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LOCAL INDETERMINACY IN CONTINUOUS-TIME MODELS: THE ROLE OF RETURNS TO SCALE

Published online by Cambridge University Press:  22 August 2012

Jean-Philippe Garnier ,
Kazuo Nishimura  and
Alain Venditti
Jean-Philippe Garnier
Affiliation:
Université de Lille 3 & EQUIPPE
Kazuo Nishimura
Affiliation:
Kyoto University
Alain Venditti*
Affiliation:
CNRS–GREQAM & EDHEC
*
Address correspondence to: Alain Venditti, CNRS-GREQAM, 2 rue de la Charité, 13002 Marseille, France; e-mail: alain.venditti@univmed.fr.
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Abstract

The aim of this paper is to discuss the effect on returns to scale on the local determinacy properties of the steady state in a continuous-time two-sector economy with endogenous labor supply and sector-specific externalities. First we show that when labor is inelastic and the elasticity of intertemporal substitution in consumption is large enough, for any configuration of the returns to scale, local indeterminacy is obtained if there is a capital intensity reversal between the private and the social levels. Second, we prove that when labor is infinitely elastic, saddlepoint stability is obtained if the investment good sector has constant social returns, whereas local indeterminacy arises if the investment good sector has increasing social returns and the elasticity of intertemporal substitution in consumption admits intermediate values. Finally, our main conclusion shows that local indeterminacy requires a low elasticity of labor when the investment good has constant social returns, but requires either a low enough or a large enough elasticity of labor when the investment good has increasing social returns.

Keywords

Infinite-Horizon Growth ModelsSector-Specific ExternalitiesIndeterminacyNonlinear DynamicsOptimal Control
Type
Articles
Information
Macroeconomic Dynamics , Volume 17 , Issue 2 , March 2013 , pp. 326 - 355
Copyright
Copyright © Cambridge University Press 2012

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