29 Sep 2012

## I Really Tried

So Daniel Kuehn didn’t understand what Peter Klein was getting at when Klein wrote this:

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. [Emphasis from Kuehn.]

So I tried to explain–twice–in the comments, with this kind of analogy:

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 [t]hat 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).

And here is what I got for my troubles:

==> Daniel kept observing that if we assume utility is cardinal, then it makes sense to talk about utility as if it were cardinal.

==> Brad DeLong mocks the Austrians for holding such nutty views on utility.

==> Nick Rowe mocks the Austrians for not realizing that every economist agrees with them on utility.

Forget this, it’s time to catch up on more episodes of Breaking Bad.

#### 90 Responses to “I Really Tried”

1. Tom E. Snyder says:

I posted this in response 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”?

2. David Friedman says:

1. Your comments seem to miss the fact that Von Neumann showed how to make utility cardinal, in order to analyze choice under uncertainty, quite a long time ago.

His approach would work for friendship too, if what we want to measure is something like “how much do you enjoy the company of each friend” or even “how important to you is the existence of each friend.”

One would ask questions like “would you rather have A attend your party for sure, or a coin flip where heads meant B would attend, tails C would?” That gets you from an ordinal ranking of uncertain outcomes to a cardinal ranking of certain ones, provided only that your choices under uncertainty meet some fairly simple consistency conditions.

2. “The law of demand follows from the fact that additional units of a homogenous good are used to satisfy lower-ranked ends.”

Not necessarily. Car tires are a homogeneous good. But the utility to you of the fourth tire is greater than of the third. It’s pretty easy to come up with other such examples.

• Joseph Fetz says:

Then why is it cheaper to buy a set of four tires than it is for a set of two, or a single tire?

• Tel says:

Because the garage always buys them in fours, and if they sell one to you, they need to look around for someone who wants to buy three.

• Bob Murphy says:

Dr. Friedman I am not sure I agree that vnM’s conditions are “fairly simple.” But that’s not really what I was trying to do here. Daniel seemed not to even get what the distinction was that Klein was drawing, and in his explanations of his confusion, he kept assuming utility is cardinal. So yes, Klein’s distinction makes little sense if utility is cardinal, but it makes perfect sense if utility isn’t cardinal.

Now you are pointing out that under fairly simple (in your opinion) conditions, we can give a working definition of cardinal utility. Sure, but I was only trying to explain what Klein was even saying there, since Daniel seemed not to understand (and Brad DeLong also seemed to agree that Klein was speaking utter nonsense).

• marris says:

von Neumann has a clever hack, but suppose I really hate any kind of uncertainty? Does the hack still work?

Given A, B, C, and the choice A or coIn(B,C), I pick A. Given the choice B or coin(A,C), I pick B. Given the choice C or coin(A,B), I pick C.

I can think of a plausible story for why I’m making these choices: I hate not knowing who is or is not coming to my party. Given these reasonable responses, can you still build a cardinal utility function?

• Major_Freedom says:

Re: The car tires:

Dr. Friedman, the way I understand the passage you quoted from Murphy is not to consider each tire a homogeneous good, in which case your criticism is valid, but rather, to consider the set of 4 tires as a homogeneous good unto itself.

So the quote: “The law of demand follows from the fact that additional units of a homogenous good are used to satisfy lower-ranked ends” is correct, if we consider the first unit as a set of 4 tires, and the additional unit as an additional set of 4 tires. Here, a second set of 4 tires will be used to satisfy a lower ranked end than the first set of 4 tires.

The important thing, as I understand marginal utility in the Austrian conception, is not to focus on the physicality of the goods, but on the valuations from the subject, the actor.

Suppose another example: apples to bake a pie. If apples are going to be used for baking an apple pie, then we have to consider a “homogeneous unit” of the apple good to be the 5 or 6 apples. Then, the second unit of the homogeneous good of 5 or 6 apples will be ranked lower, etc.

David, I’m sure you and Daniel could learn a bit from comic book reading. Here you can learn what is meant by subejctive value: https://picasaweb.google.com/Lilburne2/HumanActionComics3#slideshow/5399235846776572482

I still am missing where these amazing numbers or probability have calculated any individual’s preferences accurately. The assumption that there are 4 distinct axioms to then use a mathematical formula to understand the value of that decision is absurd. These are mere categories invented by Von Neumann to attempt to apply value to human emotion or desire, which is itself still subjective and unknown. These things are only known by the individual actor. How can a mathematician ever derive such absurd calculations if they are not the individual actor performing the acts. This is where Mises was far superior to all economists and mathematicians that attempt to apply numbers to human value.

Ordinal value scales can be the only realistic prediction an economist can make. Beyond that it is completely subjective and left up to the actor. Furthermore, all action is rational, otherwise the actor would not act. Mises also made this clear in Human Action. Thus von Neumann’s attempt to give truth to cardinal utility by suggesting it can transform into ordinal utility is ridiculous. Firstly, cardinal utility is a complete misrepresentation of a person’s values. Me loving .00001 apples more than 1 apple is a huge assumption on subjective value of individuals. Perhaps to build a bridge I could suggest .0001 more amounts of steel would be necessary to strengthen its beams, but even then, who would build a bridge with such detailed modeling. Perhaps the weight or pressure one can use such numbers, indeed this is important since any amount could influence the bridge’s durability. But as a physicist, such calculations are necessary since the calculations of an unmotivated object are much easier to predict and mold. Yet the calculations of motivated object are very difficult to undertake, such as the ones used with cardinal utility.

