This quote throws light on why Friedman’s torture-me-versus-shower-you thought-experiment doesn’t get us cardinal utilities that are useful beyond the ordinal rankings they are constructed to represent - calculus is also known as the infinitesimal calculus… if you wiggle x by an infinitesimally small amount, what is the ratio by which y changes with respect to x? While it is undeniable that the human brain can and does perform interpersonal utility comparisons at a gross level (particularly in forming moral judgments), there is no way to get from there to infinitesimal variations in utility, which is what is implied in a real-valued cardinal utility suitable for use with the tools of calculus.
I’m not sure if that necessarily makes any notion of cardinal utility useless for economics, I think it boils down to specifying the limitations of the counter-factual model in representing actual human behavior.
“Austrian economists also maintain that utility is ordinal.”
That “also,” and other things you say, imply that you believe that neoclassical economists maintain that utility is ordinal. That was true a hundred years ago, and it may describe how some textbooks present the subject, but it hasn’t been an accurate description of neoclassical theory in general since Von Neumann showed how to cardinalize utility–as I already pointed out in this discussion.
Note that diminishing marginal utility of income only makes sense if utility is cardinal–and is demonstrated by the existence of the insurance industry.
Diminishing MUI means that the difference between my utility for $10,001 and my utility for $10,000 is more than the difference for $20,000 and $20,001. But if utility is only ordinal, not cardinal, that’s meaningless. All one can say is that I prefer $20,001 to $20,000 and $10,001 to $10,000, but not by how much.
Mr. Friedman, may I ask what is your opinion about the Austrian business cycle theory? You don’t have to give me an extensive answer. I would just like to know how many serious libertarians outside the Austrian school of economics actually accept it as a fact. I thank you for your answer beforehand. (I hope you can understand my English.)
And I would like to present my apologizes to the original poster. I don’t want to cause offtopic and ruin your thread.
I don’t work in macro, so don’t really have an opinion of my own. My father’s view, as best I understood it, was that the theory was logically possible but inconsistent with the available evidence.
Diminishing MUI means that the difference between my utility for $10,001 and my utility for $10,000 is more than the difference for $20,000 and $20,001
Does it? You could have a utility function of y=-x2 + 10
Consider only the first quadrant. DMU doesn’t say anything about second derivative (if, for a moment, we assume continuity and differentiability), just the first.
Marginal utility of income is the first derivative of total utility wrt income. Diminishing marginal utility of income means that marginal utility decreases with income, hence that the second derivative of total utility wrt income is negative.
It doesn’t have to be true–one can obviously write utility functions for which it isn’t. But that is what it means, and there is good reason to think it usually true. And it corresponds to risk aversion wrt income, which is also usually true.
And it doesn’t mean anything if total utility is only ordinal, not cardinal, for the reason I already pointed out.
David, the problem I see is that you define Diminishing Marginal Utility in an overly technical mathematical way, no doubt because maths is the way in which neo-classicals like to do their economics. However this is not necessary for economic analysis, and the Austrain method works quite well with ordinal value and a meaningful diminishing marginal utility (Though of course utils don’t come into it).
See Bohm-Bawerks exploration of the topic, wherein he imagines the varying purposes to which a pioneer farmers several sacks of grain could be put. The loss of any one would impact on the achievement of his least valued end. This is the diminishing marginal utility. His most valued ends are met first, additional sacks are allocated to ends that are valued such that they are lower down the ordinal scale.
There is certainly nothing ‘meaningless’ about this; however we concede that mathematical statements of ‘but by how much less valued’ are jettisoned. But we repeat ourselves.
While I agree that the real-valued utility function is probably much less useful than mainstreamers think it is, I think we have to be careful with this broad brush of “overly technical” because many Austrian arguments - particularly ABCT which is one of Austrian economics’ most important results - are, in fact, very technical. If we say “yeah but they don’t use maths”, the natural question is “so what?” What is wrong with mathematics? If you have five people in a room, then five more enter the room, are there not ten people in the room? Does not this arithmetic fact impinge on praxeology as much as any law of logic?
