Thursday, September 19, 2013

What is the Epistemological Status of the Law of Demand?

The law of demand asserts that as the price of a good rises, ceteris paribus (other things being equal), the quantity demanded falls, and as the price of a good falls, ceteris paribus, the quantity demanded rises. That is, the price and quantity demanded are negatively inclined ceteris paribus.

The ceteris paribus assumption entails that all other factors except price are held constant: incomes, prices of other goods, fashions, expectations, information, preferences/tastes, population, the weather, etc.

What is the epistemological status of such a proposition? If analytic a priori, it must be regarded as true by virtue of the meanings of the terms used. But that entails that we simply define the “law of demand” to mean that as the price of a good rises, ceteris paribus, the quantity demanded falls, etc.

Such a necessary analytic a priori statement would be tautologous and informationally vacuous, and would tell us nothing necessarily true of the real world.

It follows that, if the law of demand were really understood this way, it could only be asserted of the real world by transformation into a synthetic a posteriori statement (as pure geometry is transformed into synthetic a posteriori propositions when asserted as empirical statements about real space).

But, at that point, one must ask: how is such an assertion proven? How do we prove that the law of demand is empirically true?

The history of how neoclassical economics has unsuccessfully attempted to prove the law of demand is told by Steve Keen in Debunking Economics: The Naked Emperor Dethroned? (rev. edn. 2011). pp. 38–73, though I will leave a review of this for another post.

Keen, Steve. 2011. Debunking Economics: The Naked Emperor Dethroned? (rev. and expanded edn.). Zed Books, London and New York.


  1. It's nt empirically true at all. How could it be with a "ceteris paribus" clause and the real world to empirically test it? No two situations will ever be all things the same except one. And besides, however the law is understood, it should read: As the price of a good rises, ceteris paribus, the quantity demanded will be less than or equal.

    This covers for the fact that in an imaginary construct with all things equal except price, there is still a possibility it didn't change enough to surpass the next valued option in the marginal buyers preferences.

  2. If this is a "law" it is an extraordinarily weak one. It seems to me that it is like saying "if you drop something it falls" and calling that the "law of gravity".

    As the price of goods rise by N dollars, ceteris parius,how much, in number of items, does the demand fall? If the price falls by N dollars, ceteris paribus, by how many units does the demand fall?

    Without the numbers it is not a "law" in any scientific sense, or so it seems to me. At best it is a heuristic and that may be stretching things.

  3. Ryan Murphy made a similar point a couple years ago, if that interests you.

  4. I think there's a lot of interesting questions with this one.

    1) One possibility is that to, as you suggest, treat it as analytic. That we define "demand" and the other terms in such a way that it all becomes true by definition.

    2) It's also analytic in another sense. Since it's a counterfactual conditional statement, the antecedent will always be false so the conditional is true. That way the "Law of Demand" would be true in the same sense as

    "If 4 is prime then markets are efficient."

    3) A third possibility would be if we could test an approximation to the conditions. Think of the "ideal gas law" for example. There are no "ideal gasses" but some gasses are approximately ideal gasses and so they behave somewhat like ideal gasses.

    This wouldn't be much different than doing a physics problem in which we assume (implicitly or otherwise) that the earth is flat, there is no friction and acceleration due to gravity is constant. All statements are false but they may give OK predictions so long as the situation approximates the assumptions.

    4) The last way would be whether or not a theory that takes the law of demand true gives good predictions. This would make it empirical (abductive, not inductive) since the accuracy of the prediction justifies the assumption.

    I have my doubts on (3) and (4) (partly for reasons you give). (2) makes it worthless. (1) is limited because definitions, in my opinion, are contingent partly on their usefulness. See my On the Existence of Married Bachelors for context.

  5. As a side note, the Austrians claim that you can derive the Law of Demand from the Law of diminishing Marginal Utility which is claimed to be derived from "human action".

    I doubt any of these derivations are formally valid but that might be an interesting thing to look at: what would it take to make those arguments formally valid.

    Anyway... I'm curious about where you think we ought to even draw the line between analtic, synthetic, a priori, etc.

    Take this for example:

    You cannot checkmate with only a king and knight.

    The statement is undeniably true. Does it say something about the "real world"? (It certainly says something about a game we play.) Is it "analytic" or "synthetic"? A priori?

    1. That's an analytic a priori statement because it is using the rules of chess -- which are a language -- in a self-referential manner.

    2. Hello Phillip,

      Let me ask a few follow-up questions then with examples.

      Example 1

      Suppose that we take Newton's Principia (or a cleaned up version that was purely formalized). Suppose we derive some theorem from within this formalized version which is using "the rules of Newton" to derive the result. Is this, also, analytic a priori?

      Example 2

      Suppose we find some arithmetic statement which is expressible within our language but formally undecidable from within our system of axioms. Let's call this statement G (after Godel). Is G true? False? analytic? A priori?

      Example 3

      What if the statement "You cannot checkmate with only a king and knight" is like our statement G in example 2?

      Now perhaps chess doesn't have anything like an incompleteness theorem. (Has some graduate student made axiomatizing chess a doctoral thesis yet?) It may very well not. Chess doesn't have the recursive quality of mathematics so perhaps there is nothing like that and my question is not relevant.

      But I guess my inclination would be that I would need to see the proof. After all, my knowledge of it is more inductive. I've certainly never set down to formally prove it. But on a similar note, my knowledge of the Goldbach conjecture is inductive as well. That hasn't been formally proven either.

    3. 1. Yes. It depends on the language, formal or not, that Newton has developed.

      2. Anything to do with math is analytic a priori. Your example appears true in normal language and unprovable in the axiomatic system. The status of truth, falseness or unprovability has nothing to do with the Kantian logical category we use.

      3. Same answer as 2.

  6. Phillip, you'll have to tell me how you're defining your terms.

    Are you even making a distinction between analytic and a priori? Why even use both terms?

    If I'm understanding you, you're suggesting that something is [a priori] if provided that it is wholly determined by the language. At least that's what I took you to mean. But then what's "analytic" in your sense? Or is that what you mean by "analytic" and "a priori" is something entirely different?

    As a side note, I would probably interpret this as being less about language but rathernormative practices (language being a particular set of normative practices). The "it's all language" sounds too much like Richard Rorty to me.

    The idea that math or the rules of chess amount to being a language strikes me as an overworked metaphor (I don't much care for overworked metaphors).

    Anyway, regarding the Newtonian example, then would you disagree with Lord Keynes here.

    Because if I understand you, you seem to be suggesting that what assumptions are part of Newton's system have no bearing on whether or not it's "analytic a priori". I think the status of the entire system is probably relevant. Given that Newton's theory is motivated by empirical concerns, I have to conclude it's neither analytic nor a priori.

    Regarding (2) and (3), I think it matters a good deal. But I mean something different by analytic and a priori. I'm not sure if you're making a distinction at all.

    For more context, see my comments here.