Actors are motivated to move in subjective ways, rational within their own self-interest. Mises’ axiom of action encompasses the rigamarole Von neumann delineates within his 4 axioms, and does so with more accuracy. Von neumann’s axioms are attempts to define subjective notions of the actor, they are thus not axioms at all. Mises’ axiom is that of rational action. If the actor felt no uneasiness he would not act. Yet all actors sense uneasiness thus they are all always acting. Perhaps now you can see how equilibrium will never be attained. Milton Friedman thought it could be attained and felt the Fed should print more money to attain it, making people poorer with inflation and all. Read his books, perhaps you still have access to his library. Otherwise Rothbard can teach you what your father never knew:
http://mises.org/daily/3638/A-Note-On-Mathematical-Economics

• Matt Tanous says:

“One would ask questions like “would you rather have A attend your party for sure, or a coin flip where heads meant B would attend, tails C would?” That gets you from an ordinal ranking of uncertain outcomes to a cardinal ranking of certain ones”

Er… how? For one, this would seem to result in an ordinal ranking between a certain outcome of A coming as opposed to a random choice between B and C.

Secondly, you still have the problem of surveys. The people could change their mind at any point, might conceive as the issue in the abstract with no real consequence (changing their behavior), seek to answer the question as they think is expected, or even be outright lying for unknown reasons. You can’t prove anything like utility with surveys!

• Maurizio says:

Car tires are a homogeneous good. But the utility to you of the fourth tire is greater than of the third. It’s pretty easy to come up with other such examples.

in Man, Economy and State, Rothbard responds to this objection by noting that, in this case, a single tire cannot be considered a true unit of a supply. The proper unit would be a set of four tires. In this case, it is true that the N-th unit has less utility than the N-1-th.

In other words, for Austrians, the law of diminishing marginal utility always holds, but it does not hold for any choice of the unit. You have to be careful to pick as your unit a basket of goods such that the law holds by definition.

• Jonathon Hunt says:

To make this law hold, we organize the goods to make this law hold? Isn’t that a little circular?

• Christopher says:

To make this law hold, we organize the goods to make this law hold?

Not quite. What counts as one unit depends on the perception of the people involved. If I look at a car, I perceive it as one unit, although it consists of thousands of parts. A car parts dealer might look at the same car and see a rare bumper. For him the bumper is one unit, because that’s the way he perceives it. Note that nowhere in this definition I refer to utility.
So, according to this, there is no way to tell whether four tires are four units or one, because it depends on the perception of the person looking at it.

Then, based on this definition of units, we can talk about utility.

• Matt Tanous says:

And if you look at it as four different units to be used for separate tasks, the fourth tire does have less utility than the third. If you use them as a whole, then you are not using a unit of one tire, but a unit of four together.

• Bala says:

Just to add to what Christopher said, the proper unit is understood from the perspective of the acting man and the action. Taking from MF, if the cake you are baking requires 6 eggs, then the proper unit is 1 set of 6 eggs. The supply of eggs would then be valued in terms of sets of 6 eggs. If you have a supply of 10 units of 6 eggs each, the marginal utility of the supply is not the utility of one egg but of one set of 6 eggs or 1 unit of a supply of 10 sets of 6 eggs each.

So, there is no circularity. That the unit has to be chosen carefully is not a result of the need to comply with the law of (diminishing) marginal utility but a result of the fact that proper definition of the unit and hence the marginal unit is a prerequisite to talk meaningfully of marginal utility. If you do not define the marginal unit right, you could be way off the mark.

• Christopher says:

Well, to be fair, there is some sense of circularity built into this. If you say that 6 egg form one unit because they are used to bake a cake, you’re quite close to talking about utility.

• Bala says:

No. The unit of 6 eggs are one unit not because they are used to bake a cake but because acting man is subjectively appraising their usefulness towards the end of baking a cake. The unit of 6 eggs is a part of the recipe of the cake and that is a “technological requirement” for the particular cake acting man values.

Acting man values the cake. Hence, he appraises the usefulness of the unit of 6 eggs. I don’t see the circularity. You are mixing up “are used” with “subjective appraisement of usefulness”.

• Robert Fellner says:

Bala,

You do a great job of explaining this concept.

• Christopher says:

You do see that usefulness and utility seem kind of similar, don’t you?

• Robert Fellner says:

Sure do! Which makes sense considering the whole essence of utility and what makes something an economic good is the subjective value or “usefulness” people see in it.

Here’s an example I like. Let’s say you are a wholesale distributor of sugar. 1oz of sugar in this context has utility for you in relation to producing your end product a 5 pound bag of sugar you sell to various grocery stores.

Now that same 1 oz of sugar has totally different utility – and is actually a totally different economic good – when you are at home backing a cake and the recipe calls for 3 cups of sugar but you only have 2 cups at your disposal. It is the usefulness or ends you are using the good for that determines its relative utility to you.

So you are right that the perceived usefulness is what determines its relative utility, as that same usefulness (or subjective value) is what determines the type of economic good it is!

1 oz of sugar to the wholesaler is a totally different economic good than 1 oz of sugar to the person baking a cake, as it is to the housewife grocery shopping seeking to purchase sugar merely to have in her kitchen for possible later uses.

