IDEAS home Printed from https://ideas.repec.org/a/eee/gamebe/v66y2009i2p607-626.html
   My bibliography  Save this article

Equilibrium and optimality: Some imprints of David Gale

Author

Listed:
  • Majumdar, Mukul

Abstract

The paper is a review of some of the themes to which David Gale made lasting contributions. It touches upon a number of the fundamental issues in the Walrasian equilibrium theory (existence, uniqueness and stability), the overlapping generations model (non-optimality and indeterminacy of competitive equilibria), the von Neumann equilibrium (as a turnpike), and in the theory of decentralized intertemporal allocation through competitive prices (efficiency and golden rules, duality and existence of optimal programs).

Suggested Citation

  • Majumdar, Mukul, 2009. "Equilibrium and optimality: Some imprints of David Gale," Games and Economic Behavior, Elsevier, vol. 66(2), pages 607-626, July.
    • Handle: RePEc:eee:gamebe:v:66:y:2009:i:2:p:607-626
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0899-8256(09)00090-6
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Gale, David, 1974. "Exchange equilibrium and coalitions : An example," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 63-66, March.
    2. 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.
    3. Mill, John Stuart, 1848. "Principles of Political Economy (II): Distribution," History of Economic Thought Books, McMaster University Archive for the History of Economic Thought, volume 2, number mill1848-2.
    4. Neuefeind, Wilhelm, 1980. "Notes on Existence of Equilibrium Proofs and the Boundary Behavior of Supply," Econometrica, Econometric Society, vol. 48(7), pages 1831-1837, November.
    5. Debreu, Gerard, 1970. "Economies with a Finite Set of Equilibria," Econometrica, Econometric Society, vol. 38(3), pages 387-392, May.
    6. Cass, David, 1972. "On capital overaccumulation in the aggregative, neoclassical model of economic growth: A complete characterization," Journal of Economic Theory, Elsevier, vol. 4(2), pages 200-223, April.
    7. Bhagwati, Jagdish N & Brecher, Richard A & Hatta, Tatsuo, 1983. "The Generalized Theory of Transfers and Welfare: Bilateral Transfers in a Multilateral World," American Economic Review, American Economic Association, vol. 73(4), pages 606-618, September.
    8. Brock, W.A., 1990. "Overlapping generations models with money and transactions costs," Handbook of Monetary Economics, in: B. M. Friedman & F. H. Hahn (ed.), Handbook of Monetary Economics, edition 1, volume 1, chapter 7, pages 263-295, Elsevier.
    9. Majumdar, Mukul, 1988. "Decentralization in infinite horizon economies: An introduction," Journal of Economic Theory, Elsevier, vol. 45(2), pages 217-227, August.
    10. Gale, David, 1973. "Pure exchange equilibrium of dynamic economic models," Journal of Economic Theory, Elsevier, vol. 6(1), pages 12-36, February.
    11. Benveniste, Lawrence M., 1976. "Two notes on the malinvaud condition for efficiency of infinite horizon programs," Journal of Economic Theory, Elsevier, vol. 12(2), pages 338-346, April.
    12. James C. Moore, 2007. "General Equilibrium and Welfare Economics," Springer Books, Springer, number 978-3-540-32223-8, June.
    13. 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.
    14. Bala, Venkatesh & Majumdar, Mukul, 1992. "Chaotic Tatonnement," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 2(4), pages 437-445, October.
    15. Lars J. Olson & Santanu Roy, 2006. "Theory of Stochastic Optimal Economic Growth," Springer Books, in: Rose-Anne Dana & Cuong Le Van & Tapan Mitra & Kazuo Nishimura (ed.), Handbook on Optimal Growth 1, chapter 11, pages 297-335, Springer.
    16. Leonid Hurwicz & Mukul Majumdar, 2015. "Optimal lntertemporal Allocation Mechanisms and Decentralization of Decisions," World Scientific Book Chapters, in: Mukul Majumdar (ed.), Decentralization in Infinite Horizon Economies, chapter 2, pages 12-45, World Scientific Publishing Co. Pte. Ltd..
    17. Paul A. Samuelson, 1953. "Prices of Factors and Goods in General Equilibrium," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 21(1), pages 1-20.
    18. David Gale, 1967. "On Optimal Development in a Multi-Sector Economy," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 34(1), pages 1-18.
    19. Geistdoerfer-Florenzano, Monique, 1982. "The gale-nikaido-debreu lemma and the existence of transitive equilibrium with or without the free-disposal assumption," Journal of Mathematical Economics, Elsevier, vol. 9(1-2), pages 113-134, January.
