Camacho, C., & Pérez-Barahona, A. (2015). Land use dynamics and the environment. Journal of Economic Dynamics and Control, 52, 96–118.
Abstract: This paper builds a benchmark framework to study optimal land use, encompassing land use activities and environmental degradation. We focus on the spatial externalities of land use as drivers of spatial patterns: land is immobile by nature, but local actions affect the whole space since pollution flows across locations resulting in both local and global damages. We prove that the decision maker problem has a solution, and characterize the corresponding social optimum trajectories by means of the Pontryagin conditions. We also show that the existence and uniqueness of time-invariant solutions are not in general guaranteed. Finally, a global dynamic algorithm is proposed in order to illustrate the spatial-dynamic richness of the model. We find that our simple set-up already reproduces a great variety of spatial patterns related to the interaction between land use activities and the environment. In particular, abatement technology turns out to play a central role as pollution stabilizer, allowing the economy to reach a time-invariant equilibrium that can be spatially heterogeneous. (C) 2014 Elsevier B.V. All rights reserved.
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Camacho, C., & Perez-Barahona, A. (2014). Land use dynamics and the environment. FACCE MACSUR Mid-term Scientific Conference, 3(S) Sassari, Italy.
Abstract: This paper builds a benchmark framework to study optimal land use, encompassing land use activities and environmental degradation. We focus on the spatial externalities of land use as drivers of spatial patterns: land is immobile by nature, but location’s actions affect the whole space since pollution flows across locations resulting in both local and global damages. We prove that the decision maker problem has a solution, and characterize the corresponding social optimum trajectories by means of the Pontryagin conditions. We also show that the existence and uniqueness of steady-state solutions are not straightforward. Finally, a global dynamic algorithm is proposed in order to illustrate the spatial-dynamic richness of the model. We find that our simple set-up already reproduces a great variety of spatial patterns related to the interaction between land use activities and the environment. In particular, abatement technology turns out to play a central role as pollution stabilizer, allowing the economy to achieve stable steady-states that are spatially heterogeneous.
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Camacho, C., & Perez-Barahona, A. On the uniqueness of the solution to an optimal control problem subject to a parabolic differential equation. Journal of Economic Theory.
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