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