The mainstream treats economics as a branch of math. I really don’t see how he can be denying that. I guess somebody didn’t read my link or numerous works, such as by Mises, on what mathematical functions are inappropriate for studying human actions. I’m not even opening this stupid thread again.
just like the mainstream economists who treat utility as being cardinal, are all heterodox myths,
Hal Varian is a myth?
So, who is this Hal Varian you speak of? The sad thing about this is that all I had to do is look up “ordinal utility” in the index of his textbook.
You could have actually made a point here, but your inexperience when it comes to mainstream economics is more than apparant. For one thing, mainstream economics does not treat economics as a branch of math, but rather it uses math as a language - a rookie mistake when it comes to judging mainstream micro. Second of all, what Mises said about math has nothing to do about whether mainstream economics is just a branch of mathematics.
CAPS LOCK: CRUISE CONTROL FOR COOL
Neoclassical economists maintain that indifference curves, utility and
the utility functions from which they are derived, are ordinal, not cardinal, in
nature. They also maintain that utility cannot be measured cardinally. That is,
an individual can only prefer A to B or be indifferent between them;1 he cannot
measure how much he prefers A over B. They also maintain that interpersonal
utility comparisons are logically invalid.2 Indeed, the history of economic
thought bears eloquent witness to the fact that the concept of ordinal
utility triumphed over cardinal utility.
Austrian economists also maintain that utility is ordinal. However, they
challenge the use of mathematical utility functions by neoclassical economists
on the grounds that such functions yield cardinal utilities, “measured,” usually,
in utils.3 Neoclassicals respond by asserting that, in dealing with bundles
of goods: (1) a function that ranks bundles in accordance with an individual’s
necessarily ordinal preference ranking is an ordinal function, and the ranking
it generates is ordinal; (2) because the ranking of bundles generated by a specific
utility function (F) remains the same after any positive monotonic transformation
into another function (G), G, also, is a utility function; and, (3) in
that case, it does not make any difference whether an individual’s preferences
are represented by F, by G, or by any other function that is a positive monotonic
transformation of F (or of G for that matter).4
However, maintaining that “properly constructed” utility functions are
valid representations of, admittedly, necessarily ordinal utility is very misleading,
and confuses and obfuscates the issue, because as these functions are
to be the objects of calculus operations they necessarily require cardinal numbers.
5 Thus, the use of such functions necessarily implies that we are simultaneously
in the realms of cardinal and ordinal utility,6 which is problematical,
at best. The problem originates in their interpretation of utility functions
as ordinal and not cardinal. It is compounded by two other factors: the
assumption that utility functions are differentiable; and the failure to use, correctly
and consistently, dimensions in their work with utility functions. It is
my contention that their analysis is incorrect, both as a matter of praxeology
and as a matter of mathematics.
Neoclassical economists maintain that indifference curves, utility and
the utility functions from which they are derived, are ordinal, not cardinal, in
nature. They also maintain that utility cannot be measured cardinally. That is,
an individual can only prefer A to B or be indifferent between them;1 he cannot
measure how much he prefers A over B. They also maintain that interpersonal
utility comparisons are logically invalid.2 Indeed, the history of economic
thought bears eloquent witness to the fact that the concept of ordinal
utility triumphed over cardinal utility.
Austrian economists also maintain that utility is ordinal. However, they
challenge the use of mathematical utility functions by neoclassical economists
on the grounds that such functions yield cardinal utilities, “measured,” usually,
in utils.3 Neoclassicals respond by asserting that, in dealing with bundles
of goods: (1) a function that ranks bundles in accordance with an individual’s
necessarily ordinal preference ranking is an ordinal function, and the ranking
it generates is ordinal; (2) because the ranking of bundles generated by a specific
utility function (F) remains the same after any positive monotonic transformation
into another function (G), G, also, is a utility function; and, (3) in
that case, it does not make any difference whether an individual’s preferences
are represented by F, by G, or by any other function that is a positive monotonic
transformation of F (or of G for that matter).4
However, maintaining that “properly constructed” utility functions are
valid representations of, admittedly, necessarily ordinal utility is very misleading,
and confuses and obfuscates the issue, because as these functions are
to be the objects of calculus operations they necessarily require cardinal numbers.
