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Equilibria of Heterogeneous Economies with a Continuum of Agents

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Author Info
Santiago Mira-Navarro (Universidad de Las Palmas de Gran Canaria)
Abstract

The dynamic heterogeneous economies studied are described by a collection of heterogenous indi- viduals, their individual states and an aggregate state, such that the individuals' actions are given by the policy obtained from an optimization program and the aggregate law of motion is given by the aggregation of the individuals' actions. These economies have been used in computer simula- tions, however the analytical information about the equilibria of such economies is scarce and the classical approach of Stokey and Lucas with Prescott (1989) does not apply. This paper denes the relevant concepts of equilibria and proves the existence of such equilibria using the Schauder Fixed Point Theorem. In order to apply Schauder's theorem, a metric for the space of operators between measures is provided, and the compactness of a specic operator is proved. Moreover, the existence of a steady state for the aggregate state of the system is obtained through the Schauder-Tychonov Theorem. The results are related to models available in the literature.

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Paper provided by Centro de Altisimos Estudios Rios Perez (CAERP) in its series Centro de Alti­simos Estudios Ri­os Pe©rez(CAERP) with number 5.

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Length: 25 pages
Date of creation: 2003
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Handle: RePEc:cae:caerpp:5

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Related research
Keywords: Dynamic Programming; Spaces of Measures; Fixed Point Theorems; Heterogeneous Economies;

Find related papers by JEL classification:
C68 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Computable General Equilibrium Models
E30 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - General (includes Measurement and Data)
E60 - Macroeconomics and Monetary Economics - - Macroeconomic Policy, Macroeconomic Aspects of Public Finance, and General Outlook - - - General

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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. Huggett, Mark, 1997. "The one-sector growth model with idiosyncratic shocks: Steady states and dynamics," Journal of Monetary Economics, Elsevier, vol. 39(3), pages 385-403, August. [Downloadable!] (restricted)
  2. Hopenhayn, Hugo A & Prescott, Edward C, 1992. "Stochastic Monotonicity and Stationary Distributions for Dynamic Economies," Econometrica, Econometric Society, vol. 60(6), pages 1387-406, November. [Downloadable!] (restricted)
  3. Greenwood, J. & Huffman, G.W., 1993. "On the Existence of Nonoptimal Equilibria," RCER Working Papers 370, University of Rochester - Center for Economic Research (RCER).
  4. 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. [Downloadable!] (restricted)
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  5. Den Haan, Wouter J., 2001. "The importance of the number of different agents in a heterogeneous asset-pricing model," Journal of Economic Dynamics and Control, Elsevier, vol. 25(5), pages 721-746, May. [Downloadable!] (restricted)
  6. Magill, Michael & Quinzii, Martine, 1994. "Infinite Horizon Incomplete Markets," Econometrica, Econometric Society, vol. 62(4), pages 853-80, July. [Downloadable!] (restricted)
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  7. 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. [Downloadable!] (restricted)
  8. Aiyagari, S Rao, 1994. "Uninsured Idiosyncratic Risk and Aggregate Saving," The Quarterly Journal of Economics, MIT Press, vol. 109(3), pages 659-84, August. [Downloadable!] (restricted)
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