IDEAS home Printed from https://ideas.repec.org/a/eee/mateco/v113y2024ics0304406824000697.html
   My bibliography  Save this article

Recent advances on uniqueness of competitive equilibrium

Author

Listed:
  • Toda, Alexis Akira
  • Walsh, Kieran James

Abstract

This article reviews the recent advances in the uniqueness and multiplicity of competitive equilibria in models arising in mathematical economics, finance, macroeconomics, and trade.

Suggested Citation

  • Toda, Alexis Akira & Walsh, Kieran James, 2024. "Recent advances on uniqueness of competitive equilibrium," Journal of Mathematical Economics, Elsevier, vol. 113(C).
    • Handle: RePEc:eee:mateco:v:113:y:2024:i:c:s0304406824000697
    DOI: 10.1016/j.jmateco.2024.103008
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304406824000697
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmateco.2024.103008?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 look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. John Chipman, 2010. "Multiple equilibrium under CES preferences," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 45(1), pages 129-145, October.
    2. Ma, Qingyin & Toda, Alexis Akira, 2022. "Asymptotic linearity of consumption functions and computational efficiency," Journal of Mathematical Economics, Elsevier, vol. 98(C).
    3. Dana, Rose-Anne, 1995. "An extension of Milleron, Mitjushin and Polterovich's result," Journal of Mathematical Economics, Elsevier, vol. 24(3), pages 259-269.
    4. J. E. Stiglitz, 1970. "Non-Substitution Theorems with Durable Capital Goods," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 37(4), pages 543-553.
    5. Hens, Thorsten & Laitenberger, Jorg & Loffler, Andreas, 2002. "Two remarks on the uniqueness of equilibria in the CAPM," Journal of Mathematical Economics, Elsevier, vol. 37(2), pages 123-132, April.
    6. Piero Gottardi & Felix Kubler, 2015. "Dynamic Competitive Economies with Complete Markets and Collateral Constraints," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 82(3), pages 1119-1153.
    7. Cherrier, Beatrice & Duarte, Pedro Garcia & Saïdi, Aurélien, 2023. "Household heterogeneity in macroeconomic models: A historical perspective," European Economic Review, Elsevier, vol. 158(C).
    8. E. Eisenberg, 1961. "Aggregation of Utility Functions," Management Science, INFORMS, vol. 7(4), pages 337-350, July.
    9. Calvet, Laurent E., 2001. "Incomplete Markets and Volatility," Journal of Economic Theory, Elsevier, vol. 98(2), pages 295-338, June.
    10. Mantel, Rolf R., 1974. "On the characterization of aggregate excess demand," Journal of Economic Theory, Elsevier, vol. 7(3), pages 348-353, March.
    11. Debreu, Gerard, 1970. "Economies with a Finite Set of Equilibria," Econometrica, Econometric Society, vol. 38(3), pages 387-392, May.
    12. Felix Kubler & Karl Schmedders, 2010. "Uniqueness of Steady States in Models with Overlapping Generations," Journal of the European Economic Association, MIT Press, vol. 8(2-3), pages 635-644, 04-05.
    13. Kehoe, Timothy J & Levine, David K, 1985. "Comparative Statics and Perfect Foresight in Infinite Horizon Economies," Econometrica, Econometric Society, vol. 53(2), pages 433-453, March.
    14. Toda, Alexis Akira, 2019. "Wealth distribution with random discount factors," Journal of Monetary Economics, Elsevier, vol. 104(C), pages 101-113.
    15. Gale, David, 1973. "Pure exchange equilibrium of dynamic economic models," Journal of Economic Theory, Elsevier, vol. 6(1), pages 12-36, February.
    16. Hens, Thorsten, 2001. "An extension of Mantel (1976) to incomplete markets," Journal of Mathematical Economics, Elsevier, vol. 36(2), pages 141-149, November.
    17. Treb Allen & Costas Arkolakis, 2014. "Trade and the Topography of the Spatial Economy," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 129(3), pages 1085-1140.
    18. Daron Acemoglu & Pablo D. Azar, 2020. "Endogenous Production Networks," Econometrica, Econometric Society, vol. 88(1), pages 33-82, January.
    19. Balasko, Yves, 1980. "Number and definiteness of economic equilibria," Journal of Mathematical Economics, Elsevier, vol. 7(3), pages 215-225, December.
    20. Treb Allen & Costas Arkolakis, 2022. "The Welfare Effects of Transportation Infrastructure Improvements," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 89(6), pages 2911-2957.
