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Pré-Publication, Document De Travail Année : 2023

Long-run cycles in a growth model with natural externalities

Stefano Bosi
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Thai Ha-Huy

Résumé

In this paper, we consider an AK model augmented with a productive externality of nature and a process of natural capital accumulation where a reproduction force is moderated by the negative impact of productive pollution. Differently from the existing literature, more focused on the planner's solution, we consider a market economy and the effects of its imperfections. We introduce two distinct natural accumulation processes: a power law, more usual in economics, and a logistic law, more popular in ecology. In both cases, we observe the occurrence of cycles of period two, cycle of period a power of two and chaos through a flip bifurcation and perioddoubling bifurcations. In the case of the power law, dynamics are even richer because of the possibility of limit cycles through a Neimark-Sacker bifurcation. In the case of a power law, cycles occur under a larger Total Factor Productivity because the TFP amplifies the negative impact of pollution on natural regeneration. In the case of a logistic law, cycles take place when the saturation effect of nature as a larger negative impact on the reproduction process.
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Dates et versions

hal-03968528 , version 1 (01-02-2023)
hal-03968528 , version 2 (27-04-2023)
hal-03968528 , version 3 (19-06-2023)
hal-03968528 , version 4 (09-08-2023)

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  • HAL Id : hal-03968528 , version 4

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Stefano Bosi, Thai Ha-Huy. Long-run cycles in a growth model with natural externalities. 2023. ⟨hal-03968528v4⟩

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