To which they never mention produce the same marginal rates of substition and hence results regardless of the functional transformation as a result of the chain rule. Ho hum.
Thanks for the reply, but it didn’t exactly address the point I was trying to make. As I wrote in my previous post, you do choose between two different bundles of goods, but your evaluation of those bundles is the result of your evaluation of the utility you expect the different individual goods to yield. You buy a bundle of one stuffed goat and one carrot, but when you buy it you don’t think to yourself “I can’t wait to get home to consume this goat/carrot bundle”. The two have nothing to do with eachother, there is no relation whatsoever between the utility derived from the stuffed goat and the utility derived from the carrot. The value of the bundle is the the value (your subjective evaluation) of the services they provide individually. The hunger reduction a carrot can provide is an entirely different thing from the joy of scaring children with stuffed goats, and they must therefore be evaluated independently. You do buy a bundle, but this bundle contains two different goods, and the value of the bundle is the summation of the value the different goods, assuming they aren’t complements - which I don’t think carrots and stuffed goats are.
The answer you gave to the question of how to decide which bundle was preferable was an answer to a different question. It was an answer to how to decide which you prefer of a carrot and a calculator. Here there are only two goods you choose from and there is thus no need for anything but ordinal ranking. But the example I used was one with two bundles, each containing two different goods. You choose between stuffed goat+carrot and vacuum cleaner+calculator. You do really like stuffed goats, so you prefer the goat to all the other goods. But at the same time, you aren’t that hungry so you prefer both the vacuum cleaner and the calculator to the carrot. How do you decide which to choose? Your ordinal ranking is known, you know which goods you prefer to which. But how do you select the bundle without considering by how much you prefer the goat to the calculator and the vacuum cleaner, or by how much you prefer the vacuum cleaner and the calculator to the carrot? It can’t be done if your evaluation is only ordinal. You can order the bundles ordinally, but that ranking is the result of your evaluation of the many different ends you can use the different goods to attain.
How can you evaluate bundle I relative to bundle II without estimating the expected utility derived from the different ends that can be satisfied by the different goods included in the bundles? With only an ordinal ranking like the one I wrote down in my previous post?
Again, it has to do with the classification of a “good”. You do not choose between 2 bundles each consisting of “two goods”, but really just two “goods”. Each group, the carrot/stuffed goat and vacuum cleaner/calculator are just two goods that satisfy distinct ends: 1. Enjoying carrot/stuffed goat and 2. Enjoying vacuum cleaner/calculator. Your quote “I can wait to consume this goat/carrot bundle” is awkward phrasing, because in reality know one ever thinks with the word “consuming” or “bundle” or even “Good A/B/C etc” all together, it’s just “I can’t wait to use my stuff when I get home”.
Technically speaking, this is all subjective. You can certainly use the two most unlikely objects together. But again, you’re missing the point. Ends are always distinctly different, and therefore depending on how an individual ranks his ends he will rank his distinctly different goods accordingly. In the act of choosing, actors always choose between distinctly different single goods depending on which good can be used for a higher ranked end, and virtually every good is a “consumption package”. If you won a contest and can choose gift bag one or two, each composed of a variety of different consumer products, each gift bag is its own good. And when deciding between the two bags, you will decide based on which variety of products serves higher ranked ends. You don’t start writing down a value scale of all the single “goods” and then do some arithmetic operations based on a utility unit of account. You simply decide, and that is only up to you, what good can satisfy your ends “Wants satisfied by Products in Gift Bag 1” or “Wants satisfied by Products in Gift Bag 2”.
That value scale posited above and the one you mention for the carrot/stuffed goat etc dilemma doesn’t factor into that act of choosing, that value scale comes about only when you have all the objects and if you want to use them independently, you need to decide which one to use, or if you are buying all of them individually. In that scenario the “bundles” spilt apart and they all become four separate distinct goods, and the same thing occurs for however many goods are in the gift bag. In the case of the restaurant example, you don’t say 1. Burgers 2. Italian Ambiance 3. Pasta 4. Rowdy Bar scene, when deciding between 1.Burgers/Bar 2.Ambiance/Pasta, only if you were to choose between all four individual goods. In the case of using your “stuff” as you drive home from the mall, when you are in your car then you can decide “Am I using my carrots and goat heads together?”, “Eating Carrots first”, or “Scaring kids first?”.
Jrgen, I had similar thoughts and confusions a little while back. I believe BlackNumero was trying to bring home the essential point that choice is context dependent.