    21. Hirano, Tomohiro & Toda, Alexis Akira, 2024. "On equilibrium determinacy in overlapping generations models with money," Economics Letters, Elsevier, vol. 239(C).
    22. Konstantin Kucheryavyy & Gary Lyn & Andrés Rodríguez-Clare, 2023. "Grounded by Gravity: A Well-Behaved Trade Model with Industry-Level Economies of Scale," American Economic Journal: Macroeconomics, American Economic Association, vol. 15(2), pages 372-412, April.
    23. Douglas W. Diamond & Philip H. Dybvig, 2000. "Bank runs, deposit insurance, and liquidity," Quarterly Review, Federal Reserve Bank of Minneapolis, vol. 24(Win), pages 14-23.
    24. Kehoe, Timothy J., 1984. "Computing all of the equilibria of economies with two factors of production," Journal of Mathematical Economics, Elsevier, vol. 13(3), pages 207-223, December.
    25. S. Rao Aiyagari, 1994. "Uninsured Idiosyncratic Risk and Aggregate Saving," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 109(3), pages 659-684.
    26. Toda, Alexis Akira, 2017. "Huggett economies with multiple stationary equilibria," Journal of Economic Dynamics and Control, Elsevier, vol. 84(C), pages 77-90.
    27. Loi, Andrea & Matta, Stefano, 2021. "Minimal entropy and uniqueness of price equilibria in a pure exchange economy," Journal of Mathematical Economics, Elsevier, vol. 97(C).
    28. Ma, Qingyin & Stachurski, John & Toda, Alexis Akira, 2020. "The income fluctuation problem and the evolution of wealth," Journal of Economic Theory, Elsevier, vol. 187(C).
    29. Rodrigo Adao & Arnaud Costinot & Dave Donaldson, 2017. "Nonparametric Counterfactual Predictions in Neoclassical Models of International Trade," American Economic Review, American Economic Association, vol. 107(3), pages 633-689, March.
    30. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
    31. Balasko, Yves & Shell, Karl, 1981. "The overlapping-generations model. III. The case of log-linear utility functions," Journal of Economic Theory, Elsevier, vol. 24(1), pages 143-152, February.
    32. Rüdiger Bachmann & David Baqaee & Christian Bayer & Moritz Kuhn & Andreas Löschel & Benjamin Moll & Andreas Peichl & Karen Pittel & Moritz Schularick, 2022. "What if? The economic effects for Germany of a stop of energy imports from Russia," SciencePo Working papers Main hal-03881469, HAL.
    33. Mantel, Rolf R., 1976. "Homothetic preferences and community excess demand functions," Journal of Economic Theory, Elsevier, vol. 12(2), pages 197-201, April.
    34. Alexis Akira Toda & Kieran James Walsh & Stijn Van Nieuwerburgh, 2020. "The Equity Premium and the One Percent," The Review of Financial Studies, Society for Financial Studies, vol. 33(8), pages 3583-3623.
    35. Kieran Walsh & Eric Young, 2024. "Equilibrium Multiplicity in Aiyagari and Krusell-Smith," Working Papers 24-13, Federal Reserve Bank of Cleveland.
    36. Dana, Rose Anne, 1993. "Existence and Uniqueness of Equilibria When Preferences Are Additively Separable," Econometrica, Econometric Society, vol. 61(4), pages 953-957, July.
    37. Bar Light, 2020. "Uniqueness of equilibrium in a Bewley–Aiyagari model," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 69(2), pages 435-450, March.
    38. Li, Huiyu & Stachurski, John, 2014. "Solving the income fluctuation problem with unbounded rewards," Journal of Economic Dynamics and Control, Elsevier, vol. 45(C), pages 353-365.
    39. Dana, Rose-Anne, 1999. "Existence, uniqueness and determinacy of equilibrium in C.A.P.M. with a riskless asset," Journal of Mathematical Economics, Elsevier, vol. 32(2), pages 167-175, October.
    40. Varian, Hal R, 1975. "A Third Remark on the Number of Equilibria of an Economy," Econometrica, Econometric Society, vol. 43(5-6), pages 985-986, Sept.-Nov.
    41. Geanakoplos, John & Walsh, Kieran James, 2018. "Uniqueness and stability of equilibrium in economies with two goods," Journal of Economic Theory, Elsevier, vol. 174(C), pages 261-272.
    42. Kirkby, Robert, 2019. "Bewley–Huggett–Aiyagari Models: Computation, Simulation, And Uniqueness Of General Equilibrium," Macroeconomic Dynamics, Cambridge University Press, vol. 23(6), pages 2469-2508, September.
    43. Angeletos, George-Marios & Calvet, Laurent-Emmanuel, 2005. "Incomplete-market dynamics in a neoclassical production economy," Journal of Mathematical Economics, Elsevier, vol. 41(4-5), pages 407-438, August.