    20. Grandmont, Jean-Michel, 1985. "On Endogenous Competitive Business Cycles," Econometrica, Econometric Society, vol. 53(5), pages 995-1045, September.
    21. D. Gale, 1967. "A Geometric Duality Theorem with Economic Applications," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 34(1), pages 19-24.
    22. W. R. S. Sutherland, 1970. "On Optimal Development in a Multi-Sectoral Economy: the Discounted Case," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 37(4), pages 585-589.
    23. Benhabib, Jess & Day, Richard H., 1982. "A characterization of erratic dynamics in, the overlapping generations model," Journal of Economic Dynamics and Control, Elsevier, vol. 4(1), pages 37-55, November.
    24. Mill, John Stuart, 1848. "Principles of Political Economy (III): Exchange," History of Economic Thought Books, McMaster University Archive for the History of Economic Thought, volume 3, number mill1848-3.
    25. Debreu, Gerard, 1974. "Excess demand functions," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 15-21, March.
    26. Benveniste, Lawrence & Gale, David, 1975. "An extension of Cass' characterization of infinite efficient production programs," Journal of Economic Theory, Elsevier, vol. 10(2), pages 229-238, April.
    27. Brock, William A. & Gale, David, 1969. "Optimal growth under factor augmenting progress," Journal of Economic Theory, Elsevier, vol. 1(3), pages 229-243, October.
    28. S. G. Winter, 1967. "The Norm of a Closed Technology and the Straight-Down-the-Turnpike Theorem," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 34(1), pages 67-84.
    29. Gerard Debreu, 1956. "Market Equilibrium," Cowles Foundation Discussion Papers 10, Cowles Foundation for Research in Economics, Yale University.
    30. Lionel W. McKenzie, 2012. "turnpike theory," The New Palgrave Dictionary of Economics,, Palgrave Macmillan.
    31. Bhattacharya,Rabi & Majumdar,Mukul, 2007. "Random Dynamical Systems," Cambridge Books, Cambridge University Press, number 9780521825658.
    32. Lionel W. McKenzie, 2005. "Classical General Equilibrium Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262633302, April.
    33. Aumann, R. J. & Peleg, B., 1974. "A note on Gale's example," Journal of Mathematical Economics, Elsevier, vol. 1(2), pages 209-211, August.
    34. McFadden, Daniel & Mitra, Tapan & Majumdar, Mukul, 1980. "Pareto optimality and competitive equilibrium in infinite horizon economies," Journal of Mathematical Economics, Elsevier, vol. 7(1), pages 1-26, March.
    35. Mitra, Tapan & Majumdar, Mukul, 1976. "A note on the role of the transversality condition in signalling capital overaccumulation," Journal of Economic Theory, Elsevier, vol. 13(1), pages 47-57, August.
    36. Saari, Donald G, 1985. "Iterative Price Mechanisms," Econometrica, Econometric Society, vol. 53(5), pages 1117-1131, September.
    37. Mitra, Tapan, 1979. "On the Value Maximizing Property of Infinite Horizon Efficient Programs," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 20(3), pages 635-642, October.
    38. Roy Radner, 1961. "Prices and the Turnpike: III. Paths of Economic Growth that are Optimal with Regard only to Final States: A Turnpike Theorem," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 28(2), pages 98-104.
    39. Bhattacharya,Rabi & Majumdar,Mukul, 2007. "Random Dynamical Systems," Cambridge Books, Cambridge University Press, number 9780521532723.
    40. Lawrence M. Benveniste, 1986. "Pricing Optimal Distributions to Overlapping Generations: A Corollary to Efficiency Pricing," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(2), pages 301-306.
    41. Mill, John Stuart, 1848. "Principles of Political Economy (I): Production," History of Economic Thought Books, McMaster University Archive for the History of Economic Thought, volume 1, number mill1848-1.
    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. M. Ali Khan & Metin Uyanik, 2021. "The Yannelis–Prabhakar theorem on upper semi-continuous selections in paracompact spaces: extensions and applications," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(3), pages 799-840, April.
    2. Panek Emil, 2019. "Optimal growth processes in a non-stationary Gale economy with a multilane production turnpike," Economics and Business Review, Sciendo, vol. 5(2), pages 3-23, June.
    3. Panek Emil, 2023. "“Very strong” turnpike effect in a non-stationary Gale economy with investments, multilane turnpike and limit technology," Economics and Business Review, Sciendo, vol. 9(4), pages 5-24, December.

