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More on Diminishing Marginal Utility (or: This is Why Austrian Economics Drives Me Crazy)

July 2, 2014 41 comments

For those who are new to this blog, I am a pretty staunch libertarian, free-market kind of guy.  So naturally, there was a point in my life when I gravitated toward Austrian economics.  But the thing that really drove me away was when I realized what they believe about utility, especially “diminishing marginal utility.”  There are quite a few things that I think Austrians are wrong about (hyperinflation and Cantillon effects for instance) but the utility thing was special because it is a case where the confusion is plainly obvious if you really understand the mainstream model of consumer choice.

Of course, I figured I would just explain this to them and we would all live happily ever after.  Needless to say, that never seems to work.  But at this point it has become sort of my white whale: convincing an Austrian–just one Austrian–that diminishing marginal utility is nonsense.  Then recently I stumbled upon this paper by an Austrian, on Mises.0rg, in which an Austrian explains exactly what I have been trying, in vain, to explain.  So, what the hell, might as well give it one more try.

Here is a rough outline of the debate.

1.  Austrians claim that utility is inherently ordinal and that cardinal utility is nonsense.

Mainstream economists agree (at least officially) and have a model in which utility is purely ordinal but Austrians don’t realize it because it doesn’t look ordinal to them.

From my first year graduate text:

Toward the end of the nineteenth century, perhaps initially from introspection, the concept of utility as a cardinal measure of some inner level of satisfaction was discarded.  More importantly, though, economists, particularly Pareto, became aware that no refutable implications of cardinality were derivable that were not also derivable from the concept of utility as a strictly ordinal index of preferences.  As we shall see presently, all of the known implications of the utility maximization hypothesis are derivable from the assumption that consumers are merely able to rank all commodity bundles, without regard to the intensity of satisfaction gained by consuming a particular commodity bundle . . .

. . . To say that utility is an ordinal concept is therefore to say that the utility function is arbitrary up to any monotonic (i.e., monotonically increasing) transformation.

2.  Austrians don’t seem to believe in assuming things that can’t be proven to be necessarily true logically.

To this end they selectively reject whatever hypotheses mainstream economists arrive at because they all require some set of assumptions.

3. The one thing that Austrians feel comfortable claiming that they can prove logically without any assumptions whatsoever (except that people act) is the “law of diminishing marginal utility.”

In order to arrive at this conclusion logically, they construct a framework with “means” and “ends” and postulate that a person will always use a good (means) for the highest valued use (end) first and therefore, as they get more of the good, the value of the marginal use falls and thus you get diminishing marginal utility.  However, this is not a conclusion which logically must be true.  It is, rather, the result of an assumption which Austrians don’t notice that they are making.  McCulloch is somewhat unusual among Austrians in that he realizes this and pointed it out in 1977.  This is why the paper caught my attention.  Now that we know an Austrian said it, can we all agree that this is the case?

[See pp. 251, 252 (you can thank Mises.org for copy/paste protecting the document….)]

McCulloch1

McCulloch2

 

Notice particularly the line: “Bilimovic argues as if these are valid deductions from a rank-ordering on W, but that is not the case unless we assume that the wants are unrelated.  So there you have it, an Austrian saying exactly what I have been trying to say.  But then, having said that, he goes on to assume that “unrelatedness” and continue to deduce the law of diminishing marginal utility based on that assumption.  This wouldn’t be that annoying if he didn’t then say this:

Note that the Austrian principle of diminishing marginal utility is a theorem, rather than an assumption as with Gossen, Jevons and Walras. [p. 255]

Okay, it’s a theorem, but it is only a theorem in the sense that it follows directly from the assumption of unrelatedness of uses.  In other words, in no way does it represent something that logically must be true.  It is just something that is true if the assumptions made to get to it are true.  And we know that that assumption need not be, and probably usually isn’t, true.  This doesn’t make the theorem meaningless but it does make it no different from all of the conclusions of the mainstream model which Austrians like to claim are useless….

