Wednesday, March 12, 2014

Robinson on Marshall on Diminishing Marginal Utility

John Robinson quotes Alfred Marshall on the law of diminishing marginal utility:
“The marginal utility of a thing to anyone diminishes with every increase in the amount of it he already has.

There is however an implicit condition in this law which should be made clear. It is that we do not suppose time to be allowed for any alteration in the character or tastes of the man himself. It is therefore no exception to the law that the more good music a man hears, the stronger is his taste for it likely to become; that avarice and ambition are often insatiable; or that the virtue of cleanliness and the vice of drunkenness alike grow on what they feed upon. For in such cases our observations range over some period of time; and the man is not the same at the beginning as at the end of it. If we take a man as he is, without allowing time for any change in his character, the marginal utility of a thing to him diminishes steadily with every increase in his supply of it.”
Marshall, Principles of Economics (8th edn.), 1920.
Robinson notes that this restriction makes testing of the law of diminishing marginal utility rather difficult (Robinson 1964: 50): for how do we know preferences did not change from one time to the next when a person consumes the same good?

Marshall’s requirement of no “alteration in the character or tastes” of the person supposedly subject to the law of diminishing marginal utility is akin to the ceteris paribus assumption of the law of demand: what we have here is a restriction that, as noted by Hans Albert, comes to immunise the law against empirical testing, and effectively renders it an analytic a priori proposition, which is true merely by definition.

For example, if a person becomes serially addicted to an arcade game after the first game, and appears to derive greater utility from each successive computer game (as he does better at it), then this appears to be an exception to the law of diminishing marginal utility.

But presumably if Marshall lived today he would say that the new addiction altered the man’s “character or tastes” so that he is a different person from the one who played the first game: therefore the law of diminishing marginal utility is not violated.

But now the law has become effectively immune to any testing and a tautologous statement.

And, furthermore, since time must always intervene between one purchase of a good and an additional purchase of the same good, one must wonder how anyone at all can be known to have the same character, tastes or preferences over time given that, technically speaking, even a small or minute change in the latter qualities would render them unstable, under Marshall’s view.

Marshall, Alfred. 1920. Principles of Economics (8th edn.). Macmillan and Co., Ltd. London.

Robinson, Joan. 1964. Economic Philosophy. Penguin, Harmondsworth.


  1. For all problems with the law of diminishing marginal utility, it appears to hold remarkably well if it takes itself as the object — i.e., the more I read about it, the less useful it seems.

  2. Don't forget about Paul Samuelson -- founder of the Revealed Preference school!

    "What is assumed is that consumers are fairly consistent in their tastes and actions – that they do not flail around in unpredictable ways, making themselves miserable by persistent errors of judgement or arithmetic."

    1. To be "fairly consistent in their tastes and actions" weakens the condition of Marshall considerably it would appear: for now surely the man addicted to arcade video games arguably does have "fairly consistent" "tastes", and his behaviour seems to violate the law of diminishing marginal utility.

    2. In the context of the source its clear that he means that they have to be static for the framework to function.

      Most other textbooks don't even mention this. Likely because the authors have never thought about the assumptions underlying the theory at all. Samuelson had to when he was coming up with his Revealed Preference framework.

  3. By the way, LK, did you see that the BoE has come out endorsing endogenous money -- and referencing a bunch of PK work...

    1. The fun with that document is spotting when the 'will' facts turns into the 'should' beliefs.

      It's progress though and moves the battlefront onwards.

  4. Just because a concept (diminishing marginal utility) can be tested only in conjunction with auxiliary hypotheses (stable preferences), doesn't mean it's analytic apriori. Surely it's _logically_ possible to imagine a person with convex utility function. And the joint hypothesis problem is to some degree present in all sciences. A physicist testing hypothesis about the age of universe must assume that values of physical constants don't change over time (or he must have a theory about how they change). Or a financial economist testing market efficiency must assume a particular model of risk adjustment. That doesn't make age of universe or EMH tautologically true.

    I'm not sure what's the point in criticisms like these. Of course almost all of economics is done under the assumption that preferences are stable, and everyone knows that. With unstable preferences anything can happen, so without further assumptions about how preferences change (which again would be difficult to test on their own), there would be no point in doing economics. Unless one can point to specific situations where stability assumption is unreasonable (of which addiction is a plausible example, I aggree), or can provide a better theory that explains how preferences change, simply stating the obvious is rather unhelpful.

    1. "A physicist testing hypothesis about the age of universe must assume that values of physical constants don't change over time"

      And that is reasonable for a physicist.

      But human beings are not unconscious, eternally unchanging entities like the gravitational force.

      Of course, I am not disputing many humans display certain consistencies, regularities and relatively stable behaviours, but is the latter all your are positing here?

      E.g., is it your belief that my arcade game addict is not violating the law of diminishing marginal utility?

    2. This is one of the statistician David Freedman's classic 'nonsense defences':

      "We know all that. Nothing is perfect … The assumptions are reasonable. The assumptions don’t matter. The assumptions are conservative. You can’t prove the assumptions are wrong. The biases will cancel. We can model the biases. We’re only doing what evereybody else does. Now we use more sophisticated techniques. If we don’t do it, someone else will. What would you do? The decision-maker has to be better off with us than without us … The models aren’t totally useless. You have to do the best you can with the data. You have to make assumptions in order to make progress. You have to give the models the benefit of the doubt. Where’s the harm?"

      But the sad fact remains: if you cannot account for the preferences then you cannot apply or test utility theory. And if you cannot apply or test utility theory then all you can do is give nonsense defences. And if all you can do is give nonsense defences then maybe you should seriously ask yourself what you're doing with your life.

  5. "I am not disputing many humans display certain consistencies, regularities and relatively stable behaviours"

    OK, so what was the point again?

    "is it your belief that my arcade game addict is not violating the law of diminishing marginal utility?"

    I think that utility maximization and diminishing MU are suitable approximations for some, but not all situations. In particular, I don't think that addiction is something that can be usefully analyzed with tools of economics (i.e. positing that addict's action are a rational choice maximizing his utility, whatever shape it may have). Of course, some have tried to do just that (Becker & Murphy rational addiction model), but that's taking economic imperialism to the extreme.

    1. "Utility maximization" is yet another ridiculously unrealistic model of behaviour.

      It implies consumers have all the relevant information about what combination of goods of a vast combination of goods would "maximise" utility when that effectively means they would have something like omniscience.

      Just look at R. Sippel, 1997. “An Experiment on the Pure Theory of Consumer Behaviour,” Economic Journal 107: 1431–1444.

  6. I think the usefulness of marginal utility is seen is a scenario like this:

    If a person had five bags of wheat at a certain point in time he will use them to satisfy his most urgent needs. If he had to give up one bag he would stop using wheat in those areas that give him the least marginal utility.

    If his tastes change then his choices at timeA and at Time B may be quite different.

    If everyone's tastes changed randomly every moment then MU would not be a very useful theory.

    If every one's tastes were fixed for ever then economic would probably become more of an exact science.

    The reality is of course is somewhere in between: MU has some explanatory power but as people's tastes do change it is is not a perfect match to the real world.

    I think that is what both Samuelson and Marshall were saying.

  7. I don't think you can say that declining marginal utility applies to *everything*.

    But we can prove that it applies to *specific* things after a specific point.

    I have no doubt that the marginal utility of money starts dropping after the first billion dollars.