    44. Yves Achdou & Jiequn Han & Jean-Michel Lasry & Pierre-Louis Lionse & Benjamin Moll, 2022. "Income and Wealth Distribution in Macroeconomics: A Continuous-Time Approach," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 89(1), pages 45-86.
    45. Patrizio Bifulco & Jochen Gluck & Oliver Krebs & Bohdan Kukharskyy, 2022. "Single and Attractive: Uniqueness and Stability of Economic Equilibria under Monotonicity Assumptions," Papers 2209.02635, arXiv.org.
    46. Ma, Qingyin & Toda, Alexis Akira, 2021. "A theory of the saving rate of the rich," Journal of Economic Theory, Elsevier, vol. 192(C).
    47. Hens, Thorsten & Loeffler, Andras, 1995. "Gross substitution in financial markets," Economics Letters, Elsevier, vol. 49(1), pages 39-43, July.
    48. Alvarez, Fernando & Lucas, Robert Jr., 2007. "General equilibrium analysis of the Eaton-Kortum model of international trade," Journal of Monetary Economics, Elsevier, vol. 54(6), pages 1726-1768, September.
    49. Neng Wang, 2003. "Caballero Meets Bewley: The Permanent-Income Hypothesis in General Equilibrium," American Economic Review, American Economic Association, vol. 93(3), pages 927-936, June.
    50. Chipman, John S., 1974. "Homothetic preferences and aggregation," Journal of Economic Theory, Elsevier, vol. 8(1), pages 26-38, May.
    51. Geanakoplos, John, 1990. "An introduction to general equilibrium with incomplete asset markets," Journal of Mathematical Economics, Elsevier, vol. 19(1-2), pages 1-38.
    52. Won, Dong Chul, 2023. "A new approach to the uniqueness of equilibrium with CRRA preferences," Journal of Economic Theory, Elsevier, vol. 208(C).
    53. Per Krusell & Anthony A. Smith & Jr., 1998. "Income and Wealth Heterogeneity in the Macroeconomy," Journal of Political Economy, University of Chicago Press, vol. 106(5), pages 867-896, October.
    54. Bloise, Gaetano & Citanna, Alessandro, 2015. "Uniqueness of competitive equilibrium with solvency constraints under gross-substitution," Journal of Mathematical Economics, Elsevier, vol. 61(C), pages 287-295.
    55. Rubinstein, Mark, 1974. "An aggregation theorem for securities markets," Journal of Financial Economics, Elsevier, vol. 1(3), pages 225-244, September.
    56. Sonnenschein, Hugo, 1973. "Do Walras' identity and continuity characterize the class of community excess demand functions?," Journal of Economic Theory, Elsevier, vol. 6(4), pages 345-354, August.
    57. Geanakoplos, John D. & Polemarchakis, Heraklis M., 1991. "Overlapping generations," Handbook of Mathematical Economics, in: W. Hildenbrand & H. Sonnenschein (ed.), Handbook of Mathematical Economics, edition 1, volume 4, chapter 35, pages 1899-1960, Elsevier.
    58. Timothy J. Kehoe, 1985. "Multiplicity of Equilibria and Comparative Statics," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 100(1), pages 119-147.
    59. Dougan, William R, 1982. "Giffen Goods and the Law of Demand," Journal of Political Economy, University of Chicago Press, vol. 90(4), pages 809-815, August.
    60. Kehoe, Timothy J. & Levine, David K. & Mas-Colell, Andreu & Woodford, Michael, 1991. "Gross substitutability in large-square economies," Journal of Economic Theory, Elsevier, vol. 54(1), pages 1-25, June.
    61. Sonnenschein, Hugo, 1972. "Market Excess Demand Functions," Econometrica, Econometric Society, vol. 40(3), pages 549-563, May.
    62. Loi, Andrea & Matta, Stefano & Uccheddu, Daria, 2023. "Equilibrium selection under changes in endowments: A geometric approach," Journal of Mathematical Economics, Elsevier, vol. 108(C).
    63. repec:dau:papers:123456789/6112 is not listed on IDEAS
    64. Giménez, Eduardo L., 2022. "Offer curves and uniqueness of competitive equilibrium," Journal of Mathematical Economics, Elsevier, vol. 98(C).
    65. Alexis Akira Toda & Kieran James Walsh, 2017. "Edgeworth box economies with multiple equilibria," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 5(1), pages 65-80, April.
    66. Lorenzo Caliendo & Fernando Parro, 2015. "Estimates of the Trade and Welfare Effects of NAFTA," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 82(1), pages 1-44.
    67. Cao, Dan, 2020. "Recursive equilibrium in Krusell and Smith (1998)," Journal of Economic Theory, Elsevier, vol. 186(C).
