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Automated Economic Reasoning with Quantifier Elimination

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  • Casey B. Mulligan

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

  • Casey B. Mulligan, 2016. "Automated Economic Reasoning with Quantifier Elimination," NBER Working Papers 22922, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberwo:22922 Note: IO PE TWP
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    References listed on IDEAS

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    1. Chambers,Christopher P. & Echenique,Federico, 2016. "Revealed Preference Theory," Cambridge Books, Cambridge University Press, number 9781107087804, March.
    2. Susan K. Snyder, 2000. "Nonparametric Testable Restrictions of Household Behavior," Southern Economic Journal, Southern Economic Association, vol. 67(1), pages 171-185, July.
    3. Brown, Donald J & Matzkin, Rosa L, 1996. "Testable Restrictions on the Equilibrium Manifold," Econometrica, Econometric Society, vol. 64(6), pages 1249-1262, November.
    4. E. Glen Weyl & Michal Fabinger, 2013. "Pass-Through as an Economic Tool: Principles of Incidence under Imperfect Competition," Journal of Political Economy, University of Chicago Press, vol. 121(3), pages 528-583.
    5. Anthony Downs, 1957. "An Economic Theory of Political Action in a Democracy," Journal of Political Economy, University of Chicago Press, vol. 65, pages 135-135.
    6. Andrés Carvajal & Rahul Deb & James Fenske & John Quah, 2014. "A nonparametric analysis of multi-product oligopolies," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 57(2), pages 253-277, October.
    7. Acemoglu,Daron & Robinson,James A., 2009. "Economic Origins of Dictatorship and Democracy," Cambridge Books, Cambridge University Press, number 9780521671422, March.
    8. Casey B. Mulligan & Kevin K. Tsui, 2016. "The Upside-down Economics of Regulated and Otherwise Rigid Prices," NBER Working Papers 22305, National Bureau of Economic Research, Inc.
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    More about this item

    JEL classification:

    • B41 - Schools of Economic Thought and Methodology - - Economic Methodology - - - Economic Methodology
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools

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