That still does nothing to dismiss my point that utility functions measure value through ordinal means; rather, you just bring up non sequiturs against mathematical formalism that have nothing to do with the point I have made.
This is all one non sequitur. All that is being discussed, at least by me, is the fact that Neoclassical utility functions are ordinal in how they analyze value. I have made no other defenses, nor statements about them other than it is absurd to deny that they measure utility in an ordinal fashion.
Just FYI, I have little to no knowledge in this area, so nothing I say is meant as debate. I’m just very curious about what Student, Esuric, and Lam are debating.
You’re wasting my time. You ignored my point about inter-temporal choice, the fallacy of constant value, surplus analysis, and everything else really. I’m not talking about neoclassical static utility functions (as opposed to inter-temporal choice)–I know that they work for both ordinal and cardinal measurements, I never said otherwise. I’m talking about intrinsic differences between neoclassical and Austrian economics. If you wish to join this discussion, then by all means.
With neoclassical analysis I could entirely refute all of Stephen Kinsella’s work on IPR’s. A simple surplus analysis would suffice.
Perhaps, but you have pretty much stated that Neoclassical utility functions are not intrinsically ordinal with the statement:
While, in fact, Caplan knows that he studies value in an ordinal fashion because utility functions are, at their very heart, an ordinal means of analyzing value. Here you seem to deny the intrinsic ordinality of utility functions, and it is to this that my entire reply has been about.
Even their most realistic tool, the static utility function, which can use either ordinal or cardinal measurements, is useless, illusory (no constants when it comes to value), and frankly quite annoying.
To put it simply:
If you ask an Austrian, “What is consumer choice?” He will respond with, “an individual arranges his/her ordinal value scales according to some metric they created within their own mind, which is entirely specific to them.”
If you ask a neoclassical economist, he will respond with: u=Ax1^ax2^b => ax2/bx1 =>p1/p2=ax2/bx1 => x2=bx1p1/ap2 => p1x1+p2x2=m => p1x1+p2(bx1p1/ax2)=m => p1x1+(bx1p1/a)=m => x1[p1+bp1/a]=m => x1[p1a+bp1/a]=m => x1p1=ma/a+b => x1*=ma/(a+b)p1. (Where x1=good one, x2=good 2, a=alpha, b=beta, m=income). And there you go, that’s how you choose! This can be used to justify all sorts of things.
Wait, here’s an even better example: Q=2L+4K (l=labor, k=capital), w=3 (wage), r=8 (interest rate). Q=100 (produce 100x): Q=2L+4K => 2L=100, L*=50. Do you know what this means? It means that 50 laborers can produce 100 units of “x” without any capital. What are they producing without capital, with just their bare hands? Who knows, maybe snowballs.
I never said that. I said that neoclassical’s use cardinal measurements, which is true for inter-temporal choice. That doesn’t mean that they always use cardinal measurements. But it’s pointless anyways, since functions require constants, which don’t exist in economics. And this is merely one of the numerous differences I pointed out. All of which are intrinsic. Without utility functions, you can’t have production functions–thus, again, math fails.
While you may be efficient in making fun of the mathematical formalism, you have yet to actually elucidate the theories that are formally modeled here. Really, its just one straw-man where you clearly elucidate what Austrian economics states with respect to value theory while giving a garbled Neoclassical equation without stating any of the theory behind it. Really, Neoclassical value theory is almost exactly what you state the Austrian theory is, but the Neoclassicals go on to try and utilize mathematical techniques to analyze preferences via indifference maps, budget sets, ect. To claim that Neoclassical theory is mere equations is either a blatant lie, or a severe case of misunderstanding.
However, what you fail to note here is that Neoclassical intertemporal choice is always between concrete items in which the consumer must decide at which point to consume, what balance of the items he will choose. Intertemporal choice is essentially just a budget constrain between items that can be consumed in the present, and those that can be consumed in the future. Ergo, it follows that cardinal numbers must be utilized in the consumer’s judgment of what he will decide because he is choosing between units of goods in concreto.
False, functions only require constants if the amount of dimensions utilized to graph them is limited. Therefore, this critique can only be used against mathematical formalism is so-many dimensions, but eventually there will be enough dimensions that this will no longer apply.
I’ve stated quite a lot (and I will admit I used a lot of jargon), but if you cannot comprehend what I have stated perhaps you should think twice about critiquing Neoclassical economics, which you now presumably do not understand much about.
Two dimensions: y=2x
Three dimensions: y=zx
As a result of adding another dimension to the analysis, z can now be represented as a variable rather than a constant.