You point out unless they (carrot and goat) were compliments(or the opposite) there is little reason to believe it necessary to strictly express the decision so strictly as the comparison of 2 bundles; you may as well go and just “sum” the utilities(converting the ordinal rankings into monontonically increasing numbers). Hence with 4 goods A-D, with ordinal rankings:
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A
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B
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C
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D
Then since v(A)> v(B)>V(C)>V(D), V(A+B)>V(C+D), so A and B are valued to C and D right? Now this MAY be the case but as you implicitly acknowedge, this may not always be the case, since A and B may be compliments(or the opposite, they may not “go well” together). Furthermore I would add, value scales themselves must be entirely context dependent, and so this would also be the case given goods that are substitutes in the sense that they are capable of serving the same ends to different efficacies(Rothbard generalises the notion of substitutes to the sense that all goods are essentially substitutes for one another, but I won’t go into that here). Hence if A and B were substitutes toward achieving the same end(for instance), then it would also not necessarily be the case that A and B would be preferred to C and D, since B might serve a much less valued end.
Hence we cannot impute the valuation of bundles of goods from individual goods and vice versa(as expressed cogently first by Menger). The tradeoffs in each situation of choice represents a tradeoffs of a different sort. Strictly, the avove value scale can only help us understand the tradeoff of one good, e.g. B for either A, C or D. We cannot use it to understand any other situation, since this would have to take into account how these can be combined to acheive an alternative set of ends in a situation of an entirely different context.
Hence value scales of the form shown above are defined strictly, only to help understand a given tradeoff and more generally to explain the consequences of the fact that men act and prefer one thing to another when constrained by scarcity. These value scales are simply a school of thought, and we cannot measure them, or conceive of them in any meaningful sense of existing “out there.” As Rothbard noted in his essay on welfare economics, the only thing that can be observed from action is the demonstration of preference from a tradeoff, for the thing acquired over that given up. However valuation of ends, and how these meaningfully affect the valuation of goods we cannot know, and changes from one action to another, and as I have noted above, would occur even if valuations themselves did not change.
In conclusion, i would highly recommend a careful reading of Mises’ section on marginal utility in Human Action. Do be wary however of one error he makes in his exposition however, which I pointed out here. Hope that helps.
abskebabs, I’m pretty sure that in the passage of Human Action you’ve quoted in the thread you linked to, Mises is using an hypothetical example rather than an illustration of what is logically necessary.
Aristippus is right, of course. And my post there spells it all out.
And BTW Bob Murphy wrote that the equivalent up to monotonic functions thing is 100% correct.
This (put differently).
](https://mises.org/journals/scholar/murphy.PDF)
I’m still curious as to how we can go from that to the MU/P=MU/P while retaining ordinality. Remember the conversation we had in a thread a while back?
Sure do. Bottom line was we both don’t know how to derive that equation, despite Bob Murphy saying it can be done.
I wish a professional mathematician here would spell it all out. Meaning to show either that it is possible or that it is impossible to derive that thing using ordinals.
My hunch is still that it can’t be done, mainly because even if the numbers from an equation are purely ordinal, you still are dividing them by prices, not to mention equalizing them.
askebabs
Read the paper.
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He doesnt give a counterexample, i.e. a case where human preferences say one thing and the corresponding utility function says another. All he’s saying is that it might be wrong. I want more than that. Show me a concrete case where it’s wrong.
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Also, he appeals to arguments that IMHO miss the boat. They sound analogous to arguing that one cannot solve Diophantine equations using complex variables because there are no complex numbers in arithmatic.
Just to note; I don’t agree with everything in that paper, but I do think he makes some rather good points. It’s true he doesn’t provide counter examples, and it is worth noting it is an unpublished working paper, but his point that equivalence has not been established stands; and I don’t think we need to run in circles trying to prove a negative.
Yes, the key is whether equivalence has been established.
And that’s why I think he is wrong. If you have an ordinal preference system [for one individual at one point in time], and a is more liked than b if and only if F(a)>F(b), then that’s equivalence. I mean, what’s missing?
Might the F function have all kinds of properties the human preference does not? Sure it will, like continuity. But so what? Any statement about F involving only inequalities will neccesarily be true in the corresponding statement about preferences.
I don’t want to say much more on this for now, but a relation of representation =/= a relation of equivalence as it seems you think it does. Knowing that I value A more than B as Mahoney acknowledges could be represented as Mahoney notes without adding a whit of insight to our pre-existing knowledge by saying V(A)>V(B).
However, if I started saying V(A)>V(B) and then went on to say V(A)/V(B)=MRS from which I derive demand functions then we are entering the realm of the largely arbitrary and meaningless. What is V(A)/V(B)? 2/1, 3/2, 81/16? The subsequent theorems of Microeconomics that are then used to constrain the resulting indifference curves practically assume what they should be aiming to prove. Whether subsequent transformations of the utility function are montonically increasing or not is entirely irrelevant, given that the same MRS and demand functions will be produced regardless of the functional transformation as a result of the chain rule(the only necessary condition for the transformed functions is nonsingularity). The abritrariness lies in the original formulation of this utility function, not on subsequent transformations, which are a side issue entirely.
