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A note on the characterization of optimal allocations in OLG economies with multiple goods

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Abstract

We consider a pure exchange overlapping generations economy with finitely many commodities and consumers per period having possibly non-complete non transitive preferences. We provide a geometric and direct proof of the Balasko-Shell characterization of Pareto optimal allocation. To avoid some smoothness assumption, we replace the assumption on the curvature of the indifference surface by geometric properties of preferred sets. In particular, we use the notion of prox-regularity, introduced in variational analysis by Rockafellar and Poliquin. We provide preliminary results and explain how the multi-consumer case can be simplified by considering aggregate feasible Pareto improving transfer. We provide the proof and we show which assumptions are used for the "if" part and for the "only if" part of the criterion

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  • Jean-Marc Bonnisseau & Lalaina Rakotonindrainy, 2015. "A note on the characterization of optimal allocations in OLG economies with multiple goods," Documents de travail du Centre d'Economie de la Sorbonne 15003, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    • Handle: RePEc:mse:cesdoc:15003
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    1. Gale, D. & Mas-Colell, A., 1975. "An equilibrium existence theorem for a general model without ordered preferences," Journal of Mathematical Economics, Elsevier, vol. 2(1), pages 9-15, March.
    2. Florenzano Monique & Geistdoerfer Monique, 1980. "Equilibre économique général transitif et intransitif (l'). problèmes d'existence," CEPREMAP Working Papers (Couverture Orange) 8004, CEPREMAP.
    3. Paul A. Samuelson, 1958. "An Exact Consumption-Loan Model of Interest with or without the Social Contrivance of Money," Journal of Political Economy, University of Chicago Press, vol. 66(6), pages 467-467.
    4. Balasko, Yves & Cass, David & Shell, Karl, 1980. "Existence of competitive equilibrium in a general overlapping-generations model," Journal of Economic Theory, Elsevier, vol. 23(3), pages 307-322, December.
    5. Gale, D. & Mas-Colell, A., 1979. "Corrections to an equilibrium existence theorem for a general model without ordered preferences," Journal of Mathematical Economics, Elsevier, vol. 6(3), pages 297-298, December.
    6. Lalaina Rakotonindrainy, 2014. "Existence of equilibrium in OLG economies with durable goods," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01021382, HAL.
    7. Burke, Jonathan L., 1987. "Inactive transfer policies and efficiency in general overlapping-generations economies," Journal of Mathematical Economics, Elsevier, vol. 16(3), pages 201-222, June.
    8. Balasko, Yves & Shell, Karl, 1980. "The overlapping-generations model, I: The case of pure exchange without money," Journal of Economic Theory, Elsevier, vol. 23(3), pages 281-306, December.
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    More about this item

    Keywords

    Overlapping generations model; preference set; normal cone; equilibrium; Pareto optimality;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • D50 - Microeconomics - - General Equilibrium and Disequilibrium - - - General
    • D62 - Microeconomics - - Welfare Economics - - - Externalities

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