The various different ends are what determines, and thus change, the nature of economic good in each scenario, and thus the relative utility of said good.

This is why I said Bala did such a good job, I tend to ramble whereas I thought he nailed it in his very first sentence about the unit of 6 eggs for baking a cake!

• Christopher says:

Robert,

we were talking about Jonathon’s claim that this definition of unit seems a little circular. Now you are saying

So you are right that the perceived usefulness is what determines its relative utility, as that same usefulness (or subjective value) is what determines the type of economic good it is!

See the problem?

Utility depends on the definition of ‘unit’ and the definition of ‘unit’ depends on its usefulness/utility.

• Robert Fellner says:

Utility depends on the definition of ‘unit’ and the definition of ‘unit’ depends on its usefulness/utility.

I certainly concede they are deeply intertwined concepts.

I would only add that the definition of unit depends on the end being pursued. So 1 oz of sugar for baking a cake is a different unit than 1 oz of sugar for wholesale because they are being used towards different ends.

• Robert Fellner says:

So I wouldn’t say that unit is defined by utility – which certainly would be circular – I’d say its defined by the ends the actor is pursuing when valuing the good.

• Bala says:

Christopher,

You are still getting it wrong. You said

“Utility depends on the definition of ‘unit’ and the definition of ‘unit’ depends on its usefulness/utility.”

The correct form is

Utility depends on the definition of ‘unit’ while the definition of ‘unit’ depends on the use or the particular action and the technological recipe.

You also said

“You do see that usefulness and utility seem kind of similar, don’t you?”

Of course!! Utility IS the subjective appraisement of the usefulness. As I said, the unit is linked to the use acting man is putting it to and the number of units of the physical good that are, as per the recipe acting man possesses, essential for the action and the end sought to be attained.

So, the situation is B is defined by A and B in turn determines C. There is no circularity. You need to distinguish between “use” and “usefulness”.

• Maurizio says:

To make this law hold, we organize the goods to make this law hold?

Rothbard’s point is that a single tire is not a good, only four tires are a good. This is true for reasons other than making the law hold: it is true because a single tire does not allow the actor to reach any objective, only four tires do.

So the Austrian approach is consistent.
My concern is that it might not be _useful_. For example, the Austrian cannot say the following: “a producer produces until marginal benefit barely equals marginal cost. so, if you impose a tax on sales, the marginal unit will have more costs than benefits, so he will not produce it.” The Austrian, it seems to me, cannot say the above, because the marginal unit might be a huge set of commodities, not a single commodity, so the tax may not be big enough to make its costs more than its benefits.

• Major_Freedom says:

My concern is that it might not be _useful_. For example, the Austrian cannot say the following: “a producer produces until marginal benefit barely equals marginal cost.

Don’t worry, 99% of real world businesses don’t say that or do that either.

• Maurizio says:

care to explain? I though it was true by definition that you produce until marginal benefit barely equals marginal cost…

• Christopher says:

Statement that are true by definition are mostly either wrong of useless in practice.

• Major_Freedom says:

I though it was true by definition that you produce until marginal benefit barely equals marginal cost…

…in certain economics textbooks, probably those that deny the fact that in many instances, prices are determined by the costs of production (which is very much consistent with the Austrian notion of prices being determined by the value of the final output).

The theory of prices that assumes production is expanded until marginal revenue equals marginal costs is derived from a certain form of a prior theory: pure and perfect competition, namely, the notion of monopolistic restriction of supply for large firms.

If a seller can learn that his own costs of production are no higher than his competitors’ or potential competitors’ costs, then in pricing his goods in accordance with his costs (above his costs in order to earn the going rate of profit) – he can make it so that he is not undersold, and not attract new competitors.

If he can learn that his own costs are very much below his competitors, then he will typically set his maximum price to be as little above his competitor’s costs as possible, so that they cannot earn too many profits nor expand their capital too much, and to discourage new competition.

The reason there is such a divergence between the “marginal revenue equals marginal costs” theory, and pricing reality, is because of a pendulum effect derived from a rejection of the classical labor theory of value. Post-classicals threw the baby out with the bath water and rejected the nuanced views of folks like Ricardo and Bohm-Bawerk, who understood that in many cases, costs of production are indeed the direct determinant of prices.

Because of this, mainstream economics was led into the position of believing that because every good must be determined by the specific supply and demand for each good, that is, by its own independent marginal utility, then in the absence of a vast number of independent, insignificantly sized firms, sellers will be able to exploit a product’s elasticity of demand, and in the process, when considering the real world, they are driven to believe the world predominates with “imperfectly competitive” firms, because there are not enough sellers in each field that would eliminate such alleged exploitation.

Ergo, we now see “anti-trust law” attacks against large successful firms, who allegedly restrict supply, allegedly exploit price elasticities, and allegedly fail to expand production so that prices are consistent with marginal revenues equaling marginal costs, as ignorant theory insists it “should”.

• Matt Tanous says:

“a producer produces until marginal benefit barely equals marginal cost”

Why not? The decision to produce, as an action, will be performed until the production of one more unit (as the producers sees it) is below the subjective utility of alternate uses of labor/time/resources. I don’t see why the Austrian cannot make your statement.

Just not because of a tax, as a tax – imposed universally on all producers of a good, or the entire economy – is imputed back through a shift in the supply and demand curves for producers goods and labor services, so will not affect production, however.

• Maurizio says:

You have to be careful to pick as your unit a basket of goods such that the law holds by definition.