That’s all for now, back to revision!
Keep up the good work! Nothing says die hard economists more than talking about cardinal utility and price theory on a Friday night
No need to answer, or even read, this post right away. It stands in cyberspace, twiddling its thumbs patiently.
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I indeed do not know what “equivalence” means the way you use it. The paper argues that results may be true about the function but false about the value system. I see that as a denial of logic and mathematics. That’s why I ask for a counterexample.
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It doesn’t add to our insight by merely setting up the representation, but when we use the laws of math [which are distilled common sense] on the function we might very well learn something. For example Bob Murphy claims it gives a smooth easy way to deduce a true but otherwise difficult theorem. [Note that I am not saying I know he is right. But he might be. And if he is, it means the representation has added to our insight considerably]. And I see no apriori reason that there cannot possibly be things to be learned.
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Asking what is V(a) / V(b) is like asking what is the square root of minus 1 [certainly not a whole number] when using complex variables to solve Diophantine equations. One does not have to be able to answer at every single step “what is this thingy in the real world of economics” to use math. What appears in the final result is the only thing that has to be understood; not the intermediate steps.
As a simple example, why does “-1 times -1 equals 1” make any sense whatsoever in the real world? No reason at all. Do you therefor reject all the results of physics [=everything] that use this principle in the intermediate steps?
- I’m glad we agree that the key lies at the very start, in the original formulation of the utility function. And it seems to me that setting up “liking A more than B iff F[A] > F[B]” makes it not abitrary at all. That condition captures the essence of a human value system. Again. what’s missing?
Closing remarks for the night (for me at least).
Now, although I’d say I have fairly good math skills relatively, your math skills/knowledge of terms is clearly superior to mine.
However, whatever the negative values of 1 may result in during the intermediate steps of solving real world equations, the same type of analysis is not applicable to human action, mainly because we using deduction to describe meaningful conscious plans of humans. If we know that humans act, and we want to explain the formation of a price, we can’t make steps that are logically inconsistent, because that makes no sense when describing purposeful behavior. We say humans act…then marginal utility…then…rankings of two goods…then supply/demand curves for participants…then causal analysis of a plain state of rest=price (very basic proof obviously, but you get the point). All of this because it deals with human minds and deliberate actions, needs to be meaningful. On the other hand, physics and the natural sciences are not deductive and don’t deal with conscious purposeful agents, so each step does not need to be meaningful.
Ala rothbard:
MES
Praxeology asserts
the action axiom as true, and from this (together with a few
empirical axioms—such as the existence of a variety of resources
and individuals) are deduced, by the rules of logical inference,
all the propositions of economics, each one of which is verbal
and meaningful. If the logistic array of symbols were used, each
proposition would not be meaningful. Logistics, therefore, is far
more suited to the physical sciences, where, in contrast to the
science of human action, the conclusions rather than the axioms
are known. In the physical sciences, the premises are only hypothetical,
and logical deductions are made from them. In these
cases, there is no purpose in having meaningful propositions at
each step of the way, and therefore symbolic and mathematical
language is more useful.
Black Numero,
As you wake, you see my thank you for the compliment.
IMHO, Rothbard totally missed the boat both in what you quoted and in the paragraph after.
I ask you, what would Aristotle make of an argument like this:
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In Physics, the conclusions are known, but not the axioms.
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Therefore there is no purpose in having meaningful propositions each step of the way.
And I’ll give you my answer: Non sequitor. [2. happens to be true, but does not follow from 1.]
Let’s look at another one:
1a. The propositions of economics are verbal and meaningful.
2a. Therefore only verbal arguments should be used in econnomics.
Again, a non sequitor. In this case 2a is neither true, nor does it follow from 1a.
Also, he makes an assertion which has no proof, [because it is false], that there is some mystical gain in having each step of an argument “make sense”. A chain of logical reasoning [=math] gains nothing by that. As long as each step follows from the previous ones, it is perfect and needs nothing more. Even Rothbard must admit this, as it follows from his misuse of Occam’s razor.
In addition, statement 1. is false. After Newton, in a stroke of genius, discovered his laws of motion [which were stated verbally and meaningfully], they are treated as axioms. So the axioms are considered known by the scientific community. So that physics is now on the same footing as economics. Axioms are known, and stated verbally and meaningfully. Should physics therefor dispense with math?
