A model in continuous time and space to study economic migration

Population movements modify the environment, land-use, and shape the landscape through urbanization. Furthermore, migration has become one of the most relevant determinants of global human health and social development. The objective of this paper is to provide a framework to understand the economic and natural factors responsible for migration and population agglomerations and their environmental consequences. In this regard, we develop an economic model in continuous time and space adapting Hotelling’s migration law to make individuals react to possible improvements of their welfare. First we show that there is solution to this spatial-dynamic problem. Then, we illustrate the properties of the economy and the associated population dynamics through numerical simulations