The Experts below are selected from a list of 78 Experts worldwide ranked by ideXlab platform
Lyon, Kenneth S. - One of the best experts on this subject based on the ideXlab platform.
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The Costate Variable in a Stochastic Renewable Resource Model
Hosted by Utah State University Libraries, 2003Co-Authors: Lyon, Kenneth S., Pande SaketAbstract:In this paper we discuss the Costate Variable in a stochastic optimal control model of a renewable natural resource, which we call a fishery. The role of the Costate Variable in deterministic control models has been discussed extensively in the literature. See, for example, Lyon (1999), Clark (1990, pp. 102-107), and Arrow and Kurz (1970, pp. 35-37); however, there is little discussion of this Variable for stochastic models, even though the Costate Variable has similar roles in the two models. In both models the Costate Variable is a shadow value of the associated state Variable, and as such has the role of rationing the use of the state Variable. In addition, as has been shown in Lyon (1999), in natural resource problems the Costate Variable can be partitioned into a scarcity effect and a cost effect. We show that this same partitioning can be done in the stochastic renewable resource problem. We discuss and contrast the similarities and differences in these concepts for deterministic and stochastic models. In addition, we present a numerical example to help solidity the results
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Nonrenewable Resource Extractions With a Pollution Side Effect: A Comparative Dynamic Analysis
Hosted by Utah State University Libraries, 2002Co-Authors: Lyon, Kenneth S., Lee, Dug ManAbstract:In this paper, we present a nonrenewable resource model including environmental pollution as a state Variable. The model is analyzed to identify some of the characteristics of the optimal paths. In addition, we present a numerical example on the basis of the algebraic solutions of our qualitative model, and identify some of the characteristics of the optimal time paths for two sets of social costs of the pollutant. These results are consistent with the proposition of the previous literature that levying the shadow cost of the pollution stock reduces the consumption of resource; hence, it slows the accumulation of the pollutants in the atmosphere. One quirk in the results, however, is that extractions will persist longer in the higher pollution cost scenario. The Costate Variable for the resource stock is decomposed into a scarcity effect and a cost effect and the Costate Variable for the pollution stock is decomposed into an undesirable abundance effect and a cost effect. Both of these, however, are cost effects
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The Dynamic Structure of Optimal Tax Under Environmental Pollution
Hosted by Utah State University Libraries, 2001Co-Authors: Lee, Dug Man, Lyon, Kenneth S.Abstract:In this paper, we present a nonrenewable resource model including environmental pollution stock as a state Variable to analyze the dynamic structure of an optimal tax. Based on the optimality conditions of our model, we showed that the optimal time path of the shadow cost of environmental pollution stock is the same as that of the Costate Variable of environmental pollution stock. We derived this statement by applying the Continuous Dependence on Initial Conditions Theorem (Coddington, E.A. & N. Levinston 1984, pp. 22-27) to the optimal control problem. Thus, this result provides a theoretical basis to determine the magnitude of optimal tax to be imposed over time. In addition, we observed the characteristics of two Costate Variables included in our model. We identified that the Costate Variable for resource stock is decomposed between the scarcity 3effect and the cost effect. On the other hand, the Costate Variable for environmental pollution stock is solely due to the disutility effect
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Do Optimal Non-Renewable Resource Tariffs Suffer From Dynamic Inconsistency?
Hosted by Utah State University Libraries, 2000Co-Authors: Lyon, Kenneth S., Lee, Dug ManAbstract:In this paper we have examined optimal tariffs for non-renewable natural resources in the setting of imperfect competition. We do this because Larry Karp (1984, p. 74) states that, If the buyer attempts to exert market power, he is constrained by the dynamic optimization behavior of the seller and does not face a standard control problem. We show that when extraction costs are a function of the remaining stock of the resource, the Costate Variable can be separated into a scarcity effect and a cost effect. Karp concludes that the cost effect must be left with the producer; thereby, restricting the actions of the buyer. We, however, prove that it is not necessary to pay this cost effect to the producer; hence, we conclude that the monopsonist can extract all of the rent from the seller. The optimal tariff is neither dynamically time inconsistent, nor is it Karp\u27s consistent tariff
Lee, Dug Man - One of the best experts on this subject based on the ideXlab platform.