And what’s more, the assumption made here is more restrictive than those typically made in the mainstream model of nonsatiation, substitution and quasi-convexity.  So, essentially there is no intellectual reason to cling to this means-ends framework and the notion of diminishing marginal utility.  Frankly, I don’t even understand what Austrians think the significance of diminishing marginal utility is.  If I had to guess, I would suspect that they might say that it implies downward sloping demand (and in some cases upward sloping supply) curves, and that is sort of true but the mainstream model does it much better.

It is diminishing marginal value that implies downward sloping demand.  Value, meaning the willingness to trade-off one good for another.  For this to be diminishing, you only need to have the ratio of the marginal utilities (the marginal rate of substitution) diminishing.  It is possible for this to be the case even if there is increasing marginal utility of both goods.  Now, it is true that diminishing marginal utility of all goods will give you diminishing marginal value, so in that sense, diminishing marginal value does imply downward sloping demand curves.  But you don’t need to go that far.  All it takes is quasi-concavity.  That is why the mainstream model assumes quasi-concavity and not diminishing marginal utility, because it is the smallest assumption required to get the type of refutable implications that the model gets.  So let’s review.

1. Diminishing marginal utility is an assumption.

2. It is more restrictive than the assumptions in the mainstream consumer choice model.

3. Therefore, the mainstream model is better.

This follows logically, therefore you can’t question it.  If you don’t see the logic, I will just dismiss you as someone who clearly doesn’t understand logic.  See what I did there?  But seriously, Austrians, this is an intervention.  I’m telling you this for your own good because I love you, I love the things that you love like free markets, property rights and individual liberty, and I want what’s best for you.  The mainstream model is just a better version of your model.  It’s that simple.  Let me put snarkyness aside for a moment and try to explain why.

1. Means/ends is pointless.

The means/ends framework adds nothing.  It only makes it easier to confuse yourself and others.  Economics is about choosing between scarce alternatives.  That means we need alternatives, and we need preferences over those alternatives.  That’s it.  If you are choosing quantities of two goods, all we need to know (by which I mean assume) are your preferences over different combinations of those goods.  It makes no difference why your preferences are what they are or what “ends” you are applying the goods too.

The only thing the means/ends framework accomplishes is to take the case where a consumer has preferences over combinations of the good and make it into a two-stage problem where the stages are essentially identical.  Instead of just saying “they have certain preferences over combinations of the good” you say “they have certain preferences over different ends and the goods can each be used for different ends in different ways.”  But the only thing that matters is their preferences over the different combinations of goods because that is the decision we are trying to model.  So you try to logically deduce what those preferences look like based on what you assumed about the preferences over “ends” and the connection between the ends and the means.  Then you claim that what you are saying about their preferences over combinations of goods is not an assumption, it follows from logical deduction.  But it only follows logically from the (possibly implicit) assumptions you made about their preferences over ends and the connection between ends and means.  You just buried the assumptions one stage deeper.  But this gives you nothing, it makes it needlessly complicated.  The only thing this accomplishes is it makes it easier for you to apply false reasoning in connecting the two levels by implicitly assuming something that is not necessarily true, deceiving yourself into thinking that it is necessarily true because you don’t notice that you are assuming it, and then believing that you have proven something which you haven’t.

So why not get rid of all of that nonsense and just say that people have preferences over different combinations of goods?  I think there are two possible Austrian answers to this.  One is that this is methodologically unacceptable because we are not allowed to make assumptions about people’s preferences that aren’t objectively and immutably true.  But the Austrian making this argument must not have been reading carefully because that is what you are doing anyway and the assumption you are making is more restrictive than the one I am making.  The other argument is that then we wouldn’t be able to sit around and talk about how ridiculous mainstream economics is because then our model would be exactly like theirs. (Okay, so maybe a little snarkyness.  A fish has gotta swim.)

