Working Paper: NBER ID: w22922
Authors: 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.
Keywords: No keywords provided
JEL Codes: B41; C63; C65
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| Assumptions (C51) | Validity of economic hypotheses (C12) |
| Coefficients of parabolas (b^2 - 4c > 0) (C46) | Reformulation of hypothesis about real roots (C12) |
| Convex demand curve (D11) | Monopolist pricing behaviors (D42) |