Response to Mathematics in Economics

The following is a response to a post on Awkward Utopia titled 'Mathematics and Economics.'

I recently wrote an entry to this blog specifically lining out my ideas as to the merits of and against empirical analysis in economic science. For the formulation of theory, it has not only been held by Austrians that mathematical and empirical analysis is incorrect. As most can understand, mathematics and empirical analysis aren't the same thing and shouldn't be categorized as the same thing. Calculus isn't Statistics, they are very different fields. Personally, I categorize Statistics as a natural science and Calculus as a deductive science or logic. Calculus is basically logic taken to the extreme. In mathematical analysis though there must be strict units of measurement. Udels are not units of measurement and can never be.

I remember on the first test of my high school physics class I received a low score. Remarkably it was not because my answers were wrong per se but that I had no units to the numerical answers. I protested the grade but my teacher would simply point at my answers and say something like "45 what? Bananas? Apples? 45 what?" That left quite an impression on me and it makes sense. To the natural scientists the Austrian answer to mathematical questions make complete sense. There is a fine line and distinction between natural science and social science.

Economists have traditionally based their theories on logically deduced facts and economic laws. The title of "mathematical incompetence" is one you label with the Austrian school but i would be weary with your claims. Keynes is completely counter to Austrian thought but he recognized the incorrect use of mathematical analysis in economics. In the General Theory, there is but one graph and it is a simple illustration of shifts in the rate of interest. Keynes' theories were in fact based on *gasp* human action. The fundamental difference between Keynes and von Mises was their understandings of human action and not their disagreement on the use of it in economic science.

The approach of the Austrian school is one that is unique and has served it well. von Mises pioneered the use of praxeology in economics or better said the science of human action. von Mises, Rothbard, Hayek, Schumpeter, Hazlit, Bohm-Bawerk, Fetter, Kirzner, etc. all take after a long held tradition of Austrian economics that is loyal to the subjective theory of value and its approach to economic theory. Our methodology is not found in the nonexistence of Austrian economists that are competent in the field mathematics but a difference in the analysis of economic valuation. The subjective theory of value is a powerful tool that has served the Austrian school well and has developed theories such as the Mises-Hayek theory of the trade cycle.

So Matt, I do not know what your knowledge is of the Austrian school but I would not be so hasty as to label the Austrian school "mathematically incompetent." During my stay at the von Mises Institute over the summer, I was surprised to find out that most of the Austrian economists I look up to were in fact heavily steeped in mathematics. Hulsmann and Garrison are two of the Austrian economists of our day that are heavily steeped in mathematics, the latter having graduated college with a degree in engineering.

In conclusion, this argument presented by Matt is not logically sound. Just because most economists use mathematical formulas in their theory does not make it automatically correct nor does it make opposing schools of thought such as the Austrians "mathematically incompetent." We believe that human action can not be simplified into neat curves or equations. It is only through understanding the mechanisms of human action can the social science of Economics provide useful additions to the body of knowledge. This is probably the only thing Keynes and von Mises would have agreed upon.