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Automated Economic Reasoning with Quantifier Elimination

Listed author(s):
  • Casey B. Mulligan

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.

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Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 22922.

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Date of creation: Dec 2016
Handle: RePEc:nbr:nberwo:22922
Note: IO PE TWP
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  1. Donald J. Brown & Rosa L. Matzkin, 1995. "Testable Restrictions on the Equilibrium Manifold," Cowles Foundation Discussion Papers 1109, Cowles Foundation for Research in Economics, Yale University.
  2. Acemoglu,Daron & Robinson,James A., 2006. "Economic Origins of Dictatorship and Democracy," Cambridge Books, Cambridge University Press, number 9780521855266, December.
  3. 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.
  4. Susan K. Snyder, 2000. "Nonparametric Testable Restrictions of Household Behavior," Southern Economic Journal, Southern Economic Association, vol. 67(1), pages 171-185, July.
  5. 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.
  6. 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.
  7. 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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