IDEAS home Printed from https://ideas.repec.org/a/eee/mateco/v47y2011i6p768-776.html
   My bibliography  Save this article

Existence of equilibria in economies with externalities and non-convexities in an infinite-dimensional commodity space

Author

Listed:
  • Fuentes, Matías N.

Abstract

We prove an equilibrium existence theorem for economies with externalities, general types of non-convexities in the production sector, and infinitely many commodities. The consumption sets, the preferences of the consumers, and the production possibilities are represented by set-valued mappings to take into account the external effects. The firms set their prices according to general pricing rules which are supposed to have bounded losses and may depend upon the actions of the other economic agents. The commodity space is L∞(M,M,μ), the space of all μ-essentially bounded M-measurable functions on M.

Suggested Citation

  • Fuentes, Matías N., 2011. "Existence of equilibria in economies with externalities and non-convexities in an infinite-dimensional commodity space," Journal of Mathematical Economics, Elsevier, vol. 47(6), pages 768-776.
    • Handle: RePEc:eee:mateco:v:47:y:2011:i:6:p:768-776
    DOI: 10.1016/j.jmateco.2011.10.007
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304406811001194
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmateco.2011.10.007?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Sun, Ning, 2006. "Bewley's limiting approach to infinite dimensional economies with l.s.c. preferences," Economics Letters, Elsevier, vol. 92(1), pages 7-13, July.
    2. Schalk, S., 1996. "General Equilibrium Model with a Convex Cone as the Set of Commodity Bundles," Other publications TiSEM 93a805b3-bd6d-48e2-b0b0-f, Tilburg University, School of Economics and Management.
    3. Cornet, Bernard, 1988. "General equilibrium theory and increasing returns : Presentation," Journal of Mathematical Economics, Elsevier, vol. 17(2-3), pages 103-118, April.
    4. Bonnisseau, Jean-Marc & Meddeb, Moncef, 1999. "Existence of equilibria in economies with increasing returns and infinitely many commodities," Journal of Mathematical Economics, Elsevier, vol. 31(3), pages 287-307, April.
    5. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
    6. Bonnisseau, Jean-Marc & Cornet, Bernard, 1988. "Existence of equilibria when firms follow bounded losses pricing rules," Journal of Mathematical Economics, Elsevier, vol. 17(2-3), pages 119-147, April.
    7. Bonnisseau, Jean-Marc & Medecin, Jean-Philippe, 2001. "Existence of marginal pricing equilibria in economies with externalities and non-convexities," Journal of Mathematical Economics, Elsevier, vol. 36(4), pages 271-294, December.
    8. Bonnisseau, J.M., 1995. "Existence of Equilibria in Economies with Externalities and Non Convexities," Papiers d'Economie Mathématique et Applications 95.45, Université Panthéon-Sorbonne (Paris 1).
    9. 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.
    10. Mas-Colell, Andreu, 1986. "The Price Equilibrium Existence Problem in Topological Vector Lattice s," Econometrica, Econometric Society, vol. 54(5), pages 1039-1053, September.
    11. Bonnisseau, Jean-Marc & Cornet, Bernard, 1990. "Existence of Marginal Cost Pricing Equilibria in Economies with Several Nonconvex Firms," Econometrica, Econometric Society, vol. 58(3), pages 661-682, May.
    12. Schalk, S., 1996. "General Equilibrium Model with a Convex Cone as the Set of Commodity Bundles," Research Memorandum 740, Tilburg University, School of Economics and Management.
    13. Bonnisseau, Jean-Marc & Cornet, Bernard, 1990. "Existence of Marginal Cost Pricing Equilibria: The Nonsmooth Case," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 31(3), pages 685-708, August.
    14. Zame, William R, 1987. "Competitive Equilibria in Production Economies with an Infinite-Dimensional Commodity Space," Econometrica, Econometric Society, vol. 55(5), pages 1075-1108, September.
    15. Kajii, Atsushi, 1988. "Note on equilibria without ordered preferences in topological vector spaces," Economics Letters, Elsevier, vol. 27(1), pages 1-4.
    16. Yannelis, Nicholas C. & Zame, William R., 1986. "Equilibria in Banach lattices without ordered preferences," Journal of Mathematical Economics, Elsevier, vol. 15(2), pages 85-110, April.
    17. Kamiya, Kazuya, 1988. "On the survival assumption in marginal (cost) pricing," Journal of Mathematical Economics, Elsevier, vol. 17(2-3), pages 261-273, April.
    18. 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.
    19. 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.
    20. 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).
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Jean-Marc Bonnisseau & Matías Fuentes, 2018. "Market failures and equilibria in Banach lattices," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01960874, HAL.
