Spatial Analysis: Development of Descriptive and Normative Methods with Applications to Economic-Ecological Modelling

This paper adapts Turing analysis and applies it to dynamic bioeconomic problems where the interaction of coupled economic and ecological dynamics over space endogenously creates (or destroys) spatial heterogeneity. It also extends Turing analysis to standard recursive optimal control frameworks in economic analysis and applies it to dynamic bioeconomic problems where the interaction of coupled economic and ecological dynamics under optimal control over space creates a challenge to analytical tractability. We show how an appropriate formulation of the problem reduces analysis to a tractable extension of linearization methods applied to the spatial analog of the well known costate/state dynamics. We illustrate the usefulness of our methods on bioeconomic applications, but the methods have more general economic applications where spatial considerations are important. We believe that the extension of Turing analysis and the theory associated with dispersion relationship to recursive infinite horizon optimal control settings is new.Spatial analysis, Economic-ecological modelling

Pattern Formation, Spatial Externalities and Regulation in Coupled Economic-Ecological Systems

We develop a novel theoretical framework for studying ecosystems in which interacting state variables which are affected by management decisions diffuse in space. We identify (i) mechanisms creating spatial patterns when economic agents maximize profit at each site by ignoring the impact of their actions on other sites and (ii) a diffusion induced externality. Pattern formation mechanisms and externalities create a divergence in the spatiotemporal structures emerging under private or social objectives We develop optimal regulation which internalize the spatiotemporal externalities. Our theory is applied to the management and regulation of a semi-arid system. Supporting numerical simulations are also presented.Economic-Ecological Systems, Pattern Formation, Reaction-Diffusion, Diffusion Instability, Spatial Externalities, Regulation

Spatial Analysis: Development of Descriptive and Normative Methods with Applications to Economic-Ecological Modelling

This paper adapts Turing analysis and applies it to dynamic bioeconomic problems where the inter- action of coupled economic and ecological dynamics over space endogenously creates (or destroys) spatial heterogeneity. It also extends Turing analysis to standard recursive optimal control frame- works in economic analysis and applies it to dynamic bioeconomic problems where the interaction of coupled economic and ecological dynamics under optimal control over space creates a challenge to analytical tractability. We show how an appropriate formulation of the problem reduces analysis to a tractable extension of linearization methods applied to the spatial analog of the well known costate/state dynamics. We illustrate the usefulness of our methods on bioeconomic applications, but the methods have more general economic applications where spatial considerations are important. We believe that the extension of Turing analysis and the theory associated with dispersion relationship to recursive in…nite horizon optimal control settings is new.Spatial analysis, Pattern formation, Turing mechanism, Optimal control, bioeconomic problems

Optimal Control and Spatial Heterogeneity: Pattern Formation in Economic-Ecological Models

This paper extends Turing analysis to standard recursive optimal control frameworks in economics and applies it to dynamic bioeconomic problems where the interaction of coupled economic and ecological dynamics under optimal control over space creates (or destroys) spatial heterogeneity. We show how our approach reduces the analysis to a tractable extension of linearization methods applied to the spatial analog of the well known costate/state dynamics. We explicitly show the existence of a non-empty Turing space of diffusive instability by developing a linear-quadratic approximation of the original non-linear problem. We apply our method to a bioeconomic problem, but the method has more general economic applications where spatial considerations and pattern formation are important. We believe that the extension of Turing analysis and the theory associated with the dispersion relationship to recursive infinite horizon optimal control settings is new.Spatial analysis, Pattern formation, Turing mechanism, Turing space, Pontryagin’s principle, Bioeconomics

General Pattern Formation in Recursive Dynamical Systems Models in Economics

This paper presents a fairly general treatment of recursive infinite horizon forward looking optimizing systems on infinite dimensional spatial domains. It includes optimal control, an analysis of local stability of spatially flat optimal steady states and development of techniques to compute spatially heterogeneous optimal steady states. The paper also develops a concept of rational expectations equilibrium, a local stability analysis for spatially homogeneous rational expectations steady states, and computational techniques for spatially heterogeneous rational expectations steady states.Pattern Formation, Spatial Spillovers, Optimal Control, Spillover Induced Instability, Growth Models

Robust Control and Hot Spots in Dynamic Spatially Interconnected Systems

This paper develops linear quadratic robust control theory for a class of spatially invariant distributed control systems that appear in areas of economics such as New Economic Geography, management of ecological systems, optimal harvesting of spatially mobile species, and the like. Since this class of problems has an infinite dimensional state and control space it would appear analytically intractable. We show that by Fourier transforming the problem, the solution decomposes into a countable number of finite state space robust control problems each of which can be solved by standard methods. We use this convenient property to characterize “hot spots” which are points in the transformed space that correspond to “breakdown” points in conventional finite dimensional robust control, or where instabilities appear or where the value function loses concavity. We apply our methods to a spatial extension of a well known optimal fishing model.Distributed Parameter Systems, Robust Control, Spatial Invariance, Hot Spot, Agglomeration

Valuing Biodiversity from an Economic Perspective: AUnified Economic, Ecological and Genetic Approach

We develop a conceptual framework for valuing biodiversity from an economic perspective. We consider biodiversity important because of a number of characteristics or services that it provides or enhances. We argue for a dynamic economic welfare measure of biodiversity that complements the existing literature on benefit-cost approaches and genetic distance/phylogenic tree approaches, which to date have been more static. Using a unified model of optimal economic management of an ecosystem under ecological and genetic constraints, we identify gains realized by management policies leading to a more diverse system, using the Bellman state valuation function of the problem. We show that a more diverse system could attain a higher value even though the genetic distance of the species in the more diverse system could be almost zero. We relate this endogenous measure of the biodiversity value to ecologically/biologically oriented biodiversity metrics (species richness, Shannon or Simpson indices).

General Pattern Formation in Recursive Dynamical Systems Models in Economics

This paper presents a fairly general treatment of recursive infinite horizon forward looking optimizing systems on infinite dimensional spatial domains. It includes optimal control, an analysis of local stability of spatially flat optimal steady states and development of techniques to compute spatially heterogeneous optimal steady states. The paper also develops a concept of rational expectations equilibrium, a local stability analysis for spatially homogeneous rational expectations steady states, and computational techniques for spatially heterogeneous rational expectations steady states.Pattern formation, spatial spillovers, optimal control, spillover induced instability, growth models