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Zbl 1232.91493
Capasso, V.; Engbers, R.; La Torre, D.
On a spatial Solow model with technological diffusion and nonconcave production function. (English)
[J] Nonlinear Anal., Real World Appl. 11, No. 5, 3858-3876 (2010). ISSN 1468-1218

Summary: The classical Solow model is extended, by considering spatial dependence of the physical capital and technological progress, and by introducing a nonconcave production function. The physical capital and technological progress accumulation equations are governed by semilinear parabolic differential equations which describe their evolution over time and space. The convergence to a steady state according to different hypotheses on the production function is discussed. The analysis is focused on an S-shaped production function, which allows the existence of saddle points and poverty traps. The evolution of this system over time, and its convergence to the steady state is described mainly through numerical simulations.

MSC 2000:: *91B62 Dynamic economic models etc.
91B55
91B72 Spatial models

Keywords: Solow model; economic growth; economic geography; spatial variables; saddle-point behavior; nonconcave production function

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