this form of analysis is less mathematically tractable given that it is not cardinal. This means various neo-classical tools in the toolset can’t be applied… This means its hard to say the expected $impact of this policy proposal is $x.
This is too bad, but unavoidable if we are to remain solidly within the realms of economics and economics only.
Indeed. The schedule of wants itself is logically dependent on the order in which wants are satisfied - that is, it is re-ordered as wants are struck from the list. I believe Rothbard provides illustrations of this, though I cannot recall where. At the risk of being overly pedagogical, I’ll make my own illustration:
Here are my present wants:
Apple
Orange
Hot-dog (wiener)
Let’s say I receive an Orange. Now, my schedule of wants is:
Hot-dog (wiener)
Apple
Of course, as has already been noted, my schedule of wants can also change with nothing more than the passage of time. Assigning a cardinal value to each want is of little use because its magnitude is a function of all my other wants and their magnitudes.
“I’m kinda playing Devil’s advocate here, but couldn’t you say that the ratios between the numbers of sacks allocated to the different ends shows how much more the pioneer farmer values one end over another?”
No.
One sack might be entirely sufficient to achieve a very imporant end (feeding his family), five required to achieve some much less important end (feeding his chickens).
“But this does not mean we can do so with scientific precision, or with praxeological certainty.”
I don’t think non-Austrian neo-classical economists believe in praxeological certainty, at least if I understand the concept. I cannot think of any prediction about human behavior that is observable that one can deduce a priori. I note that in the particular case of declining marginal utility, people here had to redefine the terms–one tire isn’t a unit, even though you can buy it–in order to make behavior consistent with the theory, which meant that they were making a circular argument.
Try to find some pattern of human action that could not exist, assuming that we don’t know in advance what humans value, hence are free to make assumptions about utility functions designed to explain the behavior.
Where the duce did you purchase that book, may I ask? Last time I checked it was horribly expensive on Amazon, and I can’t find it at any local bookstore.
I have various ends, but there is no reason to assume that they are discrete rather than continuous, and no reason to assume that the production function from inputs to achieving ends consists of using one input to achieve one end, and another to achieve another … . Nor is there any reason to assume that the value to you of achieving one end is independent of what other ends you have achieved.
I think that once one takes seriously both how complicated a utility function and how complicated a production function can be, you will discover that if you limit yourself to a priori argument you can’t do much, if any, economics.
But I think Austrians agree that the utility function is arbitrarily complicated and that’s precisely the problem - calling something a “function” implies that it can be, at least in principle, formalized. The formalisms that are frequently used - such as log(x) - are precisely the opposite of complicated and, therefore, do not describe actual human behavior. Conclusions drawn on the basis of such simplified utility functions must be qualified on the basis of this simplification… they are true only to the extent that actual human behavior (which we have already agreed can be very complicated) happens to conform to log(x) or whatever function was chosen.
They didn’t redefine the terms and it’s not a circular argument. It is just that units of a good must be equally servicable or they cannot be considered as units of the same good. Someone pointed this out to you on Bob Murphy’s blog. I don’t see a reply from you there.
It can’t be “of equal utility,” since that would make marginal utility constant rather than declining. It can’t be “serve the same ends,” since the point of the argument for marginal utility is that the sixth unit is normally used to serve a less important end than the fifth.
All the tires are identical, hence equally serviceable in the ordinary language sense. What does the claim that the proper unit is four tires mean, beyond “if we let a tire be a unit, marginal utility doesn’t decline.”
Not at all. It means that they can be employed for the same objective uses. Regarding a normal car, the use of the fourth tyre is very different to that of the first three, for example.
Right it is called “Das Räderwerk der Freiheit”. Unfortunately it is not available anymore, I could not even find used ones on Amazon Market Place or even ebay. Those copies are in strong hands.. I guess the translation is not available as pdf since the publisher will have the copy right protection to the translation. Maybe it is time for an e-book version
Wow, von Neumann really has an impressive record. Though it seems (he also worked at the Manhatten project) he was in favor of dropping the nukes and ensured to maximize their destructive power…
Aristippus: “It means that they can be employed for the same objective uses.”
The fourth tire could be put on a car that had two tires, just as the third was. The third could have been put on a car with three tires, if one had been available. What’s different between them isn’t the tire, or the uses the tire can be employed for, it’s the situation of the user–whether he has three tires already on his car or only two.
But that’s precisely the factor that is supposed to justify declining marginal utility. The difference between the sixth sack of wheat and the seventh, also identical, is that the seventh gets used differently than the sixth because he already has six sacks, so no longer needs wheat for its most important uses and uses the seventh for a less important one. Just as the fourth tire gets used differently than the third.
