Methodological Individualism Meets Math

Adherents of the Austrian school of economic thought are often accused of inability to use mathematical methods. The Austrians themselves often mistrust math applied to economic theory, if it’s anything more complicated than arithmetic or basic algebra, either on the grounds that “utility is not cardinal” or simply because “Mises never used calculus”.
Therefore, it may seem that Theory of Games and Economic Behavior, by mathematician John von Neumann and economist Oskar Morgenstern, is incompatible with Austrian views. Or is it?
At first blush, the authors themselves note:

The nature of the problems investigated and the techniques employed in this book necessitate a procedure which in many instances is thoroughly mathematical.
…the mathematical deductions are frequently intricate…
…the reader who wants to acquaint himself more thoroughly with the subject expounded here, will have to familiarize himself with the mathematical way of reasoning definitely beyond its routine, primitive phases.

Is it worth reading a “thoroughly mathematical” treatment of economic behavior, especially one published in 1944? I know quite a few Austrians who would consider that a waste of time.
However, if one approaches the book with open mind, the first chapter, at least, does not look too disagreeable.
The authors recognize that economic theory is an extremely complicated matter, and is (or was at the time of the writing, but I will use the present tense) awfully underdeveloped. Note that Keynes’s magnum opus, The General Theory of Employment, Interest and Money was published in 1936, so the authors probably didn’t consider his work as a general theory of economics. They even acknowledge that the use of mathematics in economic theory was not very successful. Many reasons for this are stated, but one of them is this:

the economic problems were not formulated clearly and are often stated in such vague terms as to make mathematical treatment a priori appear hopeless because it is quite uncertain what the problems really are. There is no point in using exact methods where there is no clarity in the concepts and issues to which they are to be applied.

It is hard to disagree with this sentiment. The authors do not reject the importance of empirical knowledge (I hear some hard-core Austrians screaming), but they do not focus on empirical research. Instead: “We shall attempt to utilize only some commonplace experience concerning human behavior which lends itself to mathematical treatment and which is of economic importance.” This ends the first chapter.

In the second chapter the authors define their methodology – that understanding of economy as a whole should come from the analysis of individual members of the economy! Hey, this sounds almost like human action! Even more, they state that this approach is “now well-nigh universally agreed”. Whatever happened with economic theory (or economists) since that time…? But I digress.
So what is the driving motive of every individual? According to the authors, it’s maximizing his utility. While Austrians usually prefer to speak in terms of preferences, maximization of utility does not sound too bad. Unless it’s a cardinal utility (the previous screams become louder). Oh wait, so what is their stance on this? In fact, they side-step the issue. While the whole third chapter is dedicated to treatment of utility, the most of the book makes a simplifying assumption “that the aim of all participants in the economic system, consumers as well as entrepreneurs, is money, or equivalently a single monetary commodity.” (I hear the screams subsiding, as the screamers faint in disagreement). This attitude is definitely non-Austrian, as some human goals are not attainable for money (yes, Austrians value love), and even the material goods are only obtainable for money when a market exists.
To sooth the hurt Austrian sensibilities, let me quickly add that the authors praise in passing the contribution to the analysis of individual behavior by our old friend, Robinson Crusoe. Well, not by him as an economist, but as a subject of many thought experiments. Not only that, they actually mention Austrian School by name (with “school” capitalized, no less) and make a nod to Bohm-Bawerk. Unlike Austrians, however, the authors do not spend much time with Crusoe, saying that the case of a single actor presents only purely technical difficulties and not conceptual ones. Indeed, Crusoe can just sit down, figure out the best way to utilize the available resources, and start acting. As the authors put it, this is merely a maximization problem. Any uncertainty he may face (like bad weather) is waived away as a subject of probability theory – Crusoe can maximize the expected utility.

Thus, the authors promptly switch to a multi-person economy (a social economy, as they call it). They still see the goal of every individual as maximization of his utility (that’s money, if you forgot), but notice that, unlike in one-person economy, the actor does not control all “the variables” – goals of individuals may conflict, and maximization of one’s utility does not necessarily means maximization of another’s. And here comes an interesting moment, one which actually made me wishing to write this post. I will quote profusely:

A particularly striking expression of the popular misunderstanding about this pseudo-maximum problem is the famous statement according to which the purpose of social effort is the “greatest possible good for the greatest possible number.” A guiding principle cannot be formulated by the requirement of maximizing two (or more) functions at once.
Such a principle, taken literally, is self-contradictory, (in general one function will have no maximum where the other function has one.) It is no better than saying, e.g., that a firm should obtain maximum prices at maximum turnover, or a maximum revenue at minimum outlay. If some order of importance of these principles or some weighted average is meant, this should be stated. However, in the situation of the participants in a social economy nothing of that sort is intended, but all maxima are desired at once by various participants.

Ha! I like these guys! Tell me the last sentence is not a denial of interpersonal utility comparison! They say that to try and optimize separate well-being of all people simultaneously is impossible, but to replace these multiple independent goals by a single aggregated goal (e.g., a sum of all well-beings) is unwarranted. Note that they do not actually say it’s impossible, as any red-blooded Austrian would.

So far, the material of the book was not entirely to Austrian liking, but on the other hand, it was not radically incompatible with core tenets of the school (come on, it’s much better than Keynes!).

My belief is that there may be some value in the rest of the book, maybe something that will rehabilitate math as the tool for economic theory.

In the next installment I hope to cover the chapter three – the one discussing utility and (you wouldn’t believe it) preferences. Maybe by the end of these series we can definitely answer the question – can Austrians do math? And are they allowed to do it (or will they be smitten for this unholy practice and become Keynesians in their next life)?

Andris Birkmanis


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3 thoughts on “Methodological Individualism Meets Math

  1. Anthony 11/24/2012 at 23:51 Reply

    Morgenstern was an Austrian as far as I know.

  2. Andris Birkmanis 11/25/2012 at 11:02 Reply

    Yes, Morgenstern was an Austrian economist, and in 1931 he published “Die drei Grundtypen der Theorie des subjektiven Wertes” (The three fundamental types of the theory of subjective value), where he wrote: “Measuring utility is […] impossible because utilities are intensive magnitudes, i.e. qualities, rather than extensive magnitudes, i.e. quantities. And, according to the usual understanding, being a quantity is an indispensable precondition for measurement.”

    However, he argued that economic subjects can compare not only utilities but also utility differences. Later, Lange argued that ability to compare utility differences means ability to measure utility. Still later, Phelps Brown and Samuelson proved Lange was wrong.
    I am actually planning to discuss this in the next installment, which will be about the third chapter (utility and preferences).

  3. […] the previous post I tried to convince the reader that Theory of Games and Economic Behavior may be of some value even […]

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