Actually that is a very easy concept to express in mathematical symbols and there is a very systematic way to do it. It goes:

Price = f(supply,demand)

Whatever the function may be depend on how you believe supply and demand interacts (with the assumption that you’ve already defined supply and demand numerically)

And that goes without saying a mathematical function should only have variables that are numerical in nature. Non numerical variable do not have a place in mathematics.

Thus, we don’t use mathematics to express non-numerical ideas the same way we paint a picture if you intend to sing a song.

]]>As to the broader questions of formal methods in the social sciences, well, that is a huge topic with a vast literature. BTW I agree that the kind of dynamics you’re talking about can’t be modeled verbally. We may disagree about the value added of such modeling, however.

]]>As for explaining convergence to equilibrium, I’m not familiar with Menger’s theory. If it looks anything like the neo-Austrians’, though, it is pretty rough and doesn’t lead to specific predictions or give much better intuition than the non-mathematical “just-so” stories in the textbooks about gluts and shortages.

Convergence to equilibrium is a pretty hard and complex problem if you actually want to say something about relative speed of convergence in different markets, price dispersion along the way to equilibrium, impact of different information conditions, etc. The idea that we could make much headway on these questions without some kind of formal modeling (at least an agent-based computer model, if nothing else) seems far-fetched to me. I would be delighted to be proved wrong about this, and people are of course welcome to try, but it seems quixotic at best..

]]>And yes, you’re right, simply invoking the word “cause” doesn’t make a causal argument. But Menger Sr. does, in fact, offer a causal explanation for price determination. It’s quite distinct from, e.g., Walras’s. And he and his followers do have a theory of price dynamics. It’s only since the post-WWII formalization of the discipline that we’ve lost these notions, IMHO.

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