Translation: Neoclassical economics is often absurd. And I will continue to ignore your points about surplus analysis, capital theory, interest theory, and everything else. Instead, I will repeat that neoclassical’s also use ordinal measurements, even though you already know this. I will also accuse you of building a strawman, even though kids across the country are shown mathematical production functions where capital is able to engage in production without labor.
Translation: I’m going to keep talking as if I’ve refuted you, knowing full well that I haven’t.
Interesting. I hate to be a pain but can you give a real life example (I guess susbtituting things for your y,z and x) to make this even more clear for someone like myself, who is absolute sh*t when it comes to these sorts of things? [:D]
The standard graphs you see are two dimensional, with a y-axis and an x-axis; you can add a third dimension, z-axis, fourth, or whatever. Basically, he doesn’t know what he’s saying, and he’s trying to confuse you. Utility functions require constants, and production functions require utility functions. There are no constants in economics, thus, for the 4th time, math fails.
Are not cardinal measurments appropriate for when a consumer is deciding upon how many units of goods in concreto he is going to choose? The valuation done in utility functions, and those done in intertemporal choice are modeled differently for the analysis intertemporal choice does not involve the utility function. Rather, it is valuing units of goods against each other, and choosing which bundle of concrete goods the consumer will choose based on indifference curves.
And yet it sheds much more light on Neoclassical economics than the blantantly misguiding strawman you have erected.
Why do I need to discuss these? Perhaps I have no other point to add in the discussion of these that you have already not stated. Perhaps I believe that you are sound in your analysis of this part of Neoclassical economics, and not sound in your analysis of other portions of it.
I can pick berries with my bare hands. Is there anything unsound in this statement? If there is not, I have just given you an example of someone being able to produce without capital. Furthermore, such an analysis is certainly not in Hal R. Varian’s Intermediate Microeconomics: A Modern Approach ergo you are making a false general statement.
I agree with Esuric that lam has misconstrued the Austrian critique concerning ‘constant relations’. Also I disagree with Lam (and Caplan) that Neo-classicals avoid falling into error of cardinality vis their monotonic-transformations. There is extensive literature on this, particularly the W Barnett piece I must have posted to this board a million times now; and its mentioned extensively in the media section by ‘mainstream’ Austrians, such as Bob Murphy on the “Neo-Classical - Austrian, similar but different” tack . Block, Salerno… I listened to a lecture from J Herberner (sp?) on neo-classical utility just a few days ago… This is not even to mention their use of indifference.
Ask any Neoclassical economist why that is, and you will receive the same answer: a piece of paper, as used by textbooks, can only facilitate two dimensions clearly. But that does not mean that they cannot use more than two dimensions.
The standard graphs that one would also see are those that are trying to teach Neoclassical economics, so it would be self-defeating to include multiple dimensions in the analysis unless one were teaching to individuals with PhDs in mathematics.
No they don’t. Take the most common utility function out these, the Cobbs-Douglas utility function: U(x’,x")=x’^a.x"^b. Do you spot a single constant in there that cannot be expanded into multiple dimensions (e.g. the a, and b)?
You are using the worse possible arguments to show that math fails. With arguments like this, you are easily going to be dismissed as someone who does not understand mathematics.
I changed the comment before this response; I guess I was too late. But yeah, there’s probably some textbook out there without perfect substitute production functions.
The standard Cobb-Douglas is U=A(constant)x1^a(some preference)x2^b(some preference). I will be honest though, I’m emailing my teachers your response, all of which are standard neo-classical welfare economists. I may be wrong.
The Neo-Classical analysis of indifference relies upon the cardinality of utiility functions, that some bundle will equal in utils another bundle. therefore the chooser will be indifferent to which bumndle he gets the x units from, as he will get the same util units from one as from the other
Take an apple falling from a tree at y=9.8v. Where y is the distance that the apple has fell, v is the apple’s velocity, and 9.8 is the acceleration of the apple. However, one is not happy with this, and would like to add in another aspect: air-drag. Let us suppose, for the sake of example, that one has found that the air-drag exerted on the apple is dictated by another equation. However, one is limited in this analysis by two dimensions, hence, rather than adding air-drag as a third variable dictated by another equation, one approximates its average effect as d=0.002. As a result one is left with the equation for the falling apple as y=0.0196. However, if one could expand the equation into a third dimension to account for air-drag, one could model the falling apple’s fall as: y=9.8dv.
Disclaimer: I don’t intend for this example to be enlightening whatsoever for the dynamics of a falling apple.