Economics and Math

Daniel Kuehn asked Austrian economists here why he can’t use calculus in economic analysis implying that there is no irreconcilable difference between the Austrian and mainstream approaches to marginal utility:

I might say that although people don’t actually do calculus when making decisions, we can probably agree they’re trying to figure out the best option for them, and they are probably saying something in their head like “I’m going to keep doing this until the cost to me of doing it again is higher than the benefit of doing it again”. That’s not a very big assumption on my part, after all. And that’s a pretty fair account of all that I’m importing into the model by using calculus.

In fact, it’s not very difficult to give a response from the praxeological standpoint and show that an irreconcilable difference actually exists.

First, one needs to note that Daniel is talking here not about one choice but about several iterative choices of one more unit of certain course of action. Second, the cornerstone of praxeology is the idea that costs only exist as an integral part of a particular choice.

It follows from this that the utility and cost of one unit in the first choice may not be meaningfully compared to the utility and cost of one unit in nth choice. However, it is of course possible ex post to fit the choices into a graph with a marginal benefit and a marginal cost curve. The problem is that from the praxeological standpoint these curves are meaningless. As a corollary utility maximization (cost minimization) is an artifact of this curve-fitting.

The upshot of this discussion is that the mainstream rational choice model and the praxeological reasoning are two fundamentally different things. The latter takes the fact of choice and its logical structure as given and proceeds from it while the former is just one possible psychological model trying to make a mapping from hypothetical preexisting preferences to actual choices. This is incidentally why the mainstream rational choice model is so vulnerable to criticism from other branches of psychology like behavioral psychology, while praxeology has nothing to fear from it.

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One thought on “Economics and Math

  1. That was a response to a discussion about Coase – I don’t think Austrian economics came up. For all I know praxeology is not amenable to it.

    The iterative process you describe (and again – I’m not sure this happens so consistently – when I buy five apples from the store I don’t buy one, then a second, then a third. I pick up five apples and pay for them all at once), is comparable to numerical optimization methods. So again – if you can get the same answer to an optimization problem using calculus on the one hand or using numerical methods, then FOR MODELING PURPOSES, what is the problem with using calculus?

    I’m doing all caps because this is the part of the argument I think you are ignoring. Or do you just think we shouldn’t be modeling?

    You’re welcome to think that, but then there’s not much more to say.

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