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Nonrenewable Resource Extractions With a Pollution Side Effect: A Comparative Dynamic Analysis
Hosted by Utah State University Libraries, 2002Co-Authors: Lyon, Kenneth S., Lee, Dug ManAbstract:In this paper, we present a nonrenewable resource model including environmental pollution as a state Variable. The model is analyzed to identify some of the characteristics of the optimal paths. In addition, we present a numerical example on the basis of the algebraic solutions of our qualitative model, and identify some of the characteristics of the optimal time paths for two sets of social costs of the pollutant. These results are consistent with the proposition of the previous literature that levying the shadow cost of the pollution stock reduces the consumption of resource; hence, it slows the accumulation of the pollutants in the atmosphere. One quirk in the results, however, is that extractions will persist longer in the higher pollution cost scenario. The Costate Variable for the resource stock is decomposed into a scarcity effect and a cost effect and the Costate Variable for the pollution stock is decomposed into an undesirable abundance effect and a cost effect. Both of these, however, are cost effects
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The Dynamic Structure of Optimal Tax Under Environmental Pollution
Hosted by Utah State University Libraries, 2001Co-Authors: Lee, Dug Man, Lyon, Kenneth S.Abstract:In this paper, we present a nonrenewable resource model including environmental pollution stock as a state Variable to analyze the dynamic structure of an optimal tax. Based on the optimality conditions of our model, we showed that the optimal time path of the shadow cost of environmental pollution stock is the same as that of the Costate Variable of environmental pollution stock. We derived this statement by applying the Continuous Dependence on Initial Conditions Theorem (Coddington, E.A. & N. Levinston 1984, pp. 22-27) to the optimal control problem. Thus, this result provides a theoretical basis to determine the magnitude of optimal tax to be imposed over time. In addition, we observed the characteristics of two Costate Variables included in our model. We identified that the Costate Variable for resource stock is decomposed between the scarcity 3effect and the cost effect. On the other hand, the Costate Variable for environmental pollution stock is solely due to the disutility effect
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Do Optimal Non-Renewable Resource Tariffs Suffer From Dynamic Inconsistency?
Hosted by Utah State University Libraries, 2000Co-Authors: Lyon, Kenneth S., Lee, Dug ManAbstract:In this paper we have examined optimal tariffs for non-renewable natural resources in the setting of imperfect competition. We do this because Larry Karp (1984, p. 74) states that, If the buyer attempts to exert market power, he is constrained by the dynamic optimization behavior of the seller and does not face a standard control problem. We show that when extraction costs are a function of the remaining stock of the resource, the Costate Variable can be separated into a scarcity effect and a cost effect. Karp concludes that the cost effect must be left with the producer; thereby, restricting the actions of the buyer. We, however, prove that it is not necessary to pay this cost effect to the producer; hence, we conclude that the monopsonist can extract all of the rent from the seller. The optimal tariff is neither dynamically time inconsistent, nor is it Karp\u27s consistent tariff
Kenneth Lyon - One of the best experts on this subject based on the ideXlab platform.
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The Costate Variable in a Stochastic Renewable Resource Model
2024Co-Authors: Kenneth Lyon, Saket PandeAbstract:In this paper we discuss the Costate Variable in a stochastic optimal control model of a renewable natural resource, which we call a fishery. The role of the Costate Variable in deterministic control models has been discussed extensively in the literature. See, for example, Lyon (1999), Clark (1990, pp. 102-107), and Arrow and Kurz (1970, pp. 35-37); however, there is little discussion of this Variable for stochastic models, even though the Costate Variable has similar roles in the two models. In both models the Costate Variable is a shadow value of the associated state Variable, and as such has the role of rationing the use of the state Variable. In addition, as has been shown in Lyon (1999), in natural resource problems the Costate Variable can be partitioned into a scarcity effect and a cost effect. We show that this same partitioning can be done in the stochastic renewable resource problem. We discuss and contrast the similarities and differences in these concepts for deterministic and stochastic models. In addition, we present a numerical example help solidify the results.Costate Variable, stochastic dynamic programming, deterministic dynamic programming, renewable resource model, simulation
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The dynamic structure of optimal tax under environmental pollution
2024Co-Authors: Dug Lee, Kenneth LyonAbstract:In this paper, we present a nonrenewable resource model including environmental pollution stock as a state Variable to analyze the dynamic structure of an optimal tax. Based on the optimality conditions of our model, we showed that the optimal time path of the shadow cost of environmental pollution stock is the same as that of the Costate Variable of environmental pollution stock. We derived this statement by applying the Continuous Dependence on Initial Conditions Theorem (Coddington, E.A. & N. Levinston 1984, pp. 22-27) to the optimal control problem. Thus, this result provides a theoretical basis to determine the magnitude of optimal tax to be imposed over time. In addition, we observed the characteristics of two Costate Variables included in our model. We identified that the Costate Variable for resource stock is decomposed between the scarcity 3effect and the cost effect. On the other hand, the Costate Variable for environmental pollution stock is solely due to the disutility effect.nonrenewable resource, environmental pollution stock, Costate Variables