2. You need more than just action.

Nothing follows logically from the single axiom that people act.  Their preferences matter.  Since we can’t observe preferences but only action, there is nothing we can say about those preferences that must be true a priori.  If you can’t say anything about those preferences that can’t possibly not be true, you can’t say anything about action period.  If you try, you will just end up assuming something without realizing it.  A careful and responsible approach to modeling action must be very explicit about what it assumes and try to cut those assumptions down to the smallest, simplest, most realistic and least restrictive assumptions possible for the model to “work” and tell you something interesting.  This is what the mainstream model has done and–I can’t stress this enough–our assumptions are less restrictive than yours!

3.  Continuous quantities!

First of all, discreet quantities are not more realistic.  Gasoline, flour, tap water, electricity, labor, cheese, ground beef, and a million other goods are actually measured in continuous quantities.  But more importantly, the consumption of any good properly understood, should be modeled as consumption per some unit of time.  So it’s not the number of cars you buy on a given day on the horizontal axis of the “cars” market, it is the average cars you use up in a year or something like that which is a rate and is inherently continuous.  But even more importantly, it makes everything so much easier and more sensical to use continuous quantities.  I sometimes wonder if you are purposely sabotaging yourselves by forcing yourselves to work with a model that is so unmanageable that no worthwhile conclusions can possibly be drawn from it.  It doesn’t have to be that way.

4.  It really is ordinal utility.

Just because we use a function to represent preferences doesn’t mean they are cardinal.  The numbers have no significance in the model beyond identifying which bundles are preferred to the one in question, which ones it is preferred to and which are neither (in which case the person is indifferent between them).  That is all the numbers mean.  You can plug in any function that preserves the rank ordering and you will get the same results.  This is something we are aware of and are careful about (at least some of us are).  Representing ordinal preferences this way allows us to apply a much higher degree of logic to the problem in much simpler ways than your framework.  This, is a benefit not a drawback.   Typically, we don’t even assign numbers or even a function we just say let there be some function which conforms to the minimum necessary assumptions mentioned above.  The fact that we put an actual function to it with numerical values in order to teach undergraduate students does not make the underlying model cardinal.

So there it is.  If you acquiesce on these points, you arrive at the standard mainstream model.  This has been an Austrian intervention.  Sure it’s one guy doing an intervention on a whole gang of people who all act as a mutual support group for each other, and yes, that does seem to run counter to the established rules for interventions.  So maybe it’s wishful thinking to expect it to be successful.  But that doesn’t mean I can’t waste my life trying.  Maybe if I can get through to one person, and then he can get through to one person, one day all of us true, old-school, ordinal-utility types will be able to band together and have an intervention with the Scott Sumners of the world when they say things like this (good grief!):

As an aside, I believe about 90% of all negative and positive utility in life occurs during dreams, as the feelings tend to be more intense than during waking hours.  (We forget most dreams.) It is only the bigotry of awake people (who control the printing presses) that privileges waking life.

 

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Utilitarianism is a Stupid Idea

May 8, 2014 7 comments

I don’t know what it is about utility but I just can’t seem to read anything about it, with the exception of my boring old “mainstream” economics textbooks, without getting supremely disturbed.  I have spent a lot of effort trying to explain to Austrians how they don’t understand the concept as it is used in mainstream economics.  But whenever I read something by Sumner on the subject I find myself much more sympathetic to their (still misguided) complaints.  To be fair to Sumner, he might be the best monetary economist in the blogosphere and he is about as “conservative” a one as you will find anywhere.  So I agree with much of what he says on most subjects but he frequently disrupts my adoration by reminding me of his utilitarian ways.  Though he often claims to be a libertarian (and in many ways he is), in my opinion utilitarianism in its most common applications is inherently incompatible with individual liberty.

