Renan-Ulrich Goetz

The Dynamics of Spatial Pollution - The Case of Phosphorus Runoff from Agricultural Land

Negative production externalities have been the concern of many economic studies. In the case where the pollutants accumulate over time these studies are conducted within a dynamic framework. Besides the intertemporal aspect, the heterogeneity of space may be an important consideration for the economic analysis of negative production externalities. Traditionally, economists think of space in the form of a distance measure. However, two locations next to each other and at an equal distance from a receiving medium, may demonstrate completely different vulnerability to negative agricultural production externalities. Thus, we must not only consider site characteristics in a land classification system, but must also consider the characteristics of the receiving medium to depict the environmental vulnerability of locations. We base our analysis on the full-information approach by employing a land classification system and considering the use of improved monitoring technology to account for heterogeneity in residue (pollutant) production. For the sake of concreteness of the analysis we consider the example of Phosphorus runoff into a lake, but also discuss our results in the context of Nitrate leaching. We assume that a social planner for the watershed of a lake exists and that she/he wants to maximize the net benefits resulting from agricultural production taking account of the monetary damage due to pollution of the lake. To obtain an analytical solution more easily, we propose the framework of a two stage optimal control problem. In the first stage we solve the spatial problem by determining the optimal trajectories of the control variables in the dimension of space given by the range of the land classification system. The solution of the social planners decision problem in the first stage is depicted by the value function which is defined as the value of the maximization of the net benefit from agricultural production allocated over space subject to the law of motion and other conditions appropriate for the problem. Thus, the value function, evaluated along the optimal path of the control variables, reflects the value of the solution for the optimal control problem of the first stage (spatial problem) given some parameters. In the second stage we solve for the optimal intertemporal allocation of the already optimized spatial allocation. For this purpose the value function is used as the benefit function. In the policy analysis, we address questions related to zone taxes, zone permits and zone standards. Most importantly, however, we present a modeling approach which consists of the simultaneous solution of the micro level (farm) and macro level (aggregate supply and demand) production over space and time. In particular, it allows us to derive relationships between long-run and short-run supply and input demand functions.

Diversification in Agricultural Production: A Dynamic Model of Optimal Cropping to Manage Soil Erosion

A dynamic economic model of soil erosion is presented where the intensity of use of inputs and the choice of crops allow the farmer to control soil losses. The results show that it is predominately optimal to approach the singular-path/steady-state equilibrium most rapidly by the cultivation of a single crop. At the steady state, however, a mix of crops is cultivated. The promotion of erosion control practices on only high-erosion crops may reduce the long-run soil stock, whereas a tax on the land cultivated with a particular crop is shown to be effective in increasing the long-run soil stock. Copyright 1997, Oxford University Press.

Maximum principle for a size-structured model of forest and carbon sequestration management

Abstract The paper analyzes nonlinear optimal control of integral–differential equations that describe the optimal management of a forest taking into account intra-species competition and carbon sequestration. The objective function includes the revenues from timber production, operational expenses, and the net benefits from carbon sequestration. A dual system is derived and a necessary extremum condition is established.

The Gains from Differentiated Policies to Control Stock Pollution when Producers Are Heterogeneous

We derive optimal input taxes to control stock pollution problems generated by heterogeneous agents. The taxes vary over time and in response to differences of asset quality and technology choice. We also derive second-best policies and compare them to the efficient policy and also among themselves. Different policies will affect the timing for when, and the extent to which, conservation technologies are adopted. A numerical example, based on the California drainage problem, shows significant efficiency gains from the optimal policy compared to no intervention, but much of the gains are lost with second-best interventions. The gains from optimal policies do not always increase with the degree of heterogeneity. Copyright 2008, Oxford University Press.

Using the Escalator Boxcar Train to Determine the Optimal Management of a Size-Distributed Forest When Carbon Sequestration Is Taken into Account

We present a theoretical model to determine the optimal management of a size-distributed forest.The decision model is given in form of a distributed optimal control problem that cannot be solved analytically. Thus, the paper presents a numerical technique that allows transforming the original distributed control problem into an ordinary control problem. The method has the advantage that it does not require programming numerical algorithms but rather can be implemented with standard commercial optimization packages such as GAMS. The empirical application of our model for the case of forest management allows determining the selective cutting regime when carbon sequestration is taken into account.

Optimal harvesting in forestry: steady-state analysis and climate change impact

We perform the steady-state analysis of a nonlinear partial differential equation model that describes the dynamics of a managed size-structured forest. The harvesting policy is to maximize the net benefits from timber production over an infinite planning horizon. The existence and uniqueness of the steady-state trajectories are analysed. Closed-form steady states are obtained in meaningful special cases and are used to estimate how climate change affects the optimal harvesting regime, diameter of cut trees, number of logged trees, and net benefits in the long run.

Sustainable dynamics of size-structured forest under climate change

Abstract This work investigates the impact of global climate change on the sustainable growth of forest, namely, on its aggregated characteristics such as the number of trees, the basal area, and the amount of carbon sequestrated in the stand. The forest dynamics is described by a nonlinear size-structured population model. The existence of a steady state regime is proven and explicit formulas for the aggregated characteristics are obtained. A numeric simulation on realistic data illustrates and extends the analytic results obtained.