Does the latest round of Keynesian spending validate or invalidate Keynes' theory?

Economics Economics Questions
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False, a bundle does not merely equal the amount of utility that another function has, rather it also entails that the consumer values the two different bundles equally. The cardinal numbers of utility functions do not matter, the only thing that matters is how the cardinal numbers are ordinally ranked in comparison with one another.

Say what you want about the possibility of indifference, but it is still an ordinal analysis.

You actually need to know what you are talking about in order to see it.

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A Neoclassical would reply nothing.

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ok, jot down for me the worlds simplest Mengerian value scale, an ordered ranking, which will becessarily have a 1st ranked good and a 2nd (and last) ranked good. then tell me that the fellow who’s scale it is is indifferent between the two goods, and they have equal utility

if you can do this without contradiction you may have point

If you would write a scholarly response to W Barnett’s paper, (the one that spells out in great detail the standard Austrian position on the Neo-Classical Math Fail pf Ordinality/Cardinality).I would welcome the attempt. You may of course get the benefit of input on the topic from learned Austrian Scholars whom I presume you have some respect for… (as opposed to me, whom you have made it clear you do not)

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Would the Austrian critique of this be something along the lines of, before the apple hits the ground, Murray Rothbard coming out of nowhere with a louisville slugger, knocking it through his neighbors window, saying “Try again Neo-Classhole!”

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The fact that there is indifference in Neoclassical economics does not entail that Neoclassical is not ordinal with respect to its analysis of value.

I frankly don’t care. All I’m concerned about are the fallacies about Neoclassical economics as stated in this thread. Feel free to give Barnett’s argument here, but if it is already contained in what you have hitherto stated, it is unsound.

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In my opinion, the problem’s not within the indifference curve as much as it’s in the budget line. The budget line has given prices (circularity).

Which fallacies exactly?

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http://mises.org/journals/qjae/pdf/qjae6_1_3.pdf

That is the crux of the matter. Neoclassical economists act as if they can

have both cardinal and ordinal rankings at the same time and in the same

respect. That is, they say that because they can order bundles on the basis of

the cardinal number assigned to it by a specific function, the order so generated

is a rank-order, and that the utilities being so considered are ordinal. This

is incorrect. Were it truly an ordinal ranking, it would not be absolutely necessary

to use the cardinal numbers from which the ranking was generated in

their mathematical calculations. Rather, the ordinal numbers corresponding

to the ranking generated from the cardinal numbers could themselves be usedin such calculations.

Therefore, the order generated by neoclassical utility

functions is not a rank ordering in any meaningful sense of the word.

Furthermore, neoclassical economists properly maintain that the ranking

of a set of bundles generated by one of their utility functions is invariant

under a monotonic transformation thereof.16 That is, although one bundle of

goods from a set of bundles might be assigned the number 100 by one function,

F, and the number 10,000 by another function, F2 (a monotonic transformation

of F), in either case the bundle would have the same ranking within

the set of bundles. Therefore, in order to know the rank of a basket of goods,

all one needs to know is its assigned number, and the numbers assigned to

other bundles. Note well that all that is necessary to know in order to assign

the appropriate number to each and every specific bundle is its own specific

contents. No knowledge whatsoever of the contents of any other bundle or

bundles is necessary.17 Therefore, baskets of goods may be ranked without

any comparison with the contents of other bundles. Most assuredly, such a

ranking does not qualify as ordinal in nature.

…

Put another way, let there be two (2) bundles, A and B, to which a neoclassical

utility function assigns the cardinal numbers 20 and 30, and ordinal

numbers (necessarily based thereon) 2nd and 1st, respectively. If a third bundle,

C, is now to be ranked, all that is necessary to know are the elements of

bundle C and the concomitant cardinal number assigned to it by the utility

function. Thus, if the utility function, operating on the elements of C, yields

the cardinal number 25 for C, then the ordinal ranking becomes: B is 1st, C

is 2nd, and A is 3rd. If, however, the utility function were a “true” ordinal utility

function, in order to rank C, we would need to know more than that the

ordinal numbers assigned to A and B are 2nd and 1st, respectively, and the elements

of C. We would need to know the elements A and of B, as well.

…

that results from using cardinal utility functions.

Furthermore, neoclassicists make use of indifference curve analysis

and the marginal rate of substitution (MRS) to analyze consumer choice.

