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Equilibria of heterogeneous economies with a continuum of agents

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  • Santiago Mira-Navarro

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    (Universidad de Las Palmas de Gran Canaria. Departamento de Análisis Económico Aplicado)

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    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 defines 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 specific operator is proved. Moreover, the existence of a steady state for the aggregate state of the system is obtained through the Schauder-Tychonoff Theorem. The results are related to models available in the literature.

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    File URL: http://www.bibliotecas.ulpgc.es/fcee/hemeroteca/documentos%20de%20trabajo/DocumentosDTrabajo/doc6/dt2002-08.pdf
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    Bibliographic Info

    Paper provided by Facultad de Ciencias Económicas de la ULPGC in its series Documentos de trabajo conjunto ULL-ULPGC with number 2002-08.

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    Length: 25 pages
    Date of creation: 2002
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    Handle: RePEc:can:series:2002-08

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    Related research

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

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    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.
    2. Magill, M. & Quinzii, M., 1992. "Infinite Horizon Incomplete Markets," Papers 413a, California Davis - Institute of Governmental Affairs.
    3. Krusell, P & Smith Jr, A-A, 1995. "Income and Wealth Heterogeneity in the Macroeconomic," RCER Working Papers 399, University of Rochester - Center for Economic Research (RCER).
    4. S. Rao Aiyagari, 1993. "Uninsured idiosyncratic risk and aggregate saving," Working Papers 502, Federal Reserve Bank of Minneapolis.
    5. Wouter J. Denhaan, 2000. "The Importance Of The Number Of Different Agents In A Heterogeneous Asset-Pricing Model," Computing in Economics and Finance 2000 349, Society for Computational Economics.
    6. Hakansson, Nils H, 1970. "Optimal Investment and Consumption Strategies Under Risk for a Class of Utility Functions," Econometrica, Econometric Society, vol. 38(5), pages 587-607, September.
    7. 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.
    8. Greenwood, J. & Huffman, G.W., 1993. "On the Existence of Nonoptimal Equilibria," RCER Working Papers 370, University of Rochester - Center for Economic Research (RCER).
    9. 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.
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