To be more precise, in the above example a single tire is not even a good. Only four tires are a good. (So it is not correct to say that they are a basket of goods, as I did).

• Peter G. Klein says:

It amazes me that people can jump into a conversation that’s been going on for about 150 years, think about it for ten seconds, and say “Aha, I’ve found a fatal flaw!”

Other commentators have already explained to David that the relevant unit of analysis in this case is the bundle. I’ll just add that Boehm-Bawerk discussed this problem in detail back in 1881:

http://www.econlib.org/library/BohmBawerk/bbPTC21.html

• Dan (DD5) says:

The tire example is false. Your definition for a homogeneous good is simply flawed and incompatible with subjective value theory.

One car tire alone (or a set of 2 or 3 tires) cannot provide the same service as a set of 4 tires, therefore, a full set of 4 tires is a distinct good, and NOT a 4th homogeneous good of the same type. For each tire to really be valued as a homogeneous good of the same class, they would each have to be completely interchangeable in the services they are put to use. Obviously this is not the case in your example. A set of 4 tires is not interchangeable with a set of 3 tires (or 2 or 1) as far as a 4 tire car is concerned, therefore, a set of 4 tires is a different distinct good, which is why it is valued higher for a car owner then a set of 3 tires. Now, the value of the next set of 4 tires would certainly be lower then the first set.

• Christopher says:

Dan,

what is your take on the objection that this definition assumes its result, namely utility, to define the investigated object?

• Dan (DD5) says:

It’s not a matter of arbitrary definitions, but specific criteria that are praxelogically derived from subjective value theory. In this example, the unit of analysis is a bundle. See Peter Klein’s link above.

• Anonymous says:

Dr. Friedman’s tire example is wrong. In this case, a “driveable car” is the marginal unit whose utility is realized only when it has 4 tires. By Dr. Friedman’s logic, any good can be reduced infinitesimally to smaller and smaller quanta until the last one, which then has a greater utility than all the other quanta that make it.

3. Bob Roddis says:

I always find it easier to get somewhat of a grip on where DK is coming from by reading his strange noodlings on other topics, like his love of the secret drone war and secret Fed loans.

Just like “auditing the Fed” it sounds lovely and democratic and nice, but this is an active front of a war. You’re not violating democratic principles to keep the details confidential any more than we are violating democratic principles by not trumpeting what banks are facing problems or disclosing CIA ops or publishing grandma’s medical consumption (that’s Medicare! that’s a public program! democratic accountability!).

http://factsandotherstubbornthings.blogspot.com/2012/09/the-transparency-canard-more-on-drones.html

“Democratic principles!” Yeah.

• Maurizio says:

Once all you had to do to prove yourself right is to show your argument was consistent with Stalinism; now you only need to show it is democratic.

• Major_Freedom says:

Oh come on Maurizio, surely you aren’t suggesting that democratically elected politicians ordering the assassination of citizens without due process, trial or jury, is in any way shape or form as horrible, evil, or morally contempt as Stalinists doing…the exact same thing…are you?

Violent actions are justified when 50% plus 1 of an arbitrary population of people agree to it, you uninformed extremist dogmatist ideologue.

4. Beefcake the Mighty says:

Bob only deletes comments that step on the toes of people he sucks up to.

• Joseph Fetz says:

5. Jonathan M.F. Catalán says:

In Beefcake’s defense, Bob’s explanation really does make it a lot clearer. I was caught up on the last two sentences of what Daniel quotes,

“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.

I didn’t read Klein’s post right.

• Jonathan M.F. Catalán says:

And by Bob, I mean Murphy. Not sure when “first name basis” is established on the blogosphere.

6. Daniel Kueh says:

Bob –
If we can talk about the utility of one unit and keep things ordinal how is it that we suddenly can’t talk about the utility of a group of units and keep things ordinal?

It’s a funny post, here, but I think you’re failing to address the objections people make. Brad and Nick aren’t commenting in a vacuum. We genuinely find the whole discussion silly and are still waiting for counter-arguments (which of course nobody is obligated to furnish – I’m just trying to set the record straight cause here it sounds like we’re just unthinkingly laughing at him or ignoring your argument).

7. Daniel Kueh says:

Dude – you’re moderating comments now?

Joining the dark side with Brad, huh! 🙂

• Bob Murphy says:

It’s not something I flipped on. Sometimes WordPress makes a person’s comment go into moderation and I really don’t know what the rhyme or reason is.

• Bharat says:

Perhaps it’s because he spelled his name wrong?

8. Daniel Kueh says:

Now that’s not fair to Jonathan. My understanding is his reading list is quite substantial.

9. RPLong says:

Two points here:

1 – I think all your “friendship” example really does is conflate friendship and utility. The reason you can’t say “How much did my total friendship go up at the arrival of my 8th best friend” is because you’re not talking about friendship anymore – you’re talking about utility. There most certainly *is* a marginal utility increase when your 8th-best friend arrives: it is the increase in happiness attributable to having 8 friends present instead of 7. Everything you said about friendship applies equally to “the neoclassical view of utility” as it does to the “Austrian view of utility.”

2 – The whole concept of utility is an artifact of Empiricism, anyway. Whereas, prior to Menger, people actually did think utility was some sort of cardinal value, no one thinks so anymore. In that sense, any “neoclassical economist’s” view of utility is purely theoretical and illustrative. The only reason anyone talks about marginal utility is to express the concept that satisfaction increases on the margin. It’s not really a core theoretical difference between Group X and Group Y, like Klein implies.