First, let me say that the standard economic definition of utility has nothing to do with utilitarianism.  In a strict economic sense, utility is meant only to represent a rank ordering of a person’s preferences across different bundles of goods or states of nature.  In this context it is nonsensical to compare one person’s utility (or marginal utility) to another’s nor does it matter if marginal utility is diminishing as the same ordinal preferences can be represented by many utility functions with either increasing, decreasing or constant marginal utility in any particular good.  This is all explained in any decent text and I am sure Sumner would not dispute this (I’m not accusing him of not understand the concept).

However, what utilitarians have in mind is something different.  It is the idea that “utility” represents some measure of happiness or satisfaction.  They further suppose that this happiness increases at a decreasing rate as consumption increases.  (It is worth noticing that Austrians also indulge in this assumption of diminishing marginal utility but they do so in an even more annoying way because they simultaneously deny the definition which makes it possible.)  The utilitarian then further supposes that the marginal happiness gained from additional consumption at different levels of consumption is roughly comparable across individuals and they still further suppose that, even though it is not measurable or observable in any way, it is the proper role of government to try to maximize the total utility of all people in society by redistributing wealth (or consumption if you prefer) among them.  This last supposition is where it becomes destructive.

Here’s an example.  A billionaire might get a great deal of satisfaction from a 400-foot yacht if his rival billionaire has a 300-foot yacht.  There is data that shows happiness increases all the way up the income scale.  So I do buy that argument.  But I would insist that roughly the same enjoyment would be gained from a 300-foot yacht if his rival had a 200-foot yacht.  If an 80% consumption tax reduces each billionaire’s consumption proportionately, then could it really impact their happiness?

Even though this definition of utility as a measure of happiness/fulfillment/satisfaction etc. is not useful scientifically, it is appealing because it seems like it reflects reality.  I’m not saying it doesn’t.  I agree that, in a very loose, non-scientific sense, the happiness I would gain from having an additional loaf of bread would be much less than that of a starving man who received the same loaf.  And what’s more, I act like a utilitarian to some degree in my personal life.  Every time someone donates food to the hungry or gives the foul ball they caught at a baseball game to the kid in the seat next to him, they are acting out of some form of this sentiment.

However, in those cases, they are still acting in accordance with their own personal preferences, it is just that those preferences have what might be called a utilitarian dimension to them.  They get more happiness out of giving the bread to the hungry than out of eating it or out of seeing a child smile and imagining him lying in bed clutching the foul ball and dreaming about being a major league ball-player than they would from throwing it in their closet and probably forgetting about it.

The problem with utilitarianism is when you try to apply it by force via the government.  The government I think Sumner would prefer is one which leaves people alone to make decisions about how to live their lives in most cases but just does a few things to spread the wealth around to increase total utility.  And I think Sumner’s ideal world would be a lot better than what we’ve got now.  But the problem is that that is not a suitable moral/philosophical foundation for such a system because this notion of utility is entirely imaginary which means it is entirely subjective which means that it can be used to justify any breach of individual property rights.

This way of thinking suggests that someone has a moral right to the possessions of others by virtue of being poorer than they are.  So while it is functionally possible that we could have a specific “progressive” tax system along with an entirely libertarian everything else and that would work pretty well if we had it, it would never lead to that.  The same notion of forced utility maximization across individuals, once accepted, would be (and for that matter is) used to justify all manner of other government interferences in the lives of individuals.

The land your house sits on might generate more “utility” with a highway there, or for that matter a shopping mall.  You will have higher utility if you save more money for retirement but you are too stupid to realize it so the government will just take some out of your paycheck and use it to pay you back later if you survive long enough (and to pay other older people in the interim).  Sure, maybe you could live another year or two if you got the million-dollar treatment for your cancer but would the utility you derived from that extra year really be more than that derived by all the poor children we could feed with that (“your”) money?  Yes, we’re sending you, against your will, to fight and probably die in a foreign country but your sacrifice can’t be compared to the extra utility that will be secured for future generations.  It’s not that we want to tell you what to put in your body, it’s just that when (certain) drugs are legal, crime increases and you can’t possible argue that the added utility you get from smoking dope outweighs the indirect harm that legalizing it does to your neighbors.  Plus we know that drugs are actually hurting you anyway, you are just, again, too stupid or weak to realize it, so we’re actually increasing your utility by taking them away too.  It’s win-win!  I could go on but hopefully you get the picture.

