[Abstract Review] The Mathematization of Economic Theory

The Mathematization of Economic Theory
By. Gerard Debreu.
The American Economic Review, 81(1), May 1991, pp. 1-7.

The introduction of Mathematics into Economics in the early 20th century radically changed the analytical methodology and tools in solving economics problem. It profoundly changed the natural of our profession. In the five short decades, mathematics - formulas and derivations, solved economic models with more clarity, generality, rigor, and simplicity. It becomes a “common language” for economic theory. Mathematics opens an efficient scrutiny for logical errors. The great logic solidity contributes to a fast construction of economic theories. Some of which take a comprehensive view of the economic system.

The raising importance of mathematics can be observed from the increasing pages of periodicals, the size of ES, and the graduate admissions. From 1935 to 1977, the pages increased 12 times, from 400 to 5000 pages. 1944 was the milestone for such growth and it was also the year John von Neumann and Oskar Morgenstern published the Theory of Games and Economic Behavior. The Fellows of Econometrics Society (ES) also contributes to the vast growth. In the 13 research-doctorate programs in US, over 50% of the faculty are ES member. Graduate school also requires proficiency in calculus and linear algebra upon admission. The trend is inevitable.

Physics and economics served some similarity as the application of mathematics benefited the development of both discipline. Abstract concepts were captured through axioms, equations, and calculations. But the experimental feature of physics allowed it to violate the canons of mathematical deduction. Economic theory adhere to the rules of logical discourse, but must renounce the facility of internal inconsistency because its’ lack of experiment base.
The advantages that Mathematics brought are overwhelming. Mathematical analysis in economics is no longer an option, but more or less something that judge your work and career. “The very choice of the questions to which he tries to find answers is influenced by his mathematical background” (Debreu, pg. 5). The danger is whether economics has become secondary, that the strong and solid foundation of economic theory is dominated by the fancy equations and proofs?
The over rely on mathematics is risky if economics theory weakens. It opens a gate for irresponsible models where the equations are fancy but the logics are controversy. For example the causal relationship that is observed in equation: does it really inference a causal relationship or there might be a third cause? This requires careful examinations of economics logics to avoid fallacy.

The allowance for experiment should be developed in economics. Experiment economics is already conducted on micro-level behaviors; it is an alternative tool to examine models or theories. Experiment in macro-level – national economy – is at the moment improbable because the volume is large and cost may be high.
Mathematization in economics is not perfect. It does not capture all of the factors, for example - kindness. But it did have its contribution – a common language for scholars to communicate without misunderstanding.


ECON500500 Reading and Writing in Economics
Abstract review