5 Thus, the use of such functions necessarily implies that we are simultaneously
in the realms of cardinal and ordinal utility,6 which is problematical,
at best. The problem originates in their interpretation of utility functions
as ordinal and not cardinal. It is compounded by two other factors: the
assumption that utility functions are differentiable; and the failure to use, correctly
and consistently, dimensions in their work with utility functions. It is
my contention that their analysis is incorrect, both as a matter of praxeology
and as a matter of mathematics.
yes, that one, the one who talks the talk (on page57) but does not walk the walk. (on page57 and those that follow)
I have posted for you previously William Barnetts devestating article where he shows up Neo-classical reverance for ordinality to be a sham. It made no impact I see.
You mean the discussion of cardinal utility that begins on pg. 57 and ends on pg. 58 with:
Reading a section in its entirety is very critical for understanding what the author is trying to say.
If individuals on this forum read Mises or Rothbard as you are reading Varian, they would be flayed alive, deservingly though.
I have read it in its entirety, and rest assured William Barnett is familiar with similar such treatments by neoclassicals. yes, the verbiage is grand, but the methods and techniques employed don’t add up.
p.s. please don’t flay me alive.
valid representations of, admittedly, necessarily ordinal utility is very misleading,
and confuses and obfuscates the issue, because as these functions are
to be the objects of calculus operations they necessarily require cardinal numbers.
5 Thus, the use of such functions necessarily implies that we are simultaneously
in the realms of cardinal and ordinal utility,6 which is problematical,
at best. The problem originates in their interpretation of utility functions
as ordinal and not cardinal. It is compounded by two other factors: the
assumption that utility functions are differentiable; and the failure to use, correctly
and consistently, dimensions in their work with utility functions. It is
my contention that their analysis is incorrect, both as a matter of praxeology
and as a matter of mathematics.
<mod edit: the content here deleted is only appropriate for the member issues group forum. in the main forum stick to the ideas, not questioning the honesty or intellectual capacity of those who are expressing the ideas>
Saddly, his entire point misses the mark for he ought to be challanging the ordinal ranking of utility functions in indifference maps rather than calculus done upon the singular utility function. It is just plain unconvincing.
a) you [were wrong] about what Varian said with respect to the use of cardinal utility, or
Did you read me? I was not opposed to the introductory lip-service Varian paid to Ordinallity…but rather his elecidation of modern orthodoxy which (in order to make utility mathematically tractable, has to abuse it by letting in cardinality through the back door.
b) you did not understand a rather simple point given in an intermediate micro textbook.
what was the simple point? is it a simple point that forms the locus about which Austrian and Neo-classical are agree (i.e. that Ordinallity is the thing and Cardinality to be avoided) or is it a simple point about how Neo-Classicals can have their cakes and eat them (which is the focus on Barnett’s quite thorough paper, of which I have only quoted small parts).
Oh yes, Barnett addresses indifference curves.
such as by Mises
Inconveniently for him Mises died over 50 years ago, believe it or not, that’s hampered his ability to stay up to date with the latest tools in economics. Math is just a set of tools, as Lam pointed out, it’s a language. Over time more complicated and rigorous tools are developed, math advances, perhaps it is still inadequate to capture certain aspects of the real world that formal language can, but even if that is the case, most “mainstream” economists would accept than in a trade off for the logical rigour that math brings to the discipline. Like I said, there’s been all sorts of crazy advances in math and its application to economics since Mises died, some of which has been embraced by “Austrians”, perhaps it’s still inadequate, but the response is not to repeat 50 year old criticisms but to help develop the necessary tools to express your insights.
@ Giles,
Because the newer the better, right?
@ Daniel
Because strawmen of the way to go, right?
I don’t think I ever said “the newer the better”, just that I know Mises was good and all. But did he really manage to foresee advances made 50 odd years after he died? Perhaps he did, I remain to be convinced.
@ Giles,
"but the response is not to repeat 50 year old criticisms "
Does it matter that it’s 50 years old?
