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Long cycles in a modified Solow growth model

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Abstract

In this paper we analyze the dynamics of the Solow growth model with a generic production function. For this purpose, we consider that the labor growth rate, \(L^{\prime }(t)/L(t)\), is a \(T\)-periodic function, for a fixed positive real number \(T\). We obtain the closed form solutions for the fundamental Solow equation with the new description of \(L(t)\), using a Cobb–Douglas production function. Using notions of the qualitative theory of ordinary differential equations and nonlinear functional analysis, we prove that there exists a \(T\)-periodic solution for the Solow equation with a generic production function. From the macroeconomic point of view this is a refined Solow model, which exhibits a smooth cyclic behavior in the economy with long period and relatively small amplitude.

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Correspondence to Fátima Fabião.

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This research has been supported by Fundação para a Ciência e Tecnologia, FCT, program FEDER/POCI 2010.

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Fabião, F., Teixeira, J. & Borges, M.J. Long cycles in a modified Solow growth model. J Econ Interact Coord 10, 247–263 (2015). https://doi.org/10.1007/s11403-013-0122-0

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