Automated Economic Reasoning with Quantifier Elimination

58 Pages Posted: 12 Dec 2016

See all articles by Casey B. Mulligan

Casey B. Mulligan

University of Chicago; National Bureau of Economic Research (NBER)

Date Written: December 2016

Abstract

Many theorems in economics can be proven (and hypotheses shown to be false) with “quantifier elimination.” Results from real algebraic geometry such as Tarski’s quantifier elimination theorem and Collins’ cylindrical algebraic decomposition algorithm are applicable because the economic hypotheses, especially those that leave functional forms unspecified, can be represented as systems of multivariate polynomial (sic) equalities and inequalities. The symbolic proof or refutation of economic hypotheses can therefore be achieved with an automated technique that involves no approximation and requires no problem-specific information beyond the statement of the hypothesis itself. This paper also discusses the computational complexity of this kind of automated economic reasoning, its implementation with Mathematica and REDLOG software, and offers several examples familiar from economic theory.

Suggested Citation

Mulligan, Casey B., Automated Economic Reasoning with Quantifier Elimination (December 2016). NBER Working Paper No. w22922. Available at SSRN: https://ssrn.com/abstract=2883959

Casey B. Mulligan (Contact Author)

University of Chicago ( email )

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Chicago, IL 60637
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773-702-8490 (Fax)

National Bureau of Economic Research (NBER)

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