We present a spatially structured dynamic economic growth model which takes into account the level of pollution induced by production, and a possible taxation based on the amount of produced pollution. Then we analyze an optimal harvesting control problem with an objective function composed of three terms, namely the intertemporal utility of the decision maker, the space-time average of the level of pollution in the habitat, and the disutility due to the imposition of taxation. With respect to our previous works, in this paper, the system is subject to two controls, namely the level of consumption and, in addition, the taxation on physical capital rate. The optimal controls are determined by means of a sweep-type numerical algorithm that allows to solve a system of four backward-forward reaction-diffusion equations.
Reaction-diffusion systems Integral nonlocal term Large-time behavior Control problems Economic growth Environmental quality Taxation Convex-concave production function
Mathematics Subject Classification (2010)
35K57 35Q91 93D15 49K20 91B62 91B76
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The work of S. Aniţa was supported by a grant of the Romanian Ministry of National Education, CNCS-UEFISCDI, project number PN-II-ID-PCE-2012-4-0270 (68/2.09.2013): “Optimal Control and Stabilization of Nonlinear Parabolic Systems with State Constraints. Applications in Life Sciences and Economics”. The work by V. Capasso has been supported by a Chair of Excellence at the Universidad Carlos III de Madrid.
Aniţa, S., Capasso, V., Kunze, H., La Torre, D.: Optimal control and long-run dynamics for a spatial economic growth model with physical capital accumulation and pollution diffusion. Appl. Math. Lett. 26, 908–912 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
Aniţa, S., Capasso, V., Kunze, H., La Torre, D.: Dynamics and optimal control in a spatially structured economic growth model with pollution diffusion and environmental taxation. Appl. Math. Lett. 42, 36–40 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
Aniţa, S., Capasso, V., Kunze, H., La Torre, D.: Dynamics and control of an integro-differential system of geographical economics. Ann. Acad. Rom. Sci. Ser. Math. Appl. 7, 8–26 (2015)MathSciNetzbMATHGoogle Scholar
Athanassoglou, S., Xepapadeas, A.: Pollution control with uncertain stock dynamics: when, and how, to be precautious. J. Environ. Econ. Manag. 63, 304–320 (2012)CrossRefGoogle Scholar
Beckerman, W.: Economic growth and the environment: whose growth? Whose environment? World Dev. 20, 481–496 (1992)CrossRefGoogle Scholar
Bertinelli, L., Strobl, E., Zou, B.: Sustainable economic development and the environment: theory and evidence. Energy Econ. 34, 1105–1114 (2012)CrossRefGoogle Scholar
Boucekkine, R., Camacho, C., Zou, B.: Bridging the gap between growth theory and the new economic geography: the spatial Ramsey model. Macroecon. Dyn. 13, 20–45 (2009)CrossRefzbMATHGoogle Scholar
Brito, P.: The dynamics of growth and distribution in a spatially heterogeneous world. UECE-ISEG, Technical University of Lisbon (2004)Google Scholar
Brock, W., Xepapadeas, A.: Diffusion-induced instability and pattern formation in infinite horizon recursive optimal control. J. Econ. Dyn. Control 32, 2745–2787 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
Brock, W., Xepapadeas, A.: Pattern formation, spatial externalities and regulation in coupled economic-ecological systems. J. Environ. Econ. Manag. 59, 149–164 (2010)CrossRefzbMATHGoogle Scholar
Capasso, V., Engbers, R., La Torre, D.D.: On the spatial Solow model with technological diffusion and nonconcave production function. Nonlin. Anal. Real World Appl. 11, 3858–3876 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
Fujita, M., Krugman, P., Venables, A.: The Spatial Economy. Cities, Regions and International Trade. MIT Press, Cambridge (1999)zbMATHGoogle Scholar