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Production equilibria in vector lattices with unordered preferences : an approach using finite-dimensional approximations

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  • Marakulin, Valeri M.

Abstract

The goal of the paper is to prove the existence of competitive production quasi-equilibria in linear vector lattices. We assume that the commodity space is a vector lattice endowed with a Hausdorff locally convex topology such that the positive cone is closed and the topological dual is a lattice. Preferences are not assumed to be transitive and complete. We allow also a rather arbitrary form of consumption sets which, together with production sets, satisfy a kind of proper condition. This condition "a set to be proper" is significantly weakened in comparison with other papers. The existence result is stated via the method of finite-dimensional approximations of the commodity space.

Suggested Citation

  • Marakulin, Valeri M., 1998. "Production equilibria in vector lattices with unordered preferences : an approach using finite-dimensional approximations," CEPREMAP Working Papers (Couverture Orange) 9821, CEPREMAP.
    • Handle: RePEc:cpm:cepmap:9821
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    References listed on IDEAS

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    1. Kreps, David M., 1981. "Arbitrage and equilibrium in economies with infinitely many commodities," Journal of Mathematical Economics, Elsevier, vol. 8(1), pages 15-35, March.
    2. Mas-Colell, Andreu & Richard, Scott F., 1991. "A new approach to the existence of equilibria in vector lattices," Journal of Economic Theory, Elsevier, vol. 53(1), pages 1-11, February.
    3. Richard, Scott F., 1989. "A new approach to production equilibria in vector lattices," Journal of Mathematical Economics, Elsevier, vol. 18(1), pages 41-56, February.
    4. Mas-Colell, Andreu & Zame, William R., 1991. "Equilibrium theory in infinite dimensional spaces," Handbook of Mathematical Economics, in: W. Hildenbrand & H. Sonnenschein (ed.), Handbook of Mathematical Economics, edition 1, volume 4, chapter 34, pages 1835-1898, Elsevier.
    5. Bewley, Truman F., 1972. "Existence of equilibria in economies with infinitely many commodities," Journal of Economic Theory, Elsevier, vol. 4(3), pages 514-540, June.
    6. Mas-Colell, Andreu, 1986. "The Price Equilibrium Existence Problem in Topological Vector Lattice s," Econometrica, Econometric Society, vol. 54(5), pages 1039-1053, September.
    7. BEWLEY, Truman F., 1972. "Existence of equilibria in economies with infinitely many commodities," LIDAM Reprints CORE 122, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    Cited by:

    1. Monique Florenzano & Valeri Marakulin, 2000. "Production Equilibria in Vector Lattices," Econometric Society World Congress 2000 Contributed Papers 1396, Econometric Society.

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    More about this item

    JEL classification:

    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies

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