“Mises died over 50 years ago”, actually closer to 40, though I’m being needlessly pedantic. Not sure if mainstream econ uses “all sorts” of newer maths, apart from game theory, as far as I can tell, even advanced General Equilbrium theory uses techniques known since the early 20th century at least. Not that this is a mark against it, I would be greatly impressed if one was to find a graduate student of mathematics who’d mastered the mathematics known up to 50 years ago.
The only economics professor I contacted at my University, who I thought might be interested in what I’ve been reading and doing, not only discouraged me from the Austrians but also said I was “wasting” my mathematical talent looking at the calcualation problem, after reading the draft paper on the topic I’ve been writing. I guess it makes sense in some ways, if you don’t want to do economics anymore, it’s superficially very impressive to look like some sort of “math jock” or quant to naive outsiders. Academia is weird…
Does it matter that it’s 50 years old?
Insofar as it’s likely to miss a great deal of the contributions since, yeah it is. This is nothing against Mises, if he managed to
Not sure if mainstream econ uses “all sorts” of newer maths, apart from game theory, as far as I can tell, even advanced General Equilbrium theory uses techniques known since the early 20th century at least.
What about these guys? And to say that “apart from game theory” misses the point, precisely because game theory avoids a lot of the alleged problems of the mathematical economics of Mises’ time and is amenable to various parts of Austrian theory. Or to give another example, look at behavioural economics, it seeks to paint a more realistic picture of economic actors than standard neoclassical theory and it was once considered part of “heterodox economics”,it also requires more advanced tools since it is portraying a more complicated model of man.
With regard to behavioural economics, I think it’s a mixed bag, with some of the “happiness” economics being just dressed up neo-Benthamism as de Jasay has commented on, while I think a lot of it I see as a compliment to AE, though not a replacement for it, since I consider AE to comprise the “core theory,” in much the way physics doesn’t replace mathematics, but uses it and is sure of its conclusions where the initial conditions and variables can be acertained within a certain degree to hold.
But then again I’m just a dogmatic a priorist who believes laws like the simple fact that the lower bound of a averaged distribution is less than its mean is not only apodictically certain, but has empirical relevance in the very way we interpret the empirical facts observed, as i pointed out earlier when describing a method used in Quantum Mechanics.
I believe the same is true of the rigorous and consistent part of praxeological economics, the categories it describes are not empirical propositions but a prioristic in the very essence of our anlysis ad of the actions we seek to analyse.
The fact that the mainstream insists that they don’t use cardinal utility, and that they avoid the problem by using monotonic transformations, entirely misses the central theoretical problem. Their methods and models implicitly assume cardinal utility; whenever they try to measure consumer or producer “surplus,” they are implying cardinal utility. Again, value can never be measured, it is only graded (it’s a list, not an area which can be expressed geometrically). Never mind the fact that inter-temporal choice EXPLICITLY employs cardinal utility. There are also conceptual problems with indifference curves that Kirzner mentions quite frequently (regarding the budget constraint as an infinite regress). And finally, it (math) simply complicates that which is inherently intuitive, and overly-simplifies that which is inherently complicated.
As far as the production function is concerned, the additive principle is inherently barren, the “productive set” is given (ignores entrepreneurship), and capital is aggregated into a homogenous blob called K, making it theoretically untenable as well (it too confuses causality). Varian may very well address such problems, but Besanko and Braeutigam certainly do not. The problem is not that the Austrians are unfamiliar with the mainstream, but that the mainstream is unfamiliar with the criticisms raised by heterodox schools of thought, or at the very best, they have a shallow understanding of them. So please, get off your high horse.
The behavioral school and Neo Institutional school raise a lot of the issues already raised by the Austrians a century ago, but without the rigor. Their criticisms are accepted, while the Austrians were entirely ignored. For example, “bounded rationality” is just Mises’ definition of rationality, and S.G. Winter wrote a great paper debunking the standard neo-classical production function (based on Ricardian framework, and “the average period of production”). The behaviorists write countless articles on the simplicity of standard neo-classical utility and production functions, and they try to add additional variables in order to better elucidate real world phenomena. Unfortunately, they ignore the major theoretical and fundamental problems, you need intense familiarity with multivariate calculus and differential equations just to understand what they’re saying, and their more “realistic” functions are still way too simple.
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