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Nonrenewable Resources Extractions With a Pollution Side Effect: A Comparative Dynamic Analysis
2024Co-Authors: Kenneth Lyon, Dug LeeAbstract:In this paper, we present a nonrenewable resource model including environmental pollution as a state Variable. The model is analyzed to identify some of the characteristics of the optimal paths. In addition, we present a numerical example on the basis of the algebraic solutions of our qualitative model, and identify some of the characteristics of the optimal time paths for two sets of social costs of the pollutant. These results are consistent with the proposition of the previous literature that levying the shadow cost of the pollution stock reduces the consumption of resource; hence, it slows the accumulation of the pollutant in the atmosphere. One quirk in the results, however, is that extractions will persist longer in the higher pollution cost scenario. The Costate Variable for the resource stock is decomposed into a scarcity effect and a cost effect and the Costate Variable for the pollution stock is decomposed into an undesirable abundance effect and a cost effect. Both of these, however, are cost effects.nonrenewable resource, environmental pollution stock, scarcity effect, undesirable abundance effect, cost effect
Dug Lee - One of the best experts on this subject based on the ideXlab platform.
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The dynamic structure of optimal tax under environmental pollution
2024Co-Authors: Dug Lee, Kenneth LyonAbstract:In this paper, we present a nonrenewable resource model including environmental pollution stock as a state Variable to analyze the dynamic structure of an optimal tax. Based on the optimality conditions of our model, we showed that the optimal time path of the shadow cost of environmental pollution stock is the same as that of the Costate Variable of environmental pollution stock. We derived this statement by applying the Continuous Dependence on Initial Conditions Theorem (Coddington, E.A. & N. Levinston 1984, pp. 22-27) to the optimal control problem. Thus, this result provides a theoretical basis to determine the magnitude of optimal tax to be imposed over time. In addition, we observed the characteristics of two Costate Variables included in our model. We identified that the Costate Variable for resource stock is decomposed between the scarcity 3effect and the cost effect. On the other hand, the Costate Variable for environmental pollution stock is solely due to the disutility effect.nonrenewable resource, environmental pollution stock, Costate Variables
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Nonrenewable Resources Extractions With a Pollution Side Effect: A Comparative Dynamic Analysis
2024Co-Authors: Kenneth Lyon, Dug LeeAbstract:In this paper, we present a nonrenewable resource model including environmental pollution as a state Variable. The model is analyzed to identify some of the characteristics of the optimal paths. In addition, we present a numerical example on the basis of the algebraic solutions of our qualitative model, and identify some of the characteristics of the optimal time paths for two sets of social costs of the pollutant. These results are consistent with the proposition of the previous literature that levying the shadow cost of the pollution stock reduces the consumption of resource; hence, it slows the accumulation of the pollutant in the atmosphere. One quirk in the results, however, is that extractions will persist longer in the higher pollution cost scenario. The Costate Variable for the resource stock is decomposed into a scarcity effect and a cost effect and the Costate Variable for the pollution stock is decomposed into an undesirable abundance effect and a cost effect. Both of these, however, are cost effects.nonrenewable resource, environmental pollution stock, scarcity effect, undesirable abundance effect, cost effect
Azam Chaudhry - One of the best experts on this subject based on the ideXlab platform.
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A partial Hamiltonian approach for current value Hamiltonian systems
Communications in Nonlinear Science and Numerical Simulation, 2014Co-Authors: Rahila Naz, Fazal M. Mahomed, Azam ChaudhryAbstract:Abstract We develop a partial Hamiltonian framework to obtain reductions and closed-form solutions via first integrals of current value Hamiltonian systems of ordinary differential equations (ODEs). The approach is algorithmic and applies to many state and Costate Variables of the current value Hamiltonian. However, we apply the method to models with one control, one state and one Costate Variable to illustrate its effectiveness. The current value Hamiltonian systems arise in economic growth theory and other economic models. We explain our approach with the help of a simple illustrative example and then apply it to two widely used economic growth models: the Ramsey model with a constant relative risk aversion (CRRA) utility function and Cobb Douglas technology and a one-sector AK model of endogenous growth are considered. We show that our newly developed systematic approach can be used to deduce results given in the literature and also to find new solutions.