So I think Nick Rowe’s criticism is spot-on here. And I think it’s all a result of the fact that Rothbardians refuse to use math when they think. Only someone who rejects mathematical logic could wax about the supposed differences between “the increase in total utility attributable to the marginal unit” and “the marginal increase in total utility attributable to an additional unit.” It is exactly the same thing. The only reason some people see it differently is because they don’t like to think in terms of calculus.

This is perfectly obvious when you consider how far Klein gets derailed when he starts talking about “bundles.” He takes the concept of bundles literally and then complains that the universe doesn’t really work that way. He has forgotten that, in our principles courses, we learn that “bundles” are really just abstract concepts used to illustrate Good X against all other possible goods. Again, this is a calculus concept: the change in X1 with respect to X2, holding X3, X4…. Xn constant. Simple.

Just because Austrians prefer the term ceteris paribus to del-X/del-Y doesn’t mean it’s a whole different way of looking at things. It’s two terms that indicate exactly the same thing.

• Richard Moss says:

RPLong,

You wrote;

“Only someone who rejects mathematical logic could wax about the supposed differences between “the increase in total utility attributable to the marginal unit” and “the marginal increase in total utility attributable to an additional unit.”

I presume you are attributing the bolded portion above as Klein’s? But, Klein did not say there is an increase in total utility attributed to the marginal unit. He said the marginal unit is valued for its total utility. This *is* different from saying there is an increase in total utility; that the marginal unit adds some margin of utility to a previous total utility. (Further on in the quote Klein explicitly says “There is no larger concept of “total utility,” of which marginal utility is a little slice”. Again, this is not all at consistent with what I take as your rendition of what he said).

I only think this underscores that, when it comes to treating value as being ordinal vs. cardinal, there definitely is a distinction in how value is viewed.

• RPLong says:

“Total utility” is a figure of speech corresponding to wherever one happens to sit on Rothbard’s rank of preferences. Murphy and Klein take the concept of utility-as-quantity too literally and, unsurprisingly, discover problems with that view. The neoclassical approach to utility is *not* to treat it as a quantity. That would be the classical (i.e. empiricist) treatment. Everyone in today’s world knows utility isn’t cardinal; we learn that in Econ 101.

• Richard Moss says:

RPLong,

First off you say Klein’s position is ‘too literal’. Fine, but that is not what you said above. You rendered (I say – you didn’t challenge me) his position as something he did not say without an explanation.

You also wrote;

“The neoclassical approach to utility is *not* to treat it as a quantity. That would be the classical (i.e. empiricist) treatment. Everyone in today’s world knows utility isn’t cardinal; we learn that in Econ 101.”

I am willing to admit that neo-classicals know that utility is not cardinal. I think Bob Murphy has explicitly recognized this in previous posts, and I don’t think Klein claimed this in his post.

But I think they certainly do *treat* it as cardinal, as I think you did above; rendering Klein’s point you treated his position as a cardinal one. And, as Murphy noted, Daniel Kuehn couldn’t discuss the issue without reverting to ‘cardinal’ concept (i.e. supposing a a given amount of pleasure, etc.).

So, I think Dr. Klein’s point stands. There is a fundamental difference on how marginal utility is viewed by Austrians and Neo-classicals. I couldn’t say whether this amounts to a hill of beans in application, or not. But, there is a difference. I don’t see the problem in calling attention to it (especially when Klein was defending Horwitz’s ‘a priori’ view of marginal utility against Caplan’s challenge that, therefore either it did not fit reality, or was, indeed, different).

• RPLong says:

First, I didn’t change my story, so when you say “that is not what you said above,” you’re either not being completely fair, or you are not seeing the forest from the trees.

When you obtain additional satisfaction (i.e. utility) from the marginal unit of something, then you are adding the “marginal utility” to whatever prior state of nature existed beforehand. You can call that state “total utility,” or you can call it “hocus pocus” or you can call it “mojo,” or you can do what the Rothbardians do and suggest that it is irrelevant to discussions of marginal utility.

But whatever you choose to call it or not call it, it is a concept nonetheless. The fact that neoclassicals call it “total utility” does not mean that they conceive of utility differently than Austrians. Like their use of mathematical notation, it just happens to be different terminology denoting the same thing.

Austrians like Klein can either choose to join the same conversation everyone else is having, or sit on the outside lamenting the nomenclature.

• Richard Moss says:

If in the future Bryan Caplan charges the Austrians with having a theory of marginal utility that doesn’t fit reality, and you convince him the Austrian position is essentially no different than his, despite what its more ‘literal’ interpreters say, maybe I could better see your point.

*sorry, hit submit by mistake before finishing.

Mr Long, I’m pretty sure that in Econ 101 we do learn that utility is cardinal. The Neoclassical economists follow more of Jevons’ perspective on utility than one does Menger’s. Murphy has explained this before. Furthermore, the idea of utility the neoclassicals have is very similar to the view that David Friedman took, quite peculiar in transforming a subjective feeling from cardinal to ordinal.