    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. 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.
    2. Céline Rochon & Herakles Polemarchakis, 2006. "Debt, liquidity and dynamics," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 27(1), pages 179-211, January.
    3. Sobel, Joel, 2009. "ReGale: Some memorable results," Games and Economic Behavior, Elsevier, vol. 66(2), pages 632-642, July.
    4. Timothy J. Kehoe & David K. Levine & Andreu Mas-Colell & Michael Woodford, 1991. "Gross Substitutes in Large Square Economics," Levine's Working Paper Archive 2057, David K. Levine.
    5. Mukul Majumdar, 2023. "Roy Radner: A Subtle Theorist," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 21(3), pages 481-522, September.
    6. Hippolyte D'Albis & Emmanuelle Augeraud-Veron, 2008. "Endogenous Retirement and Monetary Cycles," Mathematical Population Studies, Taylor & Francis Journals, vol. 15(4), pages 214-229.
    7. Venkatesh Bala & Mukul Majumdar & Tapan Mitra, 1991. "Decentralized evolutionary mechanisms for intertemporal economies: A possibility result," Journal of Economics, Springer, vol. 53(1), pages 1-29, February.
    8. Florenzano, Monique, 2009. "Two lemmas that changed general equilibrium theory," Games and Economic Behavior, Elsevier, vol. 66(2), pages 603-605, July.
    9. Simonovits, Andras, 1999. "Are there cycles in realistic overlapping cohorts models?," Structural Change and Economic Dynamics, Elsevier, vol. 10(2), pages 261-275, June.
    10. Hardle, Wolfgang & Kirman, Alan, 1995. "Nonclassical demand : A model-free examination of price-quantity relations in the Marseille fish market," Journal of Econometrics, Elsevier, vol. 67(1), pages 227-257, May.
    11. Kehoe, Timothy J. & Levine, David K., 1984. "Regularity in overlapping generations exchange economies," Journal of Mathematical Economics, Elsevier, vol. 13(1), pages 69-93, April.
    12. Molnar, Gyorgy & Simonovits, Andras, 1998. "Expectations, (in)stability and (in)viability in realistic overlapping cohorts models," Journal of Economic Dynamics and Control, Elsevier, vol. 23(2), pages 303-332, September.
    13. Paul Oslington, 2012. "General Equilibrium: Theory and Evidence," The Economic Record, The Economic Society of Australia, vol. 88(282), pages 446-448, September.
    14. Gorokhovsky, Alexander & Rubinchik, Anna, 2022. "Necessary and sufficient conditions for determinacy of asymptotically stationary equilibria in OLG models," Journal of Economic Theory, Elsevier, vol. 204(C).
    15. Takuma Kunieda & Akihisa Shibata, 2014. "Credit Market Imperfections and Macroeconomic Instability," Pacific Economic Review, Wiley Blackwell, vol. 19(5), pages 592-611, December.
    16. Erkki Koskela & Markku Ollikainen & Mikko Puhakka, 2000. "Saddles, Indeterminacy and Bifurcations in an Overlapping Generations Economy with a Renewable Resource," Econometric Society World Congress 2000 Contributed Papers 1810, Econometric Society.
    17. Ghiglino, Christian & Tvede, Mich, 2000. "Optimal Policy in OG Models," Journal of Economic Theory, Elsevier, vol. 90(1), pages 62-83, January.
    18. W D A Bryant, 2009. "General Equilibrium:Theory and Evidence," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 6875, September.
    19. Kehoe, Timothy J. & Levine, David K., 1990. "The economics of indeterminacy in overlapping generations models," Journal of Public Economics, Elsevier, vol. 42(2), pages 219-243, July.
    20. Gazzola, Gianluca & Medio, Alfredo, 2006. "Global sunspots in OLG models: Theory and computational analysis," Journal of Macroeconomics, Elsevier, vol. 28(1), pages 27-45, March.

    More about this item

    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:eee:gamebe:v:66:y:2009:i:2:p:607-626. 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/inca/622836 .

    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.