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"The most interesting issues in environmental and resource economics have an explicit temporal dimension, since variables of interest such as pollutants, greenhouse gases, biomass of biological resources, or the stocks of fossil fuels accumulate in the ambient environment or are depleted through human actions and natural processes. The purpose of these lectures is to present the mathematical tools for analyzing environmental and resource management issues in a dynamic set-up. The lectures include a brief description of differential equations and then move on to describe methods of optimal control, dynamic programing, and differential games. The final chapters cover two novel topics: (1) environmental issues characterized by deep uncertainty, and aversion to ambiguity using robust control methods and formulations of precautionary policies; and (2) the study of pollution/resource management in space and time when the environmental variables evolve in time and diffuse in space. The lectures are a valuable tool for advanced graduate students in environmental and resource economics who are studying dynamic problems."

ABSTRACTMechanisms generating patterns in spatial domains have been extensively studied in biology, but also in economics in the context of new economic geography. The Turing mechanism or Turing diffusion-induced instability has been central to the understanding of forces which endogenously generate spatial patterns, but in a context where agents do not explicitly optimize an objective. The present paper reviews tools to study, in the spirit of Turing's analysis, a mechanism generating optimal diffusion-induced instability where optimizing agents generate optimal agglomerations. By extending the maximum principle to the optimal control of partial differential equations, it is shown how under certain conditions it will be optimal to design controls so that the price-quantity system implied by the costate–state functions of the optimal control of distributed parameter systems induces optimal spatial patterns. These methods might be useful in studying pattern formation both in problems of resource management and of economic development.

The paper explores abatement investment and location responses to environmental policy, which takes the form of emission taxes or tradable emission permits and subsidies against the costs of abatement investment, under uncertainty and irreversibility. Uncertainty is associated with output price, environmental policy parameters, or technological parameters. Irreversibility is related to abatement expenses, and movements to a new location. Uncertainty is modelled by Itô stochastic differential equations, and the problem is analysed by using optimal stopping methodologies. Continuation intervals during which firms do not engage in abatement investment or relocate and intervals during which firms take the irreversible decision of undertaking abatement expenses or relocating are defined. Free boundaries are characterised for a variety of cases that include output price uncertainty, policy uncertainty expressed both in terms of continuous fluctuations of permit prices and unpredictable policy changes, and combined policy and technological uncertainty. An optimal environmental policy is defined as the combination of policy parameters that makes the free boundary corresponding to the profit maximisation problem coincide with the free boundary corresponding to a social optimisation problem.

AbstractThis paper studies the role of social networks in the management of natural resources. We consider a finite number of agents who exploit a specific natural resource. Harvesting is subject to three external effects, namely resource stock externalities, crowding externalities, and collaboration spillovers. We show that the structure of the social network—defined by the presence of collaboration links between individual agents—determines the equilibrium and the optimal harvesting amount. We then allow the agents to make decisions about creating or eliminating cooperation links, which endogenizes the structure of the network and is proved to affect total harvesting and aggregate welfare. Conservation plans are shown to change the regulator's objective and increase even further the gap between the decentralized and the optimal outcomes. We show that the optimal policy depends explicitly on the structure of the network and the 'centrality' of the associated agents. Finally, introducing heterogeneity is proved to affect both individual profits and the incentives to create cooperation links.