The ordinal approach to utility is many time uniquely deriving from the Austrian school; most specifically from Rothbard. Murphy’s approach is quite correct, I would suggest even reading his book Lessons for the Young Economist or even some great Mises articles on the ordinal approach created by Mises and Rothbard:

http://mises.org/daily/5333/SubjectiveValue-Theory

http://mises.org/daily/5903/

• Richard Moss says:

RPLong,

I think I was fair in saying you rendered Klein as saying something he didn’t. If you want to say the implication of him saying what he did say was what you rendered, then ok (I would disagree, but fair enough). My point was that you did not provide the explanation for it.

“Austrians like Klein can either choose to join the same conversation everyone else is having, or sit on the outside lamenting the nomenclature.”

I think you are being a bit dramatic here. Klein is not sitting on a sideline. He is expressing a genuine disagreement.

If in the future Bryan Caplan charges the Austrians with having a theory of marginal utility that doesn’t fit reality, and you convince him the Austrian position is essentially no different than his despite what it more literal interpreters

• Maurizio says:

Everyone in today’s world knows utility isn’t cardinal;

How can you reconcile this claim with what prof. David Friedman said in a comment above?

• Daniel Kueh says:

Preferences are ordinal. Utility is cardinal. Preferences are real. Utility is an extremely convenient fiction.

That sometimes these discussions sometimes get confused doesn’t change the fundamental point that everyone agrees that preferences are ordinal.

Mr Long, “Again, this is a calculus concept: the change in X1 with respect to X2, holding X3, X4…. Xn constant.”

The calculus concept is still very abstract. The utility approach will dervie you an unnecessary number that attempts to define utility. Utility is subjective, how can it be that a person can apply a number to utility and measure “utility” as having that number value. That is where they have arrived at an incorrect conclusion. It is the mere number applied to a subjective satisfaction (utility) that renders a subjectivist approach to cardinal utility completely incorrect. No motivated act can be said to have a measured utility in numbers, only unmotivated acts can–such as rocks, gravity and the like. IMotivated acts will always simply have to have an ordinal approach the way Mises and Rothbard delineated. It begins with teh axiom of action, and to tear apart the axiom of action with numbers that are irrelevant to the individual actor–since he thinks subjectively–turns the cardinal approach of utility into something that David Friedman tried explaining above. It is inconsistent with reality. I posted a link above to Rothbard’s perspective to mathematics in economics. Remember he was a Misesian and Mises understood economics began with the axiom of action. To use calculus to find the intricacies of action, utility, is to attempt to debunk the axiom of action itself. It is no longer praxeological and looks horrendous in practice like Von Neumann’s approach David Friedman mentioned above.

• Tel says:

There most certainly *is* a marginal utility increase when your 8th-best friend arrives: it is the increase in happiness attributable to having 8 friends present instead of 7.

Utility might go backwards if there are only 8 places at the dinner table, and you only cooked enough for 8 people. Also, maybe friend #6 always starts fights with friend #8 so it’s just best to never invite them on the same night. No guarantee that the preference graph for subsets of friends is acyclic (actually in the case of friends, highly unlikely to be acyclic).

The only reason anyone talks about marginal utility is to express the concept that satisfaction increases on the margin.

Hmm, I seem to remember that in order to calculate derivatives, you need a cardinal measurement. At least, what does the partial derivative of a well ordered set produce? What is it with respect to?

• Bhara says:

I think the correct mainstream formulation would be to argue for the marginal utility to be the delta in total utility, not simply some addition. In this case, the change would be negative.

So that being said, wouldn’t the Austrian definition also apply the same way? Since the Austrian definition is that marginal utility is the value of the satisfaction reaped from the marginal unit, even that must take account of the fact that previous units exist. Therefore, the satisfaction of the marginal unit in this case will also be negative; in other words, it is no longer a ‘good’ but a ‘bad’. Diminishing marginal utility in the Austrian sense still applies; the utility of this 8th friend is still less than the 7th, but it happens to be negative is well.

To summarize, my point is that both the delta in total utility (the mainstream definition) and the satisfaction reaped from the introduction of the 8th unit (the Austrian definition) are equivalent even in a case of the addition of a negative.

• Bharat says:

Hm, I realize I’m just assuming you’re arguing against the neoclassical definition of marginal utility based on what you say further below; let me know if I’m wrong.

• RPLong says:

To your first point, you’re not describing a ceteris paribus situation. If you don’t hold all other things constant, then sure, anything is possible. Maybe friend #8 is a psychopath. Maybe the added weight of friend #8 causes my floor to collapse. Maybe I’ve been cursed by a witch such that I turn into a newt whenever I am in the presence of more than 7 close friends. Maybe a hunded billion things. What does that prove?

To your second point, a derivative most certainly does NOT require cardinal measurements. Mathematical axes in economics describe hypothetical vector spaces, not necessarily cardinal measurements of anything. *I* cannot quantify *your* utility by modeling *my* preferences, but that doesn’t mean that I can’t quantify *my own* utility by modeling *my* preferences. The “trick” is knowing what you’re talking about and venturing no further.

• Matt Tanous says:

“There most certainly *is* a marginal utility increase when your 8th-best friend arrives: it is the increase in happiness attributable to having 8 friends present instead of 7.”

How many utils? Or happies? Or whatever.

You are slipping into cardinal utility. The lesser marginal utility of having an 8th unit as compared to the 7th unit means I value the 8th unit less than the 7th unit – I want to use it for an end that is less valuable than the ends I have already used the first 7 units for. I can’t somehow add these things up. It’s equivalent to adding up the enjoyment from baking a cake and a plate of biscuits.

