## Friday, September 28, 2012

### I don't understand this

I don't want to get into the "apodictically certain" stuff in the post. I'm not sure what the point of even worrying about that is. But I didn't understand this point by Peter Klein:

"Both the Austrian and neoclassical approaches to demand begin with an ordinal preference ranking. But the understandings of marginal and total utility are completely different. For Menger, marginal utility applies only to discrete units of a homogenous stock of a good. The fourth apple is allocated to a lower-valued use than the third apple, and so on. The law of demand follows from the fact that additional units of a homogenous good are used to satisfy lower-ranked ends. Note that for the Austrians, the term “marginal” applies to the units, not the utilities. “Marginal utility” is the total utility of the marginal unit, not the marginal utility of a unit. There is no larger concept of “total utility,” of which marginal utility is a little slice."

The bolded part, specifically.

What is the difference? Why would you make a claim like that? Isn't this just fundamental theorem of calculus stuff? I don't see what the difference is.

1. Fwiw, I don't get it either.

2. Is he not just saying that , to use the example of the apples, that what matters is the utility of the fourth apple , which is the marginal unit, not the additional (marginal) utility added by the fourth apple to the total utility of apples. In other words you will compare the utility of the fourth apple to the utility of alternatives goods when deciding which one to buy . This is meaningful comparison. Adding the marginal utility of successive apples together to get total utility of apples would not be possible of meaningful.

1. Right, but what is the difference between:

1. I will compare the utility of the fourth apple to the first orange

and

2. I will compare the utility added by the fourth apple to total utility to the first orange.

I understand the meaning of what Klein is saying. It just seems like a distinction without a difference.

2. I don't think that the debate here is particularly important. I think the neoclassical approach can work. But, it's complicated (especially if you get into Von Neumann's approach) and I find Bohm-Bawerk's system simpler.

For example, if have a spare 15 euro then I look at the purchases available to me and decide which ones I prefer the most. I then make that purchase. I don't have to attribute utilities to them, only a preference order. I may prefer to buy a shirt for example, I don't need to work out how much more I prefer that to the next available choice.

I never have to compare the utility added by the fourth apple to the first orange. Nor will I compare the utility of the fourth apple to the total utility. Those are not an important questions.

3. If you don't think that total utility is a meaningful concept then statement 2. would not be seen as a valid way to choose between the 4th apple and and the 1st orange

1. I guess I don't understand how the total utility of a single good can be critical while the total utility from a handful of goods is meaningless.

How does that make sense rob?

And if it doesn't make sense to make that distinction, how is Klein's other distinction sensible?

2. And if the answer is that the accumulated utility of the first three apples somehow changes when you add a fourth, then that's all the more reason to think in terms of derivatives rather than the total utility of the marginal apple.

4. I have argued with Austrians on this; I think they get into serious trouble when they start talking about diminishing marginal utility, because it certainly invites (if not requires) a cardinal conception of utility. I think there's a way one could handle it properly without painting oneself into a corner, but I think in practice Austrians a lot of times breeze through discussions of DMU in a way that only really works if utility is cardinal. Like to say, "the 4th unit of the good gives less utility than the 3rd unit" is a little weird, because you can't choose between the 3rd and the 4th unit. You can choose between the ends to which they are devoted, but then you run into trouble with using the 3rd egg to make an omelette etc.

Having said that, no Daniel, those statements are not equivalent. I can speak of the utility of the 4th apple meaning "the significance I attach to it," without meaning "what is the delta of total utility when I add a 4th apple?" Just like I can say I feel more friendship for my 4th best friend than I feel for a stranger, without implying that I have friendship units.

1. I don't get the "friendship units" point.

But on the apples, I agree - we can talk about the significance we attach to the fourth apple.

Now, either that fourth apple changes the total utility you have accumulated at the moment of choice or it doesn't.

If it doesn't change the accumulated utility, then there's no difference between saying "the amount by which my accumulated utility changes when I add one apple" and "the utility of this additional apple".

If the additional apple does change the accumulated utility of the first three apples, all the more reason to talk in terms of derivative and not the significance of the fourth apple itself.

Or am I missing something?

Of course cardinality makes this easier to talk about (that's why 99% of economists use cardinality to talk about it!), but I don't see how that point depends on cardinality.