If utility is simply additive in different uses, and what you can use a unit for doesn’t depend on how many units you have, then the usual argument gives you declining marginal utility. Without those assumptions it doesn’t, because having N units may make the N+1 unit more useful rather than less–as in my example.
At a complete tangent, because I’m an admirer of Von Neuman …
Teller, his memoirs, recounts a visit by Von Neumann in which the latter got into a conversation with Teller’s son, I’m guessing ten or so, on the Santa Claus Problem. How can Santa possibly visit every house in the world in one night?
The two came up with a solution. On Christmas, the Easter Bunny has nothing to do. On Easter, Santa has nothing to do. So the two must have a deal, with each helping the other out on his day. Problem solved.
I find the picture of one of the most brilliant thinkers of the 20th century engaged in that sort of intellectual play with a child charming. For someone who wants to watch that mind at work, try the first two chapters of The Theory of Games and Economic Behavior. Accessible, interesting, and the one part of the book wher he is making real progress, actually finding a reasonable definition of a solution and proving that it exists. After that things get much more difficult. I like to say that one reason I don’t work in game theory is that, when looking for problems to work on, problems that stumped Von Neuman go at the bottom of my list.
First of all, I want to say that I’m really enjoying this thread, and I hope other people are too.
Now, there’s a lot thats been said and could be said, but I want to try to stick to what I see as the most interesting and salient points. Feel free to call me out on having skipped on anything of interest to any of you.
David,
If we are talking about the Bohm-Bawerkian exegisis, I am not sure what makes you say that utility is additive. Who is adding utlities and for what purpose, and with what degree of precision. We merely have a scale of ends to satisfy, that happen to be attainable by homogenous means, and hence subject to the law of Diminishing Marginal Utility (of Homogenous goods)
In a later post you write:
I’m not sure what is being referred to here, is there perhaps a link to a debate or an essay at another location? Without knowing what is underlying this response, I can only suggest that one tire may or may not be a unit of consideration, given what we are analysing and given the subjective valuations of the agents we are considering. Think of the farmer with sacks of grains. We made statements about the marginal units (the sacks) that were equally servicable to the ranked ends, we left out discussion of the individiual grains in the sacks…and no one seemed to mind
You are correct that one may have a higher order end, in which lower order ends are subsumed but I don’t think this poses any particular problems. Otherwise, you may be mistakenly attributing a permanence to ends that the theory does not warrant.
I.e. If you are saying that you would value the end of graduating with a certification differently depending on whether you achieved a seperate end , being enrolled into school A over school B. Then this can be split out into more complex rank ordered ends.
1)graduate , school A
2)graduate , school B
3)dont graduate, school A
4) dont graduate, school B
5) dont graduate, dont get accepted into any school.
furthermore the values that the agent associates with the ends are not frozen perminantly. If evidence that School B has better success rate, and has a more pleasant campus life than School A, the valuations and hence the ordering are reshuffled in light of that.
an equally servicable unit of a good means that the unit of good in question is equally fit to fill the role of the means to achieving a given end as is its counterparts.
I.e. where one egg is as good as the other for baking. Where one tire is as good as the other for being fitted to a particular car; whereas tires can come in many shapes and sizes and are hence not equally servicable in cases where their servicability hinges on their shape and size;
The utility is declining with the addition of +1 homogenous units as, given their equivalence to being fitted to tasks, the most urgent tasks have been met, and though we abandon a concept of ‘depth’ of the decline as we do not count difference in utils, we can understand their servicing ends of lower ordinal rankings. lower rankings… diminishing utility (of homogenous goods).
Really it should be called the Theory of Diminishing Marginal Utility of Homogenous Goods. Neither neo-classicals nor Austrians (that I know!) would claim that their is diminishing marginal utility of Heterogenous goods.
When apparent exceptions to the Theory of Diminishing Marginal Utility of Homogenous Goods are offered up, it often pays to consider whether heterogeneity hasn’t been snuck in at the backdoor…
I could be wrong but this seems to be ‘Gesselian’. Gessel tried to explain diminishing marginal utility, by appeal to psychological notions of satiatability.
I.e. you can eat only so much delicious icecream before funtime turns to badtime. But it needs be said that this is not the Misesian conception. The Misesian is broader, it does not rely on psychology and so must apply to economic agents who may differ in psychology…
I guess the tire thing refers to this discussion at Bob Murphy’s blog. I think Bala gave a good explanation, though I need to read the different takes on this in more depth before I can form an educated opinion..