• RPLong says:

What? No. Two of the same good is never equivalent to one unit each of two different goods.

Saying “I get 3 utils of happiness from one apple, and I would be 1 util better off if I had another apple,” is cardinal utility. That’s wrong.

Saying, “I get satisfaction from one apple, and I would get even more satisfaction from having an additional apple, albeit to a smaller degree than I was satisfied by the first apple” is both entirely ordinal and entirely consistent with both Austrian and neo-classical economics.

All I’m saying is that you can express this with words or mathematical notation, and it makes no difference. It does not alter “the way you look at marginal utility.” That’s silly.

You have to be able to think abstractly, though…

10. Bharat says:

Do Austrian use the terms ‘value’ and ‘utility’ interchangeably?

• Bharat says:

Austrians*

• Bharat says:

(I always believed they do; this is just a clarification for me)

• Christopher says:

No, the value of a product equals its marginal(!) utility – not its utility per se.

• Christopher says:

Just an example:

You just ran a marathon and are extremely thirsty. So you decide to drink one bottle of water – this particular bottle of water has an extremely high utility.

However, if your basement is filled with so much bottled water that you could never drink all of it even in one year, the value of the bottle you are drinking to you is pretty low, because it equals the utility of the last bottle of water that you would drink after you have finished all other bottles.

• Tel says:

Thus if gnomes sneak into everyone’s basements with tiny hammers and smash most of the stockpiled water supply, then the value of the remaining water increases for everyone.

The attack of the gnomic value adders!

Let’s hope the little people aren’t on Krugman’s payroll, or they’ll break your windows too.

• Christopher says:

I’m not sure where you are coming from, but yes, if there are only a few bottles of water left on this planet value per unit for water will be pretty high. But that doesn’t mean destroying water increases the aggregate value of water. In any event, this has nothing to do with what Krugman means when he talks about the new iPhone.

I think you are confusing something here.

• Bala says:

Not exactly. “Value” is associated with ends and means while utility is associated with means alone. Means are valued because of the value of the end-satisfaction they enable and the subjective appraisement of their usefulness in satisfying the end. Hence, you could say that value of means (as in their ranking on the value scale) is derived from their utility but ends are valued as such.

In my assessment, Austrians do not mix up value and utility.

• Christopher says:

So what you mean is ‘being happy’ has a value but no utility, right?

I think we are talking about two different kind of values then. I think what Bharat meant was economic values (like prices) as opposed to moral or immaterial values like satisfaction or having a healthy family.

If we are talking about economic values, I think you can’t make that distinction because it seems difficult to me to attribute economic values to ends.

I dont know, maybe I’m just not getting you point.

• Bharat says:

I was talking about value as ‘subjective value’, what I assumed was equivalent to the satisfaction reaped from a good. For example, if we say Tommy chooses to eat ice cream rather than pizza, he values and prefers the ice cream over the pizza, that ‘value’ being the satisfaction gained when he consumes the ice cream and the ‘value’ that he predicts would have been his satisfaction had he instead chosen the pizza.

Although I’m not sure it’s appropriate for me to say what my definition was when I was basically asking for definitions haha (asking if there is a distinction is basically the same as asking for one or two definitions, right?).

• Christopher says:

So Tommy gains more pleasure from eating ice cream that he gains from eating pizza. So we can say that ice cream has a higher utility for him. But to say what he values more, we need more information.

Let imagine lucky Tommy lives in a town full of ice cream parlors. They are literally all over the place on every corner. But there is only one pizza place which happens to be on the other side of the town. When he feels like eating ice cream, he wouldn’t dream of walking 10 miles to get on. He would say “It’s not worth it. I can just get ice cream right here instead.” So ice cream is nothing that he would spend half a day walking through town for. He doesn’t value it enough. But when he feels like eating pizza he puts his boots on and goes for a hike. Because since there is no alternative, it makes sense to do so.

Ice cream has a higher utility per se, but pizza has a higher marginal utility and therefor a higher value.

Another example would be water and diamonds. A bottle of water has a much higher utility than a diamond and yet people are willing to pay much higher prices for diamonds. Or think of oxygen! Although the breath I just took had an extraordinary high utility for me, I’d not pay one cent for it.

• Bhara says:

Okay, I finally understand what you were trying to tell me as well. Thanks Chris.

• Bharat says:

Oh okay, this makes sense, thanks Bala.

• Bala says:

Happy to clarify. However, I wish to add the point that this is actually a very fine though fundamental point. The best of us sometimes do get confused on this point (including Prof. Murphy himself. If you doubt what I say, check out what he says on page 65 of his dissertation. It reveals the confusion very well.)

https://files.nyu.edu/rpm213/public/files/Dissertation.pdf

• Bharat says:

You have a keen eye, but just to make sure, is this what you’re talking about?

“In sense (i), time preference refers to the greater valuation, on the margin, of a
present good over a future good, or of present ‘consumption’ over future
‘consumption.’ It is the “nub and kernel” of Böhm-Bawerk’s theory of interest. If
an individual possesses time preference in sense (i), then he values a present apple
at time t1 more than he values a risk-free claim (given to him at t1) for an apple that
will be delivered in t2.”

• Bala says:

You are right. The very statement is incorrect. In fact, so is sense (ii) given on the following page. As I understand it, Time Preference refers to the preference for end satisfaction now over end satisfaction in the future. The preference, and hence the “greater” valuation of a present good over a future good is a consequence of this point, though not the primary definition of time preference. Prof. Murphy is mistaking the manifestation of time preference for time preference itself.