    2. Jean-Marc Bonnisseau & Matías Fuentes, 2020. "Market Failures and Equilibria in Banach Lattices: New Tangent and Normal Cones," Journal of Optimization Theory and Applications, Springer, vol. 184(2), pages 338-367, February.
    3. Holmberg, Pär & Tangerås, Thomas & Ahlqvist, Victor, 2018. "Central- versus Self-Dispatch in Electricity Markets," Working Paper Series 1257, Research Institute of Industrial Economics, revised 27 Mar 2019.
    4. Jean-Marc Bonnisseau & Matias Fuentes, 2022. "Increasing returns, externalities and equilibrium in Riesz spaces," Documents de travail du Centre d'Economie de la Sorbonne 22025, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    5. Jean-Marc Bonnisseau & Matías Fuentes, 2022. "Increasing returns, externalities and equilibrium in Riesz spaces," Working Papers halshs-03908326, HAL.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Jean-Marc Bonnisseau & Matías Fuentes, 2020. "Market Failures and Equilibria in Banach Lattices: New Tangent and Normal Cones," Journal of Optimization Theory and Applications, Springer, vol. 184(2), pages 338-367, February.
    2. Jean-Marc Bonnisseau & Matías Fuentes, 2018. "Market failures and equilibria in Banach lattices," Documents de travail du Centre d'Economie de la Sorbonne 18037, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    3. Charalambos Aliprantis & Kim Border & Owen Burkinshaw, 1996. "Market economies with many commodities," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 19(1), pages 113-185, March.
    4. Jean-Marc Bonnisseau, 2000. "The Marginal Pricing Rule in Economies with Infinitely Many Commodities," Econometric Society World Congress 2000 Contributed Papers 0262, Econometric Society.
    5. Bonnisseau, Jean-Marc & Meddeb, Moncef, 1999. "Existence of equilibria in economies with increasing returns and infinitely many commodities," Journal of Mathematical Economics, Elsevier, vol. 31(3), pages 287-307, April.
    6. Aliprantis, Charalambos D. & Border, Kim C. & Burkinshaw, Owen, 1997. "Economies with Many Commodities," Journal of Economic Theory, Elsevier, vol. 74(1), pages 62-105, May.
    7. Tourky, Rabee, 1999. "Production equilibria in locally proper economies with unbounded and unordered consumers," Journal of Mathematical Economics, Elsevier, vol. 32(3), pages 303-315, November.
    8. Messaoud Deghdak & Monique Florenzano, 1999. "Decentralizing Edgeworth equilibria in economies with many commodities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 14(2), pages 297-310.
    9. J. M. Bonnisseau & A. Jamin, 2008. "Equilibria with Increasing Returns: Sufficient Conditions on Bounded Production Allocations," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 10(6), pages 1033-1068, December.
    10. Podczeck, Konrad, 1996. "Equilibria in vector lattices without ordered preferences or uniform properness," Journal of Mathematical Economics, Elsevier, vol. 25(4), pages 465-485.
    11. Abramovich, Y A & Aliprantis, C D & Zame, W R, 1995. "A Representation Theorem for Riesz Spaces and Its Applications to Economics," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 5(3), pages 527-535, May.
    12. Aliprantis, Charalambos D., 1997. "Separable utility functions," Journal of Mathematical Economics, Elsevier, vol. 28(4), pages 415-444, November.
    13. Aliprantis, C. D. & Tourky, R. & Yannelis, N. C., 2000. "The Riesz-Kantorovich formula and general equilibrium theory," Journal of Mathematical Economics, Elsevier, vol. 34(1), pages 55-76, August.
    14. 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.
    15. Martins-da-Rocha, V. Filipe & Riedel, Frank, 2010. "On equilibrium prices in continuous time," Journal of Economic Theory, Elsevier, vol. 145(3), pages 1086-1112, May.
    16. Monique Florenzano & Valeri Marakulin, 2000. "Production Equilibria in Vector Lattices," Econometric Society World Congress 2000 Contributed Papers 1396, Econometric Society.
    17. Aliprantis, Charalambos D. & Tourky, Rabee & Yannelis, Nicholas C., 2000. "Cone Conditions in General Equilibrium Theory," Journal of Economic Theory, Elsevier, vol. 92(1), pages 96-121, May.
    18. Jean-Marc Bonnisseau & Matías Fuentes, 2022. "Increasing returns, externalities and equilibrium in Riesz spaces," Working Papers halshs-03908326, HAL.
    19. Jean-Marc Bonnisseau & Matías Fuentes, 2022. "Increasing returns, externalities and equilibrium in Riesz spaces," Post-Print halshs-03908326, HAL.
    20. Charalambos Aliprantis & Rabee Tourky, 2009. "Equilibria in incomplete assets economies with infinite dimensional spot markets," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 38(2), pages 221-262, February.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:mateco:v:47:y:2011:i:6:p:768-776. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jmateco .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.