Utilitarianism, at its core, is just a made-up method of collective reasoning.  This type of collective reasoning is at the heart of every usurpation of individual liberty.  It is the foundation of every form of socialism, communism, fascism, etc.  The only alternative to collectivism is to elevate the rights of the individual above all such notions.  This means we have to be willing to look at a rich guy and a poor guy and think that it would be better if the rich guy cut back on his yachts to buy a house for the poor guy without also thinking that we aught to force him to do it.  Once you start down that path, forever will it dominate your destiny.

 

 

Categories: Philosophy Tags: , ,

Diminishing Marginal Utility (Again)

February 24, 2013 14 comments

I have already done this post, but I want to try it again (I will link to past attempts at the bottom in order to encourage readers to try this one first). I have a strange fixation with Austrians’ notion of “marginal utility.” I think it’s partially because, when I was a first-year graduate student, I thought the same thing and tried to argue it to my micro theory professor and he assured me that it was impossible to verify (or justify) diminishing marginal utility. I was pretty sure it was possible but he was one of the few professors I’ve ever had that I was pretty sure was smarter than me so I gave him the benefit of the doubt and applied myself pretty hard to figuring out what he meant. In the end, it turns out he was right and understanding why was really the key, for me, to understanding the purpose of utility in economics.

In addition to my personal history with this issue, there is the fact that this represents a point of convergence for several Austrian misconceptions.  This is important to me because I am what I would call an “Austrian sympathizer.”  I am a big proponent of free markets, I want to end the Federal Reserve and have free money, and I have little use for most empirical economic research (I think it goes too far to say there is no role for observation in economics).  That being said, the Austrian School tends to be a sort of intellectual abyss that sucks in reasonably bright people and essentially takes them out of the fight.  It gets ahold of people when they are sophomores in college and essentially tells them that everything they don’t understand about mainstream economics in fact doesn’t make sense because of a few supposed fundamental flaws underlying it.  This gives them an intellectual escape route by which they may avoid developing a level of understanding of mainstream economics which would be sufficient to offer any real pertinent criticism.  As a result, Austrians end up talking mainly to other Austrians about how great Mises and Rothbard were, while occasionally lashing out and being mostly ignored on mainstream economists blogs and producing little to no original research.  So I think that if I can figure out how to get this point across to a thoughtful reader, I may be able to save some people from this fate.

So this will be a specific response to this post but the exact same issue comes up all the time in Austrian circles.  The issue is whether diminishing marginal utility follows logically from the axiom that “humans act.”  I have no argument with the notion that human action is axiomatic but this does not imply diminishing marginal utility.  I will try to make three points.  First, I will try to clear up some confusion about what utility actually means.  Second I will try to use Austrian-like reasoning to show that the logic used by Austrians is flawed.  Finally, I will try to explain what mainstream economics really does with utility and why there is nothing inappropriate going on there (not even anything that violates any Austrian beliefs… except for using math, that is), show mathematically that you cannot infer diminishing marginal utility from it,  and attempt to demonstrate how careless the Austrian approach is in comparison.

