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COMPARATIVE DYNAMICS IN STOCHASTIC MODELS WITH RESPECT TO THE L∞–L∞ DUALITY: A DIFFERENTIAL APPROACH

Published online by Cambridge University Press:  14 March 2012

Kenji Sato  and
Makoto Yano
Kenji Sato
Affiliation:
Kyoto University
Makoto Yano*
Affiliation:
Kyoto University
*
Address correspondence to: Makoto Yano, Institute of Economic Research, Kyoto University, Yoshida-honmachi, Sakyo-ku, Kyoto 606-8501, Japan; e-mail: [email protected].
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Abstract

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.

Keywords

Stochastic Optimal Growth ModelComparative DynamicsInfinite-Dimensional Differential Approach
Type
Articles
Information
Macroeconomic Dynamics , Volume 16 , Supplement S1: Nonlinear Dynamics in Equilibrium Models , April 2012 , pp. 127 - 138
Copyright
Copyright © Cambridge University Press 2012

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