IDEAS home Printed from https://ideas.repec.org/p/mse/cesdoc/22025.html
   My bibliography  Save this paper

Increasing returns, externalities and equilibrium in Riesz spaces

Author

Listed:

Abstract

This paper studies the appropriate pricing rule and its associated equilibrium concept when there are market imperfections in a Riesz space setting. We extend the notion of marginal pricing equilibria to situations with non convex production sets and external factors in an abstract vector lattice whose topological dual is a sublattice of its order dual. Our main result guarantees that a non-competitive equilibrium exists and it is related with first order condition for profit maximization at the time that it encompasses a wide range of economic situations since previous results in the literature become particular cases of it. Furthermore, we developed a new properness assumption that takes into account the non convexity of the production correspondences together with the presence of externalities which in some sense is a weakening of some known conditions in competitive economies

Suggested Citation

  • 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.
    • Handle: RePEc:mse:cesdoc:22025
    as

    Download full text from publisher

    File URL: http://mse.univ-paris1.fr/pub/mse/CES2022/22025.pdf
    Download Restriction: no
    File URL: https://shs.hal.science/halshs-03908326
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Romer, Paul M, 1986. "Increasing Returns and Long-run Growth," Journal of Political Economy, University of Chicago Press, vol. 94(5), pages 1002-1037, October.
    2. Bonnisseau, Jean-Marc & Cornet, Bernard, 1988. "Valuation equilibrium and pareto optimum in non-convex economies," Journal of Mathematical Economics, Elsevier, vol. 17(2-3), pages 293-308, April.
    3. Krugman, Paul, 1980. "Scale Economies, Product Differentiation, and the Pattern of Trade," American Economic Review, American Economic Association, vol. 70(5), pages 950-959, December.
    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. Jones, Larry E, 1984. "A Competitive Model of Commodity Differentiation," Econometrica, Econometric Society, vol. 52(2), pages 507-530, March.
    6. Mas-Colell, Andreu, 1975. "A model of equilibrium with differentiated commodities," Journal of Mathematical Economics, Elsevier, vol. 2(2), pages 263-295.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. Podczeck, Konrad, 1996. "Equilibria in vector lattices without ordered preferences or uniform properness," Journal of Mathematical Economics, Elsevier, vol. 25(4), pages 465-485.
    13. Rabee Tourky, 1999. "The limit theorem on the core of a production economy in vector lattices with unordered preferences," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 14(1), pages 219-226.
    14. Paulina Beato, 1982. "The Existence of Marginal Cost Pricing Equilibria with Increasing Returns," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 97(4), pages 669-688.
    15. Guesnerie, Roger, 1975. "Pareto Optimality in Non-Convex Economies," Econometrica, Econometric Society, vol. 43(1), pages 1-29, January.
    16. Cornet, B., 1986. "The second welfare theorem in nonconvex economies," LIDAM Discussion Papers CORE 1986030, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    17. 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.
    18. Charalambos D. Aliprantis & Kim C. Border, 2006. "Infinite Dimensional Analysis," Springer Books, Springer, edition 0, number 978-3-540-29587-7, October.
    19. 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).
    20. Lucas, Robert Jr., 1988. "On the mechanics of economic development," Journal of Monetary Economics, Elsevier, vol. 22(1), pages 3-42, July.
    Full references (including those not matched with items on IDEAS)

    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, 2022. "Increasing returns, externalities and equilibrium in Riesz spaces," Working Papers halshs-03908326, 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. 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 & Matías Fuentes, 2018. "Market failures and equilibria in Banach lattices," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01960874, HAL.
    5. 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.
    6. Jean-Marc Bonnisseau, 2000. "The Marginal Pricing Rule in Economies with Infinitely Many Commodities," Econometric Society World Congress 2000 Contributed Papers 0262, Econometric Society.
    7. Aliprantis, Charalambos D. & Tourky, Rabee & Yannelis, Nicholas C., 2001. "A Theory of Value with Non-linear Prices: Equilibrium Analysis beyond Vector Lattices," Journal of Economic Theory, Elsevier, vol. 100(1), pages 22-72, September.
    8. Aliprantis, Charalambos D. & Florenzano, Monique & Tourky, Rabee, 2006. "Production equilibria," Journal of Mathematical Economics, Elsevier, vol. 42(4-5), pages 406-421, August.
    9. 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.
    10. Monique Florenzano & Valeri Marakulin, 2000. "Production Equilibria in Vector Lattices," Econometric Society World Congress 2000 Contributed Papers 1396, Econometric Society.
    11. 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.
    12. Carlos Hervés-Beloso & V. Martins-da-Rocha & Paulo Monteiro, 2009. "Equilibrium theory with asymmetric information and infinitely many states," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 38(2), pages 295-320, February.
    13. Aliprantis, Charalambos D. & Florenzano, Monique & Tourky, Rabee, 2005. "Linear and non-linear price decentralization," Journal of Economic Theory, Elsevier, vol. 121(1), pages 51-74, March.
    14. Basile, Achille & Graziano, Maria Gabriella & Papadaki, Maria & Polyrakis, Ioannis A., 2017. "Cones with semi-interior points and equilibrium," Journal of Mathematical Economics, Elsevier, vol. 71(C), pages 36-48.
    15. Mikhail Golosov & Larry E. Jones & Michèle Tertilt, 2007. "Efficiency with Endogenous Population Growth," Econometrica, Econometric Society, vol. 75(4), pages 1039-1071, July.
    16. 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.
    17. 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.
    18. Bosi, G. & Mehta, G. B., 2002. "Existence of a semicontinuous or continuous utility function: a unified approach and an elementary proof," Journal of Mathematical Economics, Elsevier, vol. 38(3), pages 311-328, November.
    19. Anthony Horsley & Andrew Wrobel, 2005. "Continuity of the equilibrium price density and its uses in peak-load pricing," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(4), pages 839-866, November.
    20. 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.

    More about this item

    Keywords

    Riesz space; marginal pricing rule; non-competitive equilibrium; sigma-locally tau-uniform properness;
    All these keywords.

    JEL classification:

    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium

    Statistics

    Access and download statistics

    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:mse:cesdoc:22025. 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: Lucie Label (email available below). General contact details of provider: https://edirc.repec.org/data/cenp1fr.html .

    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.