Utility vs. Value

Austrians are essentially conflating the mainstream concepts of utility, and value.  (The Wikipedia page on value, alas, is not that great.)  Let me say, at this point that I am working from mainstream definitions.  There is no right or wrong definition of a term and I have no interest in debating which word is best used to mean something so I will explain the difference in mainstream terms and then go on to explain how the Austrian argument doesn’t make sense for either.  Mainstream economics uses the term value to represent the amount of other goods someone is willing to give up for something.  Utility refers to a mathematical representation of a person’s ordered preferences over different bundles of goods.  I will get deeper into what this means in the third section but there is an important distinction worth bringing up now.  Value measures the willingness of someone to undertake a certain action in relation to real-world variables.  If a person’s value of a cheeseburger is two pieces of pizza, this means that if the price of that cheeseburger were 1.9 pieces of pizza, they would trade for it and if it were 2.1 pieces, they would not.  Utility is not a tangible, real-world thing, nor does it bear any relationship to such a thing.  If I say that someone’s utility of a cheeseburger is 6, this means nothing, unless you knew that person’s utility of other things as well.  If I tell you that their utility of a slice of pizza is 5, then I’ve told you that they prefer the cheeseburger to the pizza.  But if I tell you that their utility of a cheeseburger is 2 and their utility of a slice of pizza is 1, I have told you the exact same thing, the numbers don’t matter.  They don’t measure how happy you are to have a cheeseburger or a pizza.  If your utility of a hamburger and a slice of pizza are 2 and 1 respectively, it doesn’t mean that the cheeseburger makes you twice as happy.  In other words, it is an ordinal measurement, not a cardinal measurement.

Okay, now here is the crazy thing.  Austrians are well aware that utility is only appropriate as an ordinal ranking.  In fact, they frequently criticize mainstream economics for using cardinal utility.  Here is someone from Mises.org:

 Mainstream economists such as John Hicks believe otherwise; for them, DMU means that d^2U / dx^2 < 0. (I.e. the second derivative of utility with respect to units of some good X is negative.) Naturally, Hicks thought that the ordinal approach to utility would make the law of DMU nonsensical.

But for Austrians, DMU doesn’t mean that “the increment in utils gets smaller as you add more units of a good.” Rather, it just means that, say, the 4th unit of a good is more valuable than the 5th unit. No unit of utility is required to make this claim, just as we can say an apple is preferred to an orange without relying on units of utility.

Translation: when we say “utility,” we really mean value.  When we say we don’t believe in cardinal utility, we mean we don’t believe in utility.

Austrians think that ordinal means you can’t do math on it (that’s why they like the idea so much haha…) and this is sort of true.  The thing is, economists are using a cardinal function to represent an ordinal utility function in such a way that the conclusions derived from the mathematical model are consistent with an ordinal utility function.  If you don’t get what this means, I don’ blame you, it’s kind of subtle, but it doesn’t mean that mainstream micro is nonsense, it just means you don’t get it.  It’s worth trying to understand (I will try to explain more a little later).

But then, after complaining about the mainstream using cardinal utility, which they don’t, they go on to make a purely cardinal claim about utility, namely that it is diminishing.  The word “marginal” means the change in something when something else changes.  The marginal utility of a good means the magnitude of the change in utility when the quantity of the good consumed increases.  So claiming that marginal utility is decreasing means that the magnitude of the difference between the utility of the fourth unit and the fifth unit is smaller than the magnitude of the difference between the utility of the third and fourth units.  But the notion that there is a magnitude associated with these differences at all is a fundamentally cardinal notion.

When confronted with this contradiction, Austrians just say “well that’s not what we mean by marginal utility” ala my favorite South Park episode but in reverse (see above quote).  But that is what the words mean….

Anyway, going forward, I will assume that what they mean when they say “marginal utility” is marginal value (again, see above quote) and I will refer to it as such.  With this in mind, I will proceed to point out that diminishing marginal value does not follow logically from human action in the way claimed.

Diminishing Marginal Value

The claim which has been made is that diminishing marginal value follows directly from the axiom of human action.  The way this was demonstrated was by telling a story where it was intuitively plausible that value would be diminishing.  But this doesn’t logically prove that value must always be diminishing.  By the way, this is the problem with refusing to use math, you end up considering things “proven” when you don’t feel like putting any additional effort into thinking of a counterexample. Luckily, I will provide a couple.  First, let me say that mainstream economists do assume diminishing marginal value (or at least things about utility which amount to the same), and I think it is a very reasonable assumption.  And observation, for the most part, backs this up. So it’s hard to make an example where you would say “yeah there clearly wouldn’t be diminishing marginal value in that case.”  All I’m doing here is showing that you can’t prove diminishing marginal value in the way Austrians claim you can.

