Spatial Dynamics for a Generalized Solow Growth Model

Zhong, Yue; Huang, Wenyi

doi:10.1155/2018/6945032

Cited by 6 publications

(7 citation statements)

References 26 publications

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“…These delays are related to the gestation time in physical capital and maturation time in human capital. In addition, spatial versions of the Solow's Swan model of economic growth have been developed and applied to different economic situations (Camacho and Zou 2004;Camacho et al 2008;Capasso et al 2010;Ding et al 2021;Xepapadeas and Yannacopoulos 2016;Zhang 2020;Zhang et al 2022;Zhong and Huang 2018). In (Ding et al 2021), the authors introduced human capital into the Solow model to compare the importance of physical capital and human capital on economic growth.…”

Section: Spatial Solow Model For Physical Capital With Nononcave Prod...mentioning

confidence: 99%

“…In (Ding et al 2021), the authors introduced human capital into the Solow model to compare the importance of physical capital and human capital on economic growth. In (Zhong and Huang 2018), a generalized Solow model with continuous space and bounded time was developed. Moreover, concave and nonconcave production functions were introduced into the generalized Solow model in close regions.…”

Section: Spatial Solow Model For Physical Capital With Nononcave Prod...mentioning

confidence: 99%

“…However, implicit methods without stability problems to solve the spatial Solow model numerically can be found in (Camacho and Zou 2004;Camacho et al 2008;Capasso et al 2010). In (Zhong and Huang 2018), the authors developed a numerical scheme for the system of partial differential equations related to the generalized Solow model. In this work, we developed a numerical scheme for the particular mathematical model and varied it depending on the boundary conditions related to government policies on the border of a country and other factors.…”

Section: Numerical Simulationsmentioning

confidence: 99%

“…These delays were related to the gestation time in physical capital and maturation time in human capital. Moreover, spatial versions of Solow's Swan model of economic growth have been developed (Camacho and Zou 2004;Camacho et al 2008;Capasso et al 2010;Xepapadeas and Yannacopoulos 2016;Zhang 2020;Zhong and Huang 2018). In (Zhong and Huang 2018), the authors investigated a generalized Solow model with continuous space and bounded time.…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, spatial versions of Solow's Swan model of economic growth have been developed (Camacho and Zou 2004;Camacho et al 2008;Capasso et al 2010;Xepapadeas and Yannacopoulos 2016;Zhang 2020;Zhong and Huang 2018). In (Zhong and Huang 2018), the authors investigated a generalized Solow model with continuous space and bounded time. They introduced, concave and nonconcave production functions into the generalized Solow model in close regions, and they obtained the steady states of the model under some conditions.…”

Section: Introductionmentioning

confidence: 99%

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Mathematical Modeling of Physical Capital Diffusion Using a Spatial Solow Model: Application to Smuggling in Venezuela

et al. 2022

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This study proposes a mathematical modeling approach for the physical capital diffusion through the borders of countries. Physical capital is considered a crucial variable for the economic growth of a nation. Here, we use an extension of the economic Solow model to describe how smuggling affects the economic growth of countries. In particular, we focus on the situation in Venezuela from 2012 to 2015. In this regard, we rely on a nonconcave production function instead of the classical Cobb–Douglas production function. Moreover, we investigate the effect of different physical capital fluxes on economic growth. The physical capital diffusion through the borders of a country is modeled based on a parabolic partial differential equation describing the dynamics of physical capital and boundary conditions of the Neumann type. Smuggling is present at numerous borders between countries and may include fuel, machinery, and food. This smuggling through the borders places challenges on a particular country’s economy. The smuggling problem usually is related to a non-official exchange rate different from the official rate or subsidies. We study the effect of smuggling on the physical capital of a country using an extended Solow model. Numerical simulations are obtained using an explicit finite difference scheme describing how the physical capital diffusion through the border of a country affects its economic growth. The study of physical capital is a paramount aspect of the economic growth of several countries. The results show that when boundary conditions of Neumann type are different from zero, the dynamics of the physical capital differ from the classical economic behavior observed in the classical spatial Solow model without physical capital flux through the borders of countries. In particular, the numerical results show that the physical capital of a country decreases faster as the flux increases on the boundaries. Thus, we can conclude that avoiding smuggling through the frontiers is a crucial factor affecting economic growth.

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