2. Daniel, I'm using "friendship" because that was the best example I could come up with, when teaching, of something that people believe in as an ordinal thing, but that sounds funny as a cardinal thing. So: it makes perfect sense to rank people according to the friendship you feel toward them. You can have a best friend, a 2nd-best friend, and so on. You could even say stuff like, "If some of my friends had to die in a plane crash, I would prefer that the group of XYZ survived instead of ABC" etc. So you can ordinally rank people in terms of friendship.

You could also say stuff like, "Am I better friends with my 8th best friend or with a stranger?" That makes sense.

But it doesn't really sound right to say, "Suppose I have my 1st through 7th best friends at a party, and then the 8th best friend shows up. How much did my total friendship go up? That's what I mean by marginal friendship."

So if you can at least see what that just plain sounds funny, then you can try to get Klein's point about marginal utility. It's not that the stuff you are saying in these comments (and your original post) is wrong, it's that it's meaningless (if utility isn't cardinal).

3. Oh I see - that's actually a good way of explaining the ordinal point. I had never heard that before.

I'm not sure it's meaningless with this, though. Let's say you have a certain amount of pleasure hanging out with friends A and B (your first and second best friend), and you have room for one more person in whatever you're doing so you are deciding between friend C and friend D.

You can say "I like C better than D - considering ONLY the utility from those individual units, because C is my third best friend, I will choose C". That's Klein's "Austrian" way. Or you could say "the change in the total pleasure I am going to have from this activity after adding C to A and B is greater than the change in total pleasure I am going to have if I were to add D to A and B" (that's the neoclassical way).

If the valuation of A and B doesn't change when you add an extra person, these two are still equivalent. However, if it DOES change (say, because of different group dynamics) that's actually a reason to prefer the "neoclassical" method (it always seems weird to refer to "neoclassical" when Menger is in the conversation as a "non-neoclassical").

4. Maybe in the Austrian view you are always comparing sets. So u{A,B,C} > u{A,B,D} > u{A,B}. That's all compatible with completely ordinal utility, without any need for "summing" or "totaling".

5. I think I see your point. If one is comparing 2 bundles of goods - 4 apples v 3 apples and 1 orange then one must have a concept of total utility to make that comparison.

I think Klein (following Menger?) is assuming that one makes the choices sequentially: first you choose an apple as the marginal good that gives highest utility, then as a total separate decision you choose the second apple etc. Each decision just looks at the utility of the marginal good , and total utility is not relevant (or possible to calculate according to Klein).

I just looked at the Klein article and he says:

"Note that if the consumer is ranking bundles, not individual units of goods, and the bundles are heterogeneous, then Menger’s concept of marginal utility does not apply. The consumer attaches a total utility to each ranked good— i.e., to each bundle—but there are no marginal utilities of individual units of goods, because we have no ordinal rankings of individual goods, only bundles"

So he seems to recognize the issue and gets by it (or perhaps sweeps it aside) by saying that bundles of goods can be treated as single goods for the purposes of marginal utility analysis.

However it seems likely to me that when choosing how to spend their money most people would tend to think in terms of the total bundle of goods they will buy and how that will maximize their total utility rather than in terms of the marginal utility of each individual purchase.

My conclusion: I think I need to read Menger !

1. "The consumer attaches a total utility to each ranked good— i.e., to each bundle—but there are no marginal utilities of individual units of goods, because we have no ordinal rankings of individual goods, only bundles"

It sounds like an attempt to have a better psychological understanding of utility. If I go to the store and buy a dozen eggs in a carton, I don't consider the marginal utility of each egg.

In fact, after I have checked to see that no egg is broken, unless an egg sticks out to me, I consider the eggs as equivalent. It makes no sense, then, for me to consider the eggs as having different utilities. This can make a difference in some circumstances. I do not know how the Austrians think about these things, but let me give a possible example.

Suppose that I am considering the value of my vote. One way of looking at it is to say that my vote hardly counts, its marginal utility is almost infinitesimal. Why bother? But perhaps an Austrian could reason this way: U(my vote | everybody else's vote} may be tiny, but, since I do not know everybody else's vote, I cannot write that. Just like the eggs in the carton, I cannot consider my vote differently from anybody else's. I cannot take their votes as given. It therefore makes no sense to talk about the marginal utility of my vote.

6. Hmmm. It sounds like the Austrian concept of utility may be conditional. That is, we can write

U(A|B) , meaning the utility of A given B, but not U(A), the utility of A. Anyway, that's a possible way of formalizing it. What it means philosophically is another question.

