Research Paper on Application of the Spatial Solow Model to the Mathematical Modeling of Physical Capital Diffusion: Smuggling in Venezuela

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Title: Application of the Spatial Solow Model to the Mathematical Modeling of Physical Capital Diffusion: Smuggling in Venezuela

Abstract: In this study, a mathematical modeling strategy for the physical capital diffusion across national boundaries is proposed. For a country’s economic health, physical capital is regarded as a key factor. Here, we describe how smuggling affects a nation’s economic growth using an extension of the economic Solow model. We concentrate particularly on the circumstances in Venezuela from 2012 to 2015. Instead of the traditional Cobb-Douglas production function in this case, we rely on a nonconcave production function. We also look into how various physical capital fluxes affect economic growth. Based on a parabolic partial differential equation describing the dynamics of physical capital and Neumann type boundary conditions, the diffusion of physical capital across a nation’s borders is modeled. Smuggling occurs at many international borders and can involve things like food, machinery, and fuel. The economy of a particular nation is challenged by this border smuggling. The issue of smuggling is typically connected to subsidies or an unofficial exchange rate that differs from the official rate. Using an expanded Solow model, we examine how smuggling affects a nation’s physical capital. Utilizing an explicit finite difference scheme, numerical simulations are obtained to show how a country’s economic growth is impacted by the physical diffusion of capital across its border. One of the most important factors in the economic development of many nations is the study of physical capital. The findings demonstrate that the dynamics of physical capital differ from the classical economic behavior seen in the classical spatial Solow model without physical capital flux across international borders when boundary conditions of Neumann type are different from zero. The numerical results specifically demonstrate that as the flux on the borders increases, a country’s physical capital decreases more quickly. We can therefore draw the conclusion that preventing border smuggling is a significant factor affecting economic growth.

Keywords: Solow model; mathematical modeling; physical capital; numerical simulation; Neumann boundary conditions

Paper Quality: SCOPUS / Web of Science Level Research Paper

Subject: Economics

Writer Experience: 20+ Years

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