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Explicit Saddle Path for Optimal Growth Models

Khelifi, Atef (2010): Explicit Saddle Path for Optimal Growth Models. Published in: International Journal of Economics and Finance , Vol. 2, No. 5 (November 2010): pp. 116-121.

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This paper shows that the standard optimal growth model can be solved explicitly by using a utility function describing preferences for consumption and savings. Such a maximising criterion including the flow of savings can actually be strongly motivated by two arguments. First, and most importantly, the basic assumption of a representative agent who wishes to consume and save a part of his income each time, can be interpreted as an implicit assumption of some degree of preference for thriftiness. Second, this function formalizes also the concept of Max Weber’s spirit of capitalism (with a direct preference for wealth), which makes the model similar to the one of Heng-Fu Zou (1994) except that his specification includes the capital stock. The resulting model offers elegant and very simple closed form solutions which can be used easily (and quantitatively) on real data. It presents the same golden rule balanced growth path solutions as the Solow model (1956), with a faster (explicit) transition.

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