1. The value of the use to which the last unit is put may depend on the previous units.

A rancher has some free-range cows grazing on his land.  There is an adjacent plot of land owned by his neighbor which he would like to keep his cows off of.  The boundary between the two plots is 1 mile long (let’s just assume this is a straight line and the rest of the property is enclosed by a natural boundary.  Can we prove logically that the value of the first foot of fence must be greater than the value of the 5280th foot?

2.  The options available may change depending on the quantity at hand.

A man has some amount of grain and a (fertilized) chicken egg.  It takes 10 lbs. of grain to raise a chicken to point that it’s worth eating, and let’s say it takes 10 lbs. to keep the man alive long enough to raise the chicken.  As most people are aware, raising animals is less calorically efficient than just eating their feed (the quantities here are completely made up and bear no relation to reality).  It is obvious that if the man has only 10 lbs. of grain, he would eat it all, assuming he doesn’t want to die.  If he gets an 11th lb. he will eat it as well, along with the egg, since it’s not enough to raise the chicken to maturity.  This will be true until he gets 20 lbs.  Now assume that when he has 20 lbs. he decides to raise the chicken.  Can we prove that the 20th lb. must have been worth less than the 19th lb.?

3.  A variation on #2 which relied on a discontinuity in the budget constraint (he couldn’t convert small amounts of grain into small fractions of a chicken).  We can get a similar result without this feature.

Assume the same man can trade grain for chicken at a price of 10 lbs. of grain/lb. of chicken.  So he can use the chicken for one of two purposes, eating or trading for chicken.  Let’s assume that this is for a period of several days.  When he has ten lbs. he eats it all.  Therefore, this must be the highest value use right?  When he has 20 lbs. he eats 15 lbs. and trades 5 lbs. for 1/2 lb. of chicken.  When he has 40 lbs. he eats 10 lbs. and trades 30 for 3 lbs. of chicken.  When he has 100 lbs. he trades it all for 10 lbs. of chicken.  Did these preferences violate the axiom of human action?

Now you may be saying “okay, but he still probably values the 100th lb. less than the 90th lb. and I agree.  But look at what is going on here.  The Austrian assertion that there must be diminishing marginal value is based on the reasoning that he will use the first units for the most valuable uses and later units for less valuable units.  But the most valuable use may very well depend on how many units you have.  If you only have ten lbs. of grain, you need the calories so the most valuable use for all ten lbs. is to eat it.  This may be true up to 10 lbs.  But that doesn’t mean that as you keep getting more, this will continue to be the highest value use.  Let’s say this is the case for the first 15 lbs.  It may be the case that when you get to 40 lbs., the 11th-15th lbs. become more valuable converted to chicken and when you have 100 lbs., even the first lb. is more valuable as chicken.  Therefore, you cannot infer that someone always uses a good for highest value purpose “first.”  It is true that they will always use whatever they have for the highest value purpose by definition, but the highest valued purpose is state-dependent, it can change based on how much you have.  This is the fundamental flaw in the Austrian reasoning.  You can’t rank “uses” independently from income, you have to rank bundles (econ speak for combinations) of goods (or uses).  When someone’s income/endowment increases, they gain access to different bundles.  This may completely change the relationship between the values of the individual goods within those bundles.

Mainstream Microeconomics

As I said earlier, mainstream economics assumes diminishing marginal value.  We don’t claim it logically must be true.  We arrive at this assumption largely by the same logic that Austrians do.  The difference is that we derive a refutable implication from it and notice that it is not generally refuted, whereas Austrians assume that their theory can’t possibly be wrong so they don’t bother checking.  Here’s how we do it.