Basically the question was how to define the adequate unit. If you bind it to physical characteristics it is possible that the marginal utility (as I understand this so far, at least the way Austrians deal with it) doesn’t always decline. Assume I prefer to have 4 tires on my car, and after that I would use the 5th to build a swing for my child. Yet if I had only one tire I only can make the swing, but cannot use it for the car, so only when I get the 4th tire I can equip my car. It seems the 4th tire has more utility than the first 3 in this case…
I know how Rothbard deals with it, he basically says the ends define the adequate unit. If a car needs four tires then the unit is a set of 4 tires, and DMU applies only to sets of 4 tires in this case. Yet this begs the question of circularity. I don’t know if David Friedman could be satisfied with Bala’s answer that I linked above.
That they are interchangable from the point of view of the actor, and not that their physical attributes are identical. No reason to assume that this implies that they are of “equal untility” as you do. Basically,…
…the 3rd cow is interchangeable with the 2nd cow,i.e., it is is equally serviceable from the point of view of the actor and can be put to use for the higher value (more urgent) task that the 2nd cow is currently employed in.
Your 4 tire example is flawed because you are not making an analysis between “equally serviceable” goods. You are comparing between oragnes and apples, and not between homogeneous goods. This is not a matter of simply redfining things as I believe you have been implying.
The first 3 tires may only be put to use for, say, 3 differnt wheelbarrows. Each additional tire will be put to use for the next urgent end which must be of a lower utility. However, since the 4th tire suddenly makes the prospect of a car possible, it may be valued higher then all 4 individual tires employed for wheelbarrows simply because a BUNDLE of 4 tires servicing a car may be more valueable to the actor then 4 individual tires only able to service wheelbarrows. The bundle of 4 tires is a differnt good then each individual tire. Only 4 tires can service a car. Not 1 tire or 2 or even 3 tires. The actor is making a comparison between a bundle of 4 tires and 4 tires employed individually. The bundle is not interchangable with the 3rd or 2nd or 1st tire. And the 1st, 2nd, and 3rd tires are not interchanable with the bundle of 4 tires. The comparison is not between homogeneous goods as you suggest.
“one tire isn’t a unit, even though you can buy it–in order to make behavior consistent with the theory, which meant that they were making a circular argument.”
NirgrahamUK:
“I’m not sure what is being referred to here, is there perhaps a link to a debate or an essay at another location?”
My error–I think that was the discussion on Murphy’s blog, and I misremembered it as being part of this discussion.
“an equally servicable unit of a good means that the unit of good in question is equally fit to fill the role of the means to achieving a given end as is its counterparts.”
The fourth tire is identical to the third, so equally fit to fill the role. The difference isn’t in the fitness of the tires, it is in what the consumer already has–which is precisely the difference that drives declining marginal utility. Only in the case of the fourth tire, its utility is higher than that of the third, not lower. Hence declining marginal utility, although a common pattern, does not follow a priori from the logic of human choice.
“The utility is declining with the addition of +1 homogenous units as, given their equivalence to being fitted to tasks, the most urgent tasks have been met, and though we abandon a concept of ‘depth’ of the decline as we do not count difference in utils, we can understand their servicing ends of lower ordinal rankings. lower rankings… diminishing utility (of homogenous goods).”
But what ends can be serviced with what inputs depends on what else you have, hence the marginal utility of the fourth tire can be greater than that of the third–just as the marginal utility of the fifth can be less. And the tires are homogeneous goods.
Where additive utility comes in is the assumption that the utility from one sack of grain is the utility you get from achieving the end that sack suffices for, the utility from the second the utility from achieving the end that suffices for, and at that point the total is the sum of the two. But the utility of achieving both end A and ends B need not be the sum.
I’m afraid I haven’t answered everything you wrote. But you didn’t answer my essential question:
1. I value having six sacks of wheat instead of five less than I value five instead of four.
What choice I could make would demonstrate that?
Value, after all, is supposed to be defined by revealed preference–what choices we make. I offered one possible answer, but that was the one that had to assume that the value to you of an hour of leisure did not depend on how much wheat you had. Do you have a different answer that does not depend on some similar assumption?
And I don’t see who would say that the 4th time is worth ‘more than the first 3’.
If you had 4 tires on your car, and I would either steal 1 tire or 3 from you… what would you choose to lose ?
no question of circularity is raised by awareness of homogenous goods. homogenous goods are not objective, they are a product of the subjective valuations of men over material objects over which they have beliefs and expectations etc.
I notice that no-one seems troubled by the fact that we aren’t discussing ‘half’ tires, or units of 1% of the matter of a tire. and rightly so.
