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Full and constrained Pareto efficiency with incomplete financial markets

Author

Listed:
  • C. Mendolicchio

    (Università di Genova)

  • T. Pietra

    (Università di Bologna)

Abstract

We study the efficiency properties of equilibria in general equilibrium economies with incomplete financial markets. We focus the analysis on economies with a finitely large number of agents and initial endowments close to a Pareto optimal one. Consider an economy with a Pareto optimal equilibrium allocation and a sufficiently small, but nonzero, amount of trade. If the matrix of the derivatives of the indirect utility functions with respect to prices has maximal rank (equal to the number of non-numeraire commodities), then locally all the economies have a unique, constrained Pareto-efficient equilibrium. To the contrary, pick a Pareto optimal initial endowment. Then, locally, there are open sets of economies with a unique, constrained Pareto-efficient equilibrium and other open sets of economies with a unique constrained Pareto-inefficient equilibrium. The key step of the analysis is based on the observation that, in some small open neighborhood of an economy with a Pareto optimal initial endowment, we can partially characterize constrained Pareto optimal equilibria as the optimal solution of a well-defined, strictly concave optimization problem.

Suggested Citation

  • C. Mendolicchio & T. Pietra, 2021. "Full and constrained Pareto efficiency with incomplete financial markets," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(1), pages 211-234, February.
  • Handle: RePEc:spr:joecth:v:71:y:2021:i:1:d:10.1007_s00199-019-01239-y
    DOI: 10.1007/s00199-019-01239-y
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    References listed on IDEAS

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    1. Mendolicchio, C. & Pietra, T., 2019. "A re-examination of constrained Pareto inefficiency in economies with incomplete markets," Journal of Mathematical Economics, Elsevier, vol. 80(C), pages 39-55.
    2. Atsushi Kajii & Antonio Villanacci & Alessandro Citanna, 1998. "Constrained suboptimality in incomplete markets: a general approach and two applications," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 11(3), pages 495-521.
    3. Geanakoplos, J. & Polemarchakis, H., 1985. "Existence,regularity, and constrained suboptimality of competitive allocations when the asset market is incomplete," LIDAM Discussion Papers CORE 1985037, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. Joseph E. Stiglitz, 1982. "The Inefficiency of the Stock Market Equilibrium," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 49(2), pages 241-261.
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    More about this item

    Keywords

    GEI; Constrained Pareto efficiency; Numeraire assets;
    All these keywords.

    JEL classification:

    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies
    • D52 - Microeconomics - - General Equilibrium and Disequilibrium - - - Incomplete Markets

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