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Steven Horwitz, Confused?

"A Mengerian understanding of the market process rejects the claim that an economy can be fruitfully understood through the use of simultaneous equations and equilibrium constructs… The Austrian approach rejects equilibrium theory as a description of actual economic events (although some Austrians would retain it as the never-achieved endpoint of economic activity) in favor of other theoretical and metaphorical devices." -- Steven Horwitz (2000: 8)
I don't know why Horwitz identifies "simultaneous equations" with equilibrium.

Consider this applet. I think one can characterize the underlying mathematics as a system of (countably infinite) simultaneous equations. Yet, one can hardly say that the interest in this mathematics lies in an equilibrium point, at least above a certain value of a parameter.

And that mathematics has economic applications. A Ricardian model can yield a logistic equation (Bhaduri). So can a cobweb cycle with an affine supply function and a quadratic demand function (Goodwin).

Advocates of the Austrian school should strive to write so one cannot read them as not being able to do math, instead of as simply choosing not to do math.

References
  • Bhaduri, Amit (1993). Unconventional Economic Essays: Selected Papers of Amit Bhaduri, Oxford University Press
  • Horwitz, Steven (2000). Microfoundations and Macroeconomics: An Austrian Perspective, Routledge
  • Goodwin, Richard M. (1990). Chaotic Economic Dynamics, Oxford University Press

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