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Comparative Dynamics In Stochastic Models With Respect To The L∞–L∞ Duality: A Differential Approach


  • Sato, Kenji
  • Yano, Makoto


Many economic analyses are based on the property that the value of a commodity vector responds continuously to a change in economic environment. As is well known, however, many infinite-dimensional models, such as an infinite–time horizon stochastic growth model, lack this property. In the present paper, we investigate a stochastic growth model in which dual vectors lie in an L ∞ space. This result ensures that the value of a stock vector is jointly continuous with respect to the stock vector and its support price vector. The result is based on the differentiation method in Banach spaces that Yano [ Journal of Mathematical Economics 18 (1989), 169–185] develops for stochastic growth models.

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  • Sato, Kenji & Yano, Makoto, 2012. "Comparative Dynamics In Stochastic Models With Respect To The L∞–L∞ Duality: A Differential Approach," Macroeconomic Dynamics, Cambridge University Press, vol. 16(S1), pages 127-138, April.
  • Handle: RePEc:cup:macdyn:v:16:y:2012:i:s1:p:127-138_00

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    References listed on IDEAS

    1. Peleg, Bezalel & Yaari, Menahem E, 1970. "Markets with Countably Many Commodities," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 11(3), pages 369-377, October.
    2. Le Van, Cuong & Cagri Saglam, H., 2004. "Optimal growth models and the Lagrange multiplier," Journal of Mathematical Economics, Elsevier, vol. 40(3-4), pages 393-410, June.
    3. Cuong Le Van & Yiannis Vailakis, 2003. "Existence of a competitive equilibrium in a one sector growth model with heterogeneous agents and irreversible investment," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 22(4), pages 743-771, November.
    4. repec:dau:papers:123456789/13605 is not listed on IDEAS
    5. Le Van, Cuong & Nguyen, Manh-Hung & Vailakis, Yiannis, 2007. "Equilibrium dynamics in an aggregative model of capital accumulation with heterogeneous agents and elastic labor," Journal of Mathematical Economics, Elsevier, vol. 43(3-4), pages 287-317, April.
    6. Kim, K. H., 1990. "Existence and optimality of competitive equilibria. : C.D. Aliprantis, D.J. Brown, and O. Burkinshaw, Berlin: Springer-Verlag, 1989, 284 pages, 110 DM," Mathematical Social Sciences, Elsevier, vol. 20(2), pages 197-197, October.
    7. repec:hal:journl:halshs-00119098 is not listed on IDEAS
    8. Cuong Le Van & Yiannis Vailakis, 2004. "Existence of competitive equilibrium in a single-sector growth model with elastic labour," Cahiers de la Maison des Sciences Economiques b04123, Université Panthéon-Sorbonne (Paris 1).
    9. Cuong Le Van & Rose-Anne Dana, 2003. "Dynamic Programming in Economics," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00119098, HAL.
    10. repec:dau:papers:123456789/416 is not listed on IDEAS
    11. Bewley, Truman F., 1972. "Existence of equilibria in economies with infinitely many commodities," Journal of Economic Theory, Elsevier, vol. 4(3), pages 514-540, June.
    12. Robert A. Becker, 1980. "On the Long-Run Steady State in a Simple Dynamic Model of Equilibrium with Heterogeneous Households," The Quarterly Journal of Economics, Oxford University Press, vol. 95(2), pages 375-382.
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