The whole thing is akin to saying Newton was English, therefor physics should be studied in English, and Mises was Austrian, therefor Economics should be studied in Austrian.
And his next paragraph, that there is no advantage to using symbolic logic [logistics means something else], is also a big mistake. He writes, “Contrary to what might be believed, the use of verbal logic is not inferior to logistics.” It certainly is. Granted that the rules of symbolic logic are derived from verbal logic, but symbolic logic has tremendous advantages that verbal argument lacks. For instance symbolic logic would have shown him the holes in his first specious paragraph.
Bottom line:
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The intermediate steps never have to be “meaningful”. They only have to follow from the previous steps of the argument. The conclusion of course has to be meaningful. Otherwise whats the point?
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Which is the preferred language, English or german or symbolic logic, depends one thing. Which is most useful. For physics verbal language would be insuperably cumbersome. Austrian economics, at least in its current stage, is simple enough that on the contrary, it is symbolic logic that is a cumbersome distraction.
One last thing, just an aside. He appeals to Occam’s razor, which has no application to the topic he discusses. It is also not a “fundamental scientific principle.” Nor does it deal with multiplication of processes.
I don’t think simply because we use deduction that it is per se meaningful, I think we use deduction because humans purposefully act, we know the action axiom (along with other typical complaints about positivism), and therefore each step of the way must be meaningful. As in my earlier example, when analyzing the formation of a price, we are dealing with conscious humans who freely make choices, and each step along the analysis must accurately describe human decision making and thought. Whereas in the physical world, the rules are different, and since particles are unmotivated we have greater freedom in doing what we need to get a hypothesized result. I guess in Mises’s words, the telology versus causality/mechanism argument. This fits in with the Austrian principles why certain mathematics are inapplicable to forming laws about action. I think you disagree with them, but I believe that is where this argument gets its reasoning from.
Mathematics can certainly be a “useful” application towards human action. You can derive all the theorems you want using manipulation of equations, etc etc and then say these describe certain phenomeon about economics. But how many apply to the real world, let alone make sense and are meaningful and can explain purposeful action each step of the way? The tangency condition MU/P=MU/P is a prime example. In terms of human thinking, what does this mean? How can humans equalize marginal utility ordinal rankings and then divide them by a price? We find the optimal indifference basket according to which one hits the budget constraint via a calculus problem? Huh?
- I meant meaningful in the sense Rothbard meant, that the intermediate step can be translated into English and assert something about the real world. [As opposed to, say, [-1][-1]=1]
With your understanding of meaningful [=of benefit to the human] symbolic logic is also meaningful every step of the way, which R. says it isnt.
I don’t see why. The only thing of interest is the conclusion. Who cares if the middle steps, such as the use of -1 times -1 equals one, has meaning?
A good example of this is probability theory. Wondering if it is a good idea to bet that heads will land ten thousand times in a row [or another more complictaed question that needs adcnaced math], our human actor writes a string of uninterpretable equations and comes up with “the odds are a zillion to one of you winning.” That’s all he needs. He need not have an interpreatation of the process of integration from - infinity to plus infinity etc etc.
Here you have it. Analyzing the formation of a price [how much is alottery ticket with suc odds worth], dealing with a concious human being freely making a choice [to buy or not to buy, that is the question], and each step along the analysis cannot possibly describe human decision making and thought.
It is a very restrictive requirement imposed on the classical rules of reasoning, and I don’t see where it comes from. Is it common sense? Not to me. Is it derivable from the law of the excluded middle or something? No. Is it derivable from the action axiom, or any set of axioms at all that seems obvious to the average intelligent person? No. It’s mysticism.
It is like saying that if a sentient but powerless robot is programmed to think, that every program we feed into his machinery must make sense to him. But if we feed the exact same program to a non sentient robot, that’s ok. What’s the difference?
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The only arguments Ive seen that are valid about why math is inapplicable to economics deal not with the process of mathematical reasoning after the initial assumptions are made, but with the initial assumptions themselves being a farce. But once you grant the initial assumptions implicit in an equation about economic life, you can’t stop the ride anymore. The use of math will lead only to conclusions that indeed follow logically and impeccably from the intial equation.
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Let’s hold Rothbard to his own standard. He and I both agree that a verbal argument should conform to the accepted rules of Aristotelean logic, right? So please put together that paragraph of Rothbard’s into a syllogism, so I wlll see clearly how it is not a non sequitor, contrary to what I have claimed. [of course this is a trick question, because it cannot be done].If it was high school geometry and Rothbard wrote that kind of reasoning on a test, he would flunk the course.
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Time is short. That particualr equation will have to wait. Sadly it may wait for along time. Will give it my best shot Monday evening possibly. Busy till then.