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Determinacy of equilibria in dynamic models with finitely many consumers

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Author Info
Timothy J. Kehoe
David K. Levine
Paul M. Romer

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Abstract

We consider a production economy with a finite number of heterogeneous, infinitely lived consumers. We show that, if the economy is smooth enough, equilibria are locally unique for almost all endowments. We do so by converting the infinite-dimensional fixed point problem stated in terms of prices and commodities into a finite-dimensional Negishi problem involving individual weights in a social value function. By adding artificial fixed factors to utility and production functions, we can write the equilibrium conditions equating spending and income for each consumer entirely in terms of time-zero factor endowments and derivatives of the social value function.

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Paper provided by Federal Reserve Bank of Minneapolis in its series Staff Report with number 118.

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Date of creation: 1989
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Handle: RePEc:fip:fedmsr:118

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Keywords: Consumption (Economics) Production (Economic theory)

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Deneckere, Raymond & Pelikan, Steve, 1986. "Competitive chaos," Journal of Economic Theory, Elsevier, vol. 40(1), pages 13-25, October. [Downloadable!] (restricted)
  2. Benveniste, L M & Scheinkman, J A, 1979. "On the Differentiability of the Value Function in Dynamic Models of Economics," Econometrica, Econometric Society, vol. 47(3), pages 727-32, May. [Downloadable!] (restricted)
  3. Montrucchio, Luigi, 1987. "Lipschitz continuous policy functions for strongly concave optimization problems," Journal of Mathematical Economics, Elsevier, vol. 16(3), pages 259-273, June. [Downloadable!] (restricted)
  4. Bewley, Truman F., 1980. "The permanent income hypothesis and long-run economic stability," Journal of Economic Theory, Elsevier, vol. 22(3), pages 377-394, June. [Downloadable!] (restricted)
  5. Timothy J. Kehoe & David K. Levine & Paul Romer, 1989. "Steady States and Determinacy in Economies with Infinitely Lived Agents," Levine's Working Paper Archive 52, UCLA Department of Economics. [Downloadable!]
  6. Blume, Lawrence & Easley, David & O'Hara, Maureen, 1982. "Characterization of optimal plans for stochastic dynamic programs," Journal of Economic Theory, Elsevier, vol. 28(2), pages 221-234, December. [Downloadable!] (restricted)
  7. Timothy J. Kehoe & David K. Levine, 1990. "The Economics of Indeterminacy in Overlapping Generations Models," Levine's Working Paper Archive 2193, UCLA Department of Economics. [Downloadable!]
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  8. Boldrin, Michele & Montrucchio, Luigi, 1986. "On the indeterminacy of capital accumulation paths," Journal of Economic Theory, Elsevier, vol. 40(1), pages 26-39, October. [Downloadable!] (restricted)
  9. Timothy J. Kehoe & David K. Levine & Andreu Mas-Colell & William Zame, 1989. "Determinacy of Equilibrium in Large Square Economies," Levine's Working Paper Archive 46, UCLA Department of Economics. [Downloadable!]
  10. Timothy J Kehoe & David K Levine, 1985. "Comparative Statics and Perfect Foresight in Infinite Horizon Economies," Levine's Working Paper Archive 1873, UCLA Department of Economics. [Downloadable!]
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  11. Varian, Hal R, 1975. "A Third Remark on the Number of Equilibria of an Economy," Econometrica, Econometric Society, vol. 43(5-6), pages 985-86, Sept.-Nov. [Downloadable!] (restricted)
  12. Bewley, Truman, 1982. "An integration of equilibrium theory and turnpike theory," Journal of Mathematical Economics, Elsevier, vol. 10(2-3), pages 233-267, September. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Manjira Datta & Leonard Mirman & Kevin Reffett, . "Existence and Uniqueness of Equilibrium in Distorted Dynamic Economies with Capital and Labor," Working Papers 2132846, Department of Economics, W. P. Carey School of Business, Arizona State University. [Downloadable!]
    Other versions:
  2. Timothy J. Kehoe & David K. Levine & Paul M. Romer, 1990. "On characterizing equilibria of economies with externalities and taxes as solutions to optimization problems," Working Papers 436, Federal Reserve Bank of Minneapolis. [Downloadable!]
    Other versions:
  3. Christian Ghiglino & Marielle Olszak-Duquenne, 2004. "On the Impact of Heterogeneity on Indeterminacy," Cahiers du Département d'Econométrie 2004.09, Département d'Econométrie, Université de Genève. [Downloadable!]
    Other versions:
  4. Stefano Bosi & Thomas Seegmuller, 2006. "Optimal Cycles and Social Inequality: What Do We Learn from the Gini Index?," Post-Print halshs-00194182_v1, HAL. [Downloadable!]
  5. Kevin Reffett & Manjira Datta & Leonard Mirman & Olivier Morand, . "Monotone Methods for Markovian Equilibrium in Dynamic Economies," Working Papers 2133476, Department of Economics, W. P. Carey School of Business, Arizona State University. [Downloadable!]
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  6. Christian Ghiglino & Marielle Olszak-Duquenne, 2002. "The impact of heterogeneity on indeterminacy," Diskussionsschriften dp0213, Universitaet Bern, Departement Volkswirtschaft. [Downloadable!]
  7. Joël Blot & Bertrand Crettez, 2004. "On the smoothness of optimal paths," Decisions in Economics and Finance, Springer, vol. 27(1), pages 1-34, 08. [Downloadable!] (restricted)
  8. Chris Shannon & William R. Zame, 1999. "Quadratic Concavity and the Determinancy of Equilibrium," UCLA Economics Working Papers 791, UCLA Department of Economics. [Downloadable!]
  9. Christian Ghiglino & Alain Venditti, 2008. "The role of the wealth distribution on output volatility," Economics Discussion Papers 653, University of Essex, Department of Economics. [Downloadable!]
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  10. Christian Ghiglino, 2003. "Wealth inequality and dynamic stability," Diskussionsschriften dp0310, Universitaet Bern, Departement Volkswirtschaft. [Downloadable!]
    Other versions:
  11. Timothy J. Kehoe & David K. Levine & Andreu Mas-Colell & William Zame, 1989. "Determinacy of Equilibrium in Large Square Economies," Levine's Working Paper Archive 46, UCLA Department of Economics. [Downloadable!]
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