On the gamma-logistic map and applications to a delayed neoclassical model of economic growth
In this work, we study the stability properties of a delay differential neoclassical model of economic growth, based on the original model proposed by Solow (Q J Econ 70:65–94, 1956). We consider a logistic-type production function, which comes from combining a Cobb–Douglas function and a linear pollution effect caused by increasing concentrations of capital. The difference between the production function and the classical logistic map comes from the presence of a parameter \(\gamma \in (0,1)\) in the exponent of one factor. We call this new function the gamma-logistic map. Our main purpose is to obtain sharp global stability conditions for the positive equilibrium of the model and to study how the stability properties of such equilibrium depend on the relevant model parameters. This study is developed by using some properties of the gamma-logistic map and some well-known results connecting stability in delay differential equations and discrete dynamical systems. Finally, we also compare the obtained results with the ones written in related articles.
KeywordsDelay differential equation Neoclassical growth model Global stability Gamma-logistic map
Mathematics Subject Classification34K20 91B62
The author thanks Prof. Eduardo Liz for all his ideas, work and suggestions throughout the discussion of the model and the improvement of the document. Moreover, the author also acknowledges all the valuable comments coming from the referee process, which led to clearer explanations and a better motivation of the model. This research has been partially supported by Ministerio de Educación, Cultura y Deporte of Spain (Grant No. FPU16/04416), Consellería de Cultura, Educación e Ordenación Universitaria da Xunta de Galicia (Grant Nos. ED481A-2017/030, GRC2015/004 and R2016/022) and Agencia Estatal de Investigación of Spain (Grant No. MTM2016-75140-P, cofunded by European Community fund FEDER).
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Conflict of interest
The author declares that there is no conflict of interest.
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