On a Generalized Integro-Differential Spatial Model of Economic Growth
Herb Kunze
, , Simone Marsiglio
In: Kilgour, D.M., Kunze, H., Makarov, R., Melnik, R., Wang, X. Eds, 2022, Recent Developments in Mathematical, Statistical and Computational Sciences, Cham: Springer, pp. 681-692
Economic growth
Spatial Solows model
Ramsey model
Cobb-Douglas production function
Abstract
We analyze a spatial economic growth model in which production in each location is determined by the amount of output produced in other locations within an industrial cluster as well. Therefore, the evolution of capital gives rise to an integro-differential extension of the basic spatial economic growth model. We analyze the model both in a purely dynamic setting and in an optimal control framework, proposing a numerical algorithm to solve the model under the latter scenario. Different from previous studies, our algorithm allows to solve the model even in a setting in which the objective function is nonlinear, permitting thus to analyze the spatial features of the model even in its traditional formulation from economic growth theory.