The MRS in the two-good case is defined as: dy/dx(dU = 0) = -Ux/Uy.27 Therefore,

using either U1 or U2 as the utility function, dy/dx = -y/x. However,

utility maximization requires that the MRS be equal to the negative of the

ratio of the price of x to that of y (-px/py). Therefore for either bundle A or

C to be optimal the prices of x and y must be the same and, therefore, the

MRS = -y/x = -100/100 = -1, whereas for B or D to be optimal the price

ratios of x to y must be -100/121 or -400/420.25, respectively and, therefore,

the MRS = -y/x = -100/121 or -400/420.25, respectively. But -1, -

100/121, and -400/420.25 are cardinal numbers, not ordinal numbers. It is

difficult to see how this can be denied. Consequently, one reason that neoclassicists

are in error is precisely because, de facto, they switch from

ordinal to cardinal utility when their utility functions generate cardinal

numbers and they use these cardinal numbers in their calculations.

…

SUMMARY AND CONCLUSION

In sum, the cardinal utility numbers generated by neoclassical utility functions

provide more information than do their ordinal counterparts. In fact,

for any given set of bundles they contain all of the information implicit in

ordinal utility numbers for the same set, plus they provide additional information

concerning the intensity of the preference for any one bundle relative to any other. It is precisely because utility functions cannot be used to calculate

ordinal rankings of bundles without prior calculation of their cardinal

utility numbers that the use of utility functions is unacceptable for economic

purposes. Moreover, although meaningless with respect to the reality of actual

individuals’ preferences, this extra information is harmful because it is misleading.

I conclude by reiterating the purpose of this article. I have attempted to

demonstrate that neoclassical utility functions are an invalid means of analyzing

consumer behavior for three reasons: first, and most important,

because such functions, and their attendant rankings, are cardinal, not ordinal

in nature; second, because, with respect to the set of bundles relevant to

actual human beings, such functions are not continuous and, therefore, not

differentiable; and, third, because such functions do not correctly, consistently,

and properly include dimensions/units.

Let me put this in another way. I will accept the validity of utility functions

as soon as its proponents can show me how to perform basic mathematical

or arithmetic operations on such ordinal numbers as 1st, 3rd, 6th, and

17th.
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Weren’t you suppose to provide an example without constants? In what situation is there going to be a spatial calculation using XYZ without constants? You guys are way over my head but you seem to contradict what you were originally trying to point out?

If there are no constants how is it measurable?

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and Murphy’s Study Guide to Human Action.

  • Mainstream economists have tried to use �cardinal rank� to represent ordinal rank; thus, they arbitrarily assign numbers to ordinal rankings:

    • e.g.,
      A – 95
      B – 85
      C – 75
    • However, as Austrians note, A, B, and C are not like grades, but are states of mind.
    • Cardinal numbers are not a representation of ordinal rank: they are a �representation� plus a quantitative difference between the rankings.
    • The mainstream response was to do linear transformations, which don�t change the function, but only the gap-size.
    • The Austrians responded that linear transformations don�t change the ratios. The only way to �represent� ordinal ranks would be through all cardinal functions.

  • The mainstreamers then tried to use the concept of indifference – the possibility of being indifferent between two options – to equate utility:

    • _Leap of Faith_This is wrong: to say that someone is indifferent is to say that they can�t make a choice; if they can make a choice, then they were not indifferent; however, to say that someone can�t make a choice is not to say that he or she equates utility.
    • Ordinal preference rankings:
      1st: $100
      2nd: good X
      3rd: $80
    • Cardinal preference rankings:
      ordinal rank: good – utility function
      1st: $100 – (2x,1y)(1x,2y)
      2nd: X – (1x,1y)
      3rd: $80 – (0x,1y)
    • Money is never valued in this system – only the �utility cardinality� of one good vs. another good. This is unrealistic:
      • The realistic thing to do is to consider the value scale: money vs. goods.
      • Unrealistic, because it requires us to map out a utility function for all possibilities, as if such a thing exists; in reality, individuals only demonstrate preference through action, and the idea of a utility map is contrary to that.
    • Indifference does not explain action, but only inaction.
    • Indifference is not a useful economic theoretical concept, as indifference cannot be revealed through action, nor can indifference explain action. Indifference is only useful to psychologist, entrepreneurs, and forecasters.
    • Continuity: assumption that indifference is infinitesimal, smooth. In reality there is no reason to think that economic phenomena are continuous.
    • Assumption that utility function is constant, so that we can empirically measure a demand curve. This is flatly wrong, as peoples valuations are constantly changing.
    • Summarily, indifference is simply an equivocation that allows economists to get to cardinal utility. Bah humbug.
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Very nice.