I think the real issue is that the mainstream economists do not properly circumscribe the generality of their conclusions. If you look up the definition of Von Neumann utility which Prof. Friedman has mentioned, you will see that is defined in terms of thought-experimental “lotteries” in which a “choice” is made between a bundle of goods with probability p and another bundle of goods with probability 1-p. Immediately, we can see two counterfactual aspects to this thought-experiment: actual probabilities are rarely known beforehand (outside of a casino) and payouts are never absolutely certain. This means that significant qualification of conclusions drawn on the basis of VN utility thought-experiments is required. The conclusions of such analyses only hold to the extent that not knowing probabilities beforehand doesn’t matter and not being absolutely certain of payment doesn’t matter. I think that, most of the time, both of those conditions matter a lot.
I think there is an important implication in this question, which is that somebody forces you or someone else to be tortured or take a cold shower, in which case we can use intuition and experience that very few people freely choose to be tortured while a lot more take cold shows. Hence we could conclude in this case that on the average for most people torturing will be worse, and we can make an interpersonal utility comparison and decide on it. So if we were forced to decide if someone should be forced to be tortured or given a cold shower (no other alternatives available), I guess the answer was obvious.
Yet if people voluntarily chose to do one or the other this is not possible anymore. The utility that people derive from torturing themselves because of sexual desires or religious believes or whatever cannot be compared with people who like to take cold showers.
That is where everything goes wrong. People believe that redistributing wealth was good on the basis of interpersonal utility comparisons because they think high or low income is a thing that happens to you or not independent from your own value judgments and choices which is of course not true at all. And if not more important of course because they are ignorant how wealth is created in the first place, they think it is there or not there anyway, it is only a matter of distribution..
I am not 100% sure but for my point of view the claim “interpersonal utility comparisons are not possible at all” is an overstatement. You would need to add the qualifier “in case only voluntary chosen ends are pursued”.
Yeah, I liked MOF quite a lot, and if it were available in German I would have given it away multiple times already… Unfortunately it is not, or is it, or is there something planned?
I have a question to Von Neumann. If I understand this correctly this method would only allow you for saying things like:
Bob likes 1 apple twice as much as 4 oranges,
John likes 1 apple twice as much as 2 oranges
Yet those are relative statements on two different and independent value scales. Both value scales have still no connection to each other, because it doesn’t reveal if Bob and John like one apple to the same degree, or the orange to the same degree. Is that correct?
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?
lets say you have 5 ends the attainment of which each require 1 sack. These are a,b,c,d,e
a is feeding your prize cow for the month,
b is planting crops for next year
… skip a few…
e is feeding your pet parrot for the year
As I hand you a sack, you allocate first to a. I give you another sack, you allocate to b.
By the time you have 5 sacks and are fully allocated, if I should steal a sack at random, the loss you incur is the loss of e, since with reallocation of your remaining sacks, you can still acheive a,b,c,d.
Now what are the ratio’s of sack allocation between uses. They are 1 to 1. This says nothing about how you quantitively value the attainment of your ends…
“I am not 100% sure but for my point of view the claim “interpersonal utility comparisons are not possible at all” is an overstatement. You would need to add the qualifier “in case only voluntary chosen ends are pursued”.”
It’s still an overstatement. We can observe how much trouble people are willing to go to in order to pursue ends voluntarily chosen, and form some opinion from that about how much utility they get from them.
More generally, in understanding human beings we have the advantage of ourselves being human beings. So although there is no precise way of measuring the utility other people get from things, we can get at least some information about it by observing their behavior, by introspection, and in a variety of other ways.
A German translation of Machinery was published in 2003–I don’t know if it is still in print or not. Unlike the French translation, which I only got to look at when it was done (and sent off an anguished letter pointing out multiple mistakes), for the German one I was able to interact with the translator, so I think it is reasonably accurate, subject to the limitations of my not very fluent German. For similar reasons, the German translation of my Hidden Order is the one translation of that book which I’m pretty sure is accurate.
For some reason publishers don’t encourage interaction between authors and translators.
It’s the same Von Neuman–one of the more impressive intellects of the 20th century.
A Nobel prize winning physicist is quoted as saying “There are two kinds of people. John Von Neumann and the rest of us.”
And Fermi’s comment after meeting Von Neumann, to one of his colleagues, was “That man is cleverer than I am. Just as I am cleverer than you are.”
Von Neumann utility isn’t about interpersonal comparisons–it’s a way of making utility cardinal rather than just ordinal. So your basic point is correct.