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The Second Fundamental Theorem of Positive Economics

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  • Mukherji, Anjan

    (National Institute of Public Finance and Policy)

Abstract

Welfare Economics is fortunate that there are two Fundamental Theorems of Welfare Economics. Positive Economics on the other hand is seemingly endowed with none. One of the fundamental results of Positive Economics is that a competitive equilibrium exists under fairly general conditions; this then may be called the First Fundamental Theorem of Positive Economics (FFTPE). The existing results on uniqueness and stability of competitive equilibrium are far too restrictive to be up for consideration as a Fundamental Theorem. It is to re-examine this question that we revisit the question of stability of competitive equilibrium. It is shown that if, for all distributions of the aggregate endowment, the matrix sum of the Jacobian of the excess demand function plus its transpose, evaluated at the equilibrium, have maximal rank then equilibria will be locally asymptotically stable. When this condition is not met, it is shown how redistributing resources will always make a competitive equilibrium price configuration stable and this need not involve redistributing endowments so that trades do not exist at equilibrium. This last result is quite general and the only requirement is that the rank condition referred to earlier hold at zero trade competitive equilibria and consequently may qualify to be called the Second Fundamental Theorem of Positive Economics (SFTPE).

Suggested Citation

  • Mukherji, Anjan, 2012. "The Second Fundamental Theorem of Positive Economics," Working Papers 12/98, National Institute of Public Finance and Policy.
    • Handle: RePEc:npf:wpaper:12/98
    Note: Working Paper 98, 2012
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    References listed on IDEAS

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    Cited by:

    1. Benjamin J. Gillen & Masayoshi Hirota & Ming Hsu & Charles R. Plott & Brian W. Rogers, 2021. "Divergence and convergence in Scarf cycle environments: experiments and predictability in the dynamics of general equilibrium systems," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(3), pages 1033-1084, April.
    2. Emiko Fukuda & Shuhei Sato & Junyi Shen & Ken-Ichi Shimomura & Takehiko Yamato, 2020. "Walrasian Dynamics with Endowment Changes: The Gale Example in a Laboratory Market Experiment," Discussion Paper Series DP2020-20, Research Institute for Economics & Business Administration, Kobe University, revised Apr 2021.

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    Keywords

    Stability of equilibrium ; Redistribution of resources ; Rank condition ; Fundamental theorems;
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