First we postulate that people have preferences, which is to say that given any two combinations of goods, they would either prefer one to the other or the other to the one or be indifferent between them.  Then we imagine a function into which you can put the quantities of all goods under consideration and get back a number.  This is a cardinal number but the only meaning we assign to it is to rank the bundle relative to other bundles.  In other words, a bundle with a higher utility is preferred to a bundle with lower utility.  This is the only meaning contained in the utility function.  It doesn’t matter how far apart the numbers are.  This means that multiple functions can represent the same preferences.  It even means you can represent the same preferences with diminishing marginal utility or increasing marginal utility.  Also, you can have increasing marginal utility and diminishing marginal value (also called marginal rate of substitution).

Mainstream economists use a utility function to represent ordered preferences because it is impossible to represent the infinite number of bundles which exist along a continuum of quantities in list form.  Even if you dealt only with discrete quantities it would be very cumbersome to order all possible bundles of several goods which could be available within a given budget.  Also, it would be very difficult to articulate the restrictions that you were relying on to generate the results which your model was producing (you might not only have to rank all combinations of the goods but do the model with every possible ranking of all combinations to find out how changes in preferences affect the results).

It is because all of this would be very difficult and cumbersome that Austrians have chosen to avoid it by making drastic simplifying assumptions like the preference ranking of goods is independent of income (what Austrians represent as different uses for a good is typically represented as different goods in mainstream micro).  Once you do this, it becomes kind of simple to list ranked preferences, you just say which uses are inherently most valuable and assume that as someone gets more and more of the good, they just move up the list.  But this assumption is not only logically guaranteed to be true, it is quite obviously false once you actually think about it.  To see this take Bill Gates (a rich guy).  Imagine that Bill lost all of his money and was thrown out on the street with only $10.  Now imagine what he would spend that $10 on.  Now ask yourself: do you think Bill gates currently spends at least $10 on that good?  As long as Bill gates isn’t a smoker, chances are the answer is no.  The idea that if he only had $10, he would buy Top Ramen with it, does not imply that Top Ramen is the highest-valued use of $10 when he has a hundred billion.

Okay, so mainstream economists, rather than asking: what can we prove about preferences just from the axiom of human action and finding the answer to be nothing, giving up and going home, ask: what kind of preferences would generate results that are consistent with what we actually observe.  As it turns out, diminishing marginal value is about the only interesting thing we are pretty confident about.  The reason for this is pretty straightforward, though it is entirely unrelated to the Austrian logic.  As it turns out, if people did not have diminishing marginal value (except under a very specific and unusual circumstance) they would spend all of their income on only one good.  Since we don’t observe this, we are pretty comfortable going forward assuming diminishing marginal value.  This doesn’t mean that value must logically always be diminishing but only that, for the goods people buy, it must be diminishing around the quantity where they are buying it or else the world would look different than it does.

It is worth pointing out that this does indeed require one to look at the universe and see if it fits with the model.  All models are built on assumptions and all assumptions could be wrong.    Therefore, it behooves us to check every once in a while and see if what we are saying makes sense.  The notion that we can do science with pure logic without any observation whatsoever is misguided.  For instance, you can start with the axiom of human action and I agree that this is a good axiom.  But you had to get that axiom by looking around and noticing that people do indeed act.  You say that denying it would be an action, I say yes indeed but you would still have to open your eyes to see whether or not that action took place.

One More Thing

There is one more reason I think this is an issue of particular importance.  This is not a reason not to believe in diminishing marginal utility, we should seek truth for thruth’s sake, but it is a reason to be careful to make sure you have it right.  The left often uses the notion of diminishing marginal utility to justify all sorts of social programs, economic intervention and redistribution of wealth.  It’s an elegantly simple, yet completely nonsensical argument.  If marginal utility decreases when someone gets more and more stuff, then we can increase total utility by taking from the rich and giving to the poor.  I know Austrians don’t mean it this way, but frankly they are just picking and choosing the meanings they like and ignoring the ones they don’t like.  This is a very dangerous intellectual game to play.

Here are some previous attempts at the same argument: attempt #1, attempt #2 (not as directly about DMU), attempt #3