    68. Kehoe, Timothy J. & Whalley, John, 1985. "Uniqueness of equilibrium in large-scale numerical general equilibrium models," Journal of Public Economics, Elsevier, vol. 28(2), pages 247-254, November.
    69. John Geanakoplos & Kieran James Walsh, 2018. "Inefficient liquidity provision," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 66(1), pages 213-233, July.
    70. Jonathan Eaton & Samuel Kortum, 2002. "Technology, Geography, and Trade," Econometrica, Econometric Society, vol. 70(5), pages 1741-1779, September.
    71. Loi, Andrea & Matta, Stefano, 2018. "Curvature and uniqueness of equilibrium," Journal of Mathematical Economics, Elsevier, vol. 74(C), pages 62-67.
    72. Huggett, Mark, 1993. "The risk-free rate in heterogeneous-agent incomplete-insurance economies," Journal of Economic Dynamics and Control, Elsevier, vol. 17(5-6), pages 953-969.
    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. Thomas J. Sargent & John Stachurski, 2024. "Dynamic Programming: Finite States," Papers 2401.10473, arXiv.org.
    2. Bar Light, 2020. "Uniqueness of equilibrium in a Bewley–Aiyagari model," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 69(2), pages 435-450, March.
    3. Toda, Alexis Akira, 2017. "Huggett economies with multiple stationary equilibria," Journal of Economic Dynamics and Control, Elsevier, vol. 84(C), pages 77-90.
    4. Giménez, Eduardo L., 2022. "Offer curves and uniqueness of competitive equilibrium," Journal of Mathematical Economics, Elsevier, vol. 98(C).
    5. Won, Dong Chul, 2023. "A new approach to the uniqueness of equilibrium with CRRA preferences," Journal of Economic Theory, Elsevier, vol. 208(C).
    6. Toda, Alexis Akira, 2019. "Wealth distribution with random discount factors," Journal of Monetary Economics, Elsevier, vol. 104(C), pages 101-113.
    7. David Staines, 2023. "Stochastic Equilibrium the Lucas Critique and Keynesian Economics," Papers 2312.16214, arXiv.org, revised Jun 2024.
    8. Stachurski, John & Toda, Alexis Akira, 2019. "An impossibility theorem for wealth in heterogeneous-agent models with limited heterogeneity," Journal of Economic Theory, Elsevier, vol. 182(C), pages 1-24.
    9. Rodrigo Adão & Costas Arkolakis & Federico Esposito, 2019. "General Equilibrium Effects in Space: Theory and Measurement," NBER Working Papers 25544, National Bureau of Economic Research, Inc.
    10. Bar Light, 2019. "General equilibrium in a heterogeneous-agent incomplete-market economy with many consumption goods and a risk-free bond," Papers 1906.06810, arXiv.org, revised Mar 2021.
    11. Ma, Qingyin & Toda, Alexis Akira, 2022. "Asymptotic linearity of consumption functions and computational efficiency," Journal of Mathematical Economics, Elsevier, vol. 98(C).
    12. Alexis Akira Toda & Kieran James Walsh, 2017. "Edgeworth box economies with multiple equilibria," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 5(1), pages 65-80, April.
    13. 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.
    14. Athreya, Kartik B., 2014. "Big Ideas in Macroeconomics: A Nontechnical View," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262019736, December.
    15. E. M. Bosker & Bastian Westbrock, 2014. "A theory of trade in a global production network," Working Papers 14-14, Utrecht School of Economics.
    16. 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).
    17. Patrizio Bifulco & Jochen Gluck & Oliver Krebs & Bohdan Kukharskyy, 2022. "Single and Attractive: Uniqueness and Stability of Economic Equilibria under Monotonicity Assumptions," Papers 2209.02635, arXiv.org.
    18. Simone Landini & Mauro Gallegati & J. Barkley Rosser, 2020. "Consistency and incompleteness in general equilibrium theory," Journal of Evolutionary Economics, Springer, vol. 30(1), pages 205-230, January.
    19. Ma, Qingyin & Stachurski, John & Toda, Alexis Akira, 2020. "The income fluctuation problem and the evolution of wealth," Journal of Economic Theory, Elsevier, vol. 187(C).
    20. Marcello D’Amato & Christian Di Pietro & Marco M. Sorge, 2024. "Left and right: a tale of two tails of the wealth distribution," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 78(4), pages 1389-1433, December.

    More about this item

    Keywords

    General equilibrium theory; Uniqueness;

    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:mateco:v:113:y:2024:i:c:s0304406824000697. 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.