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Approximate Solutions of Walrasian Equilibrium Inequalities with Bounded Marginal Utilities of Income

In: Affective Decision Making Under Uncertainty

Author

Listed:
  • Donald J. Brown

    (Yale University)

Abstract

Recently Cherchye et al. (2011) reformulated the Walrasian equilibrium inequalities, introduced by Brown and Matzkin (1996), as an integer programming problem and proved that solving the Walrasian equilibrium inequalities is NP-hard. Brown and Shannon (2002) derived an equivalent system of equilibrium inequalities,i.e., the dual Walrasian equilibrium inequalities. That is, the Walrasian equilibrium inequalities are solvable iff the dual Walrasian equilibrium inequalities are solvable. We show that solving the dual Walrsian equilibrium inequalities is equivalent to solving a NP-hard minimization problem. Approximation theorems are polynomial time algorithms for computing approximate solutions of NP-hard minimization problems. The primary contribution of this paper is an approximation theorem for the equivalent NP-hard minimization problem. In this theorem, we derive explicit bounds, where the degree of approximation is determined by observable market data.

Suggested Citation

  • Donald J. Brown, 2020. "Approximate Solutions of Walrasian Equilibrium Inequalities with Bounded Marginal Utilities of Income," Lecture Notes in Economics and Mathematical Systems, in: Affective Decision Making Under Uncertainty, pages 55-67, Springer.
    • Handle: RePEc:spr:lnechp:978-3-030-59512-8_5
    DOI: 10.1007/978-3-030-59512-8_5
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    More about this item

    Keywords

    Algorithmic game theory; Computable general equilibrium theory; Refutable theories of value; JEL classification: B41; C68; D46;
    All these keywords.

    JEL classification:

    • B41 - Schools of Economic Thought and Methodology - - Economic Methodology - - - Economic Methodology
    • C68 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computable General Equilibrium Models
    • D46 - Microeconomics - - Market Structure, Pricing, and Design - - - Value Theory

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