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We discuss the role of the elasticity of substitution in the local determinacy properties of a steady state or a stationary balanced growth path in a general multisector economy with CES technologies. Our main results are the following: We give some sufficient conditions for the occurrence of local indeterminacy in exogenous and endogenous growth models. We show that local indeterminacy takes place even without a capital intensity reversal from the private to the social level if the productive factors are weakly substitutable. Moreover, we show that the conditions for local indeterminacy in exogenous growth models and in endogenous growth models may be qualitatively different.
This article considers a two-sector model of economic growth with “labour-augmenting” intersectoral external effects stemming from the aggregate capital stock. It is shown that equilibrium balanced growth paths with a non-trivial labour allocation scheme become available. A set of sufficient conditions for the existence of multiple equilibrium growth rays is provided and their determinacy properties are then characterised. Finally, examination of a parameterised C.E.S. economy illustrates the central role of non-unitary values for the elasticity of substitution in the multiplicity issue. Copyright Springer-Verlag Berlin Heidelberg 2003
This paper deals with an OLG model with production and a single commodity, in which agents are assumed altruistic and the aggregate production function contains external effects. I prove that, if the technology satisfies a minor assumption, which encompasses positive and negative externalities, some curvature conditions on the utility function ensure local determinacy of stationary and period 2 equilibria. I prove that non-separable, strictly concave preferences are a fundamental ingredient for the occurrence of indeterminate equilibria. Finally, considering the case of unbounded growth, I establish that for any utility and production functions a unique balanced growth path is globally determinate.
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We consider a discrete-time two-sector Cobb-Douglas economy with positive sector specific external effects. We show that indeterminacy of steady states and cycles can easily arise with constant or decreasing social returns to scale, and very small market imperfections. This is in sharp contrast with most of the contributions in the literature in which increasing social returns are required to generate indeterminacy.