1. Right...

...but if "B" is "third" and "A" is "fourth" then there's no interpretation of U(A) besides U(A|B). I'm not sure what this adds.

2. B could be "three" and A "one".

As for what it might possibly add, see my reply to rob. :)

Besides, it is probably better psychology.

3. I think that utility is always conditional, even in neoclassical analysis.

Take the 6 eggs for example. Losing one of the eggs (any one of the eggs) is a small loss. You lose the possibility of making recipes that need a dozen eggs, unless you go to the bother of buying more. Losing two of the eggs maybe a larger loss because that way you lose the possibility of making recipes that require 5 or 6 eggs. And so on, each eggs becoming more valuable through the box.

This can be taken account of in neoclassical style analysis. Some of the ways of doing it are complicated though.

7. Casual empiricism suggests that a brain that gets into a state in which it thinks it does understand the bold portion is no longer capable to communication with the outside world...

8. At one time I did understand it. See Section 4 in this:
http://robertvienneau.blogspot.com/2010/03/survey-of-utility-theory.html

I repeat that section:
[START]
Some see commodities as being chosen as an indirect means to choose something more abstract. As I understand it, Kevin Lancaster depicts a commodity as a bundle of attributes. Different commodities can have some attributes in common. A choice of an element in the space of commodities can then be related to an element in a space of commodity attributes.

The early Austrian school economists thought of goods as being desired for the satisfactions of wants. Water, for example, can be used to water your lawn, to satisfy a pet's thirst, or to drink yourself. One can imagine ranking wants in disparate categories. I am thinking of the triangular tables in Chapter III of Carl Menger's Principles of Economics, in Book III, Part A, Chapter III of Eugen von Böhm-Bawerk's Positive Theory of Capital, and in Chapter IV of William Smart's An Introduction to the Theory of Value. The tables are triangular because the most pressing want in one category typically is less pressing than the most pressing want in another category. An element in the space of commodities corresponds to the set of wants that the agent would choose to satisfy with the quantities of commodities specified by that element.

This mapping from quantities of commodities to sets of wants leads to a redefinition of marginal utility, which one might as well designate by a new name - marginal use. The marginal use of a quantity of commodity is, roughly, the different wants that would be added, with a set union, to the set of wants satisfied by the the given quantities of commodities with that additional quantity of the given commodity. McCulloch shows that a ranking of wants in different categories can arise such that a measure does not exist for the space of sets of wants. (A measure in this sense is a technical term in mathematics, typically taught in courses in analysis or advanced courses in the theory of probability.) He argues that the Austrian theory of the marginal use is thus ordinal. Surprisingly, his argument implies that the law of diminishing marginal utility does not require utility to be measured on a cardinal scale.
[END]
I do not know why the Austrian conception is of any more than historical interest or what it can say that Lancaster's approach cannot.

9. Ah, Austrians:

The people who refuse to accept "yes" for an answer.

Who want to keep on arguing after everyone else has agreed with them.

Who refuse to declare victory in the war of 1871.

It's like finding *American* soldiers still fighting WW2 deep in the Philippine jungle

10. I think that the Austrian approach really is different to the other approaches. Nor are the other approaches really all the same as Robert Vienneau mentions. Lancaster's approach seem similar to Bohm-Bawerks, though I doubt it's exactly the same.

But, I don't think that all these different theories really mean that much different in practice. Today we have the choice between so many different goods and so many different combinations of goods that I doubt anyone could come up with a practical situation where the results would be different.

He's a challenge: can anyone think of a example situation where the different theories of marginalism would lead to different outcomes?

It seems that it's only interesting if you're into the philosophical underpinnings of the ideas. That doesn't interest me so much.

I still very much like Bohm-Bawerk's version though because it's simple to explain and close to how people think in practice.

11. FWIW, here is my comment to Klein's post:

From the Austrian point of view, instead of referring to “diminishing marginal utility” might it not be better to refer to the “diminishing utility of the marginal unit”?

1. If you like adding pointless words to get across the same point. The Austrian position is that there is no concept of summing the utility of units into some kind of "total utility" of which the "marginal utility" is just a piece. It refers specifically to the marginal unit, which has a diminishing utility in the sense that the units I already had, I applied to the most useful things, and if I were to give one up, it would be the least useful of what I have those units doing.

12. Bob posted on this on his blog and there's a long discussion over there in the comments which may interest some people.

http://consultingbyrpm.com/blog/2012/09/i-really-tried.html

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