Sense (ii) is worse.

11. Nick Rowe says:

Bob. I wasn’t really *mocking* the Austrians. *Teasing* them a little, yes. Don’t you think there’s just a bit of truth in what I said?

• Bob Murphy says:

Nick, if Brad DeLong had merely said we Austrians were tying ourselves up in knots, trying to explain our wacky position, that would have been fine. Or, alternatively, if you had merely said that we Austrians were tying ourselves up in knots, trying to distinguish our position from the identical one held by the mainstream, that too would have been fine.

But it was getting hit by both of you in rapid succession that made me post.

12. Jonathan M.F. Catalán says:

Nobody quote me on this (and it’s been a while since I read Menger’s Principles), but the word “utility” derives from Jevons, whereas Menger used something closer to “satisfaction,” right? Maybe the use of the word “utility” obscures the argument, because when you think of “utility” sometimes it has the same connotation as “capital,” and you get an idea of something homogenous (the “util”). But, utility may not be homogenous, and if it’s not homogenous then it can’t be aggregated.

13. Tel says:

You could make the same argument about medicine. Suppose I need some medicine and pill #1 is the one that does the best job, but if I can’t get pill #1 then I’ll go for pill #2 which is also OK. However, because of the way these things work, anyone taking both pill #1 and pill #2 has a bad reaction and dies. There’s no possible way as far as I can see to make a cardinal utility out of this (let’s presume the medicine can’t be kept on the shelf for a long time because it degrades so buying stockpiles of #2 while consuming #1 is not workable).

In fact, it’s even worse for medicine because there’s an optimal quantity to consume for the best effect so if I consume either more or less then my utility goes down (again, presuming that stockpiles are not workable).

• no name says:

this is a terrible example–there’s nothing in the cardinal definition of utility that requires that, say, u({x1,x2}) = u({x1}) + u({x2}). the concept of decreasing marginal utility alone declares this. utility functions don’t have to be smooth or monotone, especially if the domain is a finite set.

here’s a cardinal utility function that describes this, assuming you can only consume one of each pill:

u: P({x1,x2}) -> R:
u(X) = {
1, X=={x1}
.5, X=={x2}
0, X=={}
-9999, X=={x1,x2}
}

and of course I can construct ordinal preferences from this utility function.

No name, you just proved why the models of mainstream economists have been so utterly wrong for so long. Furthermore, you have proved why the stock market has gotten ever the more complicated to calculate for investors as well. Perhaps we can set up an idealized model based upon mathematical probabilities as the one you designed to predict a person’s possibilities of choosing an act, yet the reality is that the actor chooses his act subjectively. This is why the simpler ordinal value scale will always be a more effective tool in delineating economics than the more complex mathematical model. It seems to me that the better investors are those that look at the stock of money and liquidity injections into the market to watch certain stocks rise and fall. Furthermore, simpler models like profit and loss that deal with stock prices are always more effective than deep rigamarole that attempts to predict the value of a bond or security. This is because human action cannot be predicted with mathematics. It can’t even be explained with mathematics either. Human action can only be described as a subjective response to individual circumstances, and this is different for everyone. Indeed it is nice to insert all those proofs and numbers you like so much, yet the better economist can explain the market in simpler terms describing variables that are effected by human action. One cannot predict human action, this positivist form of physics is useful only with unmotivated action not motivated action. Your model looks nice though man, keep drawing them out. But be aware the problems of messing with those proofs like you do, it could leave gaping holes for other statist economists like you to design more numbers and equations to assume they can predict the market to do things in other fashions. Hence, mathematical jargon leads to unrealistic models and opens the door for central planning and statism. Good job buddy…

• no name says:

People aren’t that complex, Adrian. And as for my post, it’s a dumb toy utility function, but it contradicts Tel’s claim that it’s impossible to construct any at all. Humans aren’t as complex as we’d like to idealize them, by the way, especially with respect to making choices. If my research in behavioral econ has taught me anything, it’s that.

That said, you really think that mathematical economics leads to ‘statism?’ Clearly you’ve already decided what you want to believe without actually understanding any of it, so I won’t try to convince you, but maybe you should stop sticking your nose into matters of real scholarship.

• Bob Murphy says:

Humans aren’t as complex as we’d like to idealize them, by the way, especially with respect to making choices. If my research in behavioral econ has taught me anything, it’s that.

Do the other people in this field think the same? I thought it was the other way around–that this research showed standard models are too simplistic.

• no name says:

I admit it’s not something I’ve broached with others, and I think you’re misreading what I’m saying. I agree that in certain settings standard models are too simplistic (right now, in fact, I’m working on a paper that shows this in a particular domain).

That said, The postmodernist-esque critique I hear thrown around on the internet (including the comment I replied to) claims that behavior is so context-specific and individual-specific and subjective and emotional that it can’t be modeled, period.

On the contrary, to me it seems like most behavior I look at in micro settings is either 1) Based on heuristics, which means that context is important but doesn’t rule out modeling (and I think that modern economics has come to appreciate the importance of context, a great example being how much of IO has moved from cross-industry analysis to single-industry stylized models); or 2) Completely random.

I understand why humanists might want to argue for every individual being unique (especially college kids, whom the people making this argument usually seem to be), but economic decisionmaking isn’t a realm where there;s that much uniqueness.