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On the shape of Pareto sets in Edgeworth box economies

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  • William Thomson

    (University of Rochester)

Abstract

We study the geometry of the Pareto set in Edgeworth box economies when both agents have continuous, strictly monotonic, strictly convex, smooth, and homothetic preferences. We show that this set is either the diagonal of the box or it is a “doubly visible” curve connecting the origins of the box: imagining the curve to be opaque, an observer standing at either origin is able to see it in its entirety. We also study the case of preferences for which both goods are normal at all prices. In this case, we deduce monotonicity of the Pareto set. We also state a “converse” of each of these statements.

Suggested Citation

  • William Thomson, 2023. "On the shape of Pareto sets in Edgeworth box economies," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 11(2), pages 181-190, October.
    • Handle: RePEc:spr:etbull:v:11:y:2023:i:2:d:10.1007_s40505-023-00258-2
    DOI: 10.1007/s40505-023-00258-2
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    References listed on IDEAS

    as
    1. Ju, Biung-Ghi, 2005. "Strategy-proof risk sharing," Games and Economic Behavior, Elsevier, vol. 50(2), pages 225-254, February.
    2. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
    3. William Thomson, 1999. "Economies with Public Goods: An Elementary Geometric Exposition," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 1(1), pages 139-176, January.
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    More about this item

    Keywords

    Pareto set; Homothetic preferences; Normal goods; Double visibility;
    All these keywords.

    JEL classification:

    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies
    • D60 - Microeconomics - - Welfare Economics - - - General

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