The Costate Variable in Natural Resource Optimal Control Problems

Lyon, Kenneth S.

doi:10.1111/j.1939-7445.1999.tb00020.x

Cited by 17 publications

(12 citation statements)

References 1 publication

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“…The undesirable abundance effect is similar to the scarcity effect in the nonrenewable resource analysis (see Lyon [1999] and Lyon and Lee [2004]) and is the terminal shadow value of waste discounted to the present. The utility and productivity effects are the result of an altered path of health caused by this unit of waste reduction where dw (0) =−1.…”

Section: Optimal Growth Model With Waste Disposal and Human Healthmentioning

confidence: 83%

Optimal Discounting of Benefits From Cleanup at Waste Sites

Lyon

Caliendo

2008

Natural Resource Modeling

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This paper uses a general equilibrium optimal growth model to discuss the role of optimal discounting of future benefits from cleanup at high‐level toxic waste sites. Cleanup simultaneously generates two streams of benefits. One of these is directly from utility and the other is indirectly from the added productivity of workers. We note that the optimal discount rate is different for these two types of benefits. Along the optimal path, the former are discounted at the rate of time preference and the latter at the market rate of interest. We achieve this by identifying four components of the shadow value of the stock of toxic waste. These are the utility, productivity, cost, and abundance effects. The distinction between discount rates appears to have been overlooked in the literature but has significant implications for environmental cost‐benefit analysis due to the growing interest in applying zero time preference to environmental problems, (like waste cleanup) whose consequences extend many generations into the future. A numerical example is included to illustrate these concepts.

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Section: Optimal Growth Model With Waste Disposal and Human Healthmentioning

confidence: 83%

Optimal Discounting of Benefits From Cleanup at Waste Sites

Lyon

Caliendo

2008

Natural Resource Modeling

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“…Thus, λ i (t) is the value (at time t) to generation i of a unit of capital at time t and η i (t) is the value (at time t) to generation i of a unit of waste at time t. (Detailed discussion of the costate variable can be found in Kamien and Schwartz [1991], Hoy et al [1996] and Lyon [1999]). η i (t) is negative because waste impairs worker productivity, and −η i (t) can be viewed as the value of a unit of waste removal at time t.…”

Section: The Current Value Hamiltonian Function For Stage 2 Ismentioning

confidence: 99%

Optimal Discounting in Control Problems That Span Multiple Generations

Caliendo¹,

Lyon²

2008

Natural Resource Modeling

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ABSTRACT. The principal contribution of this paper is the linking together of separate control problems across multiple generations using the bequest motive, intergenerational altruism, rational expectations, and solution boundary conditions. We demonstrate that discounting at the market rate of interest is an endogenous characteristic of a general equilibrium, optimal control problem that spans multiple generations. Within the confines of our model, we prove that it is optimal to discount at the market rate of interest the social benefits to distant generations from immediate clean up at toxic waste sites if the current generation that bears the cleanup cost is perfectly altruistic towards future generations. Also, we show that this result holds for alternative assumptions regarding pure time preference. Moreover, the result holds regardless of whether selfish interim generations attempt to undo the provisions made for distant generations. In our distortion‐free deterministic model, the evidence for intergenerational discounting at the market rate of interest is compelling.

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“…In urban groundwater management, the shadow value plays a crucial role in adapting to scarcity. Its role is to ration resource use across time (Lyon 1999). In this framework, 1 (t) rations water consumption as the scarcity rent in Eq.…”

Section: Optimal Urban Groundwater Managementmentioning

confidence: 99%

“…(6), by relaxing the constraint, Eq. (8), by one unit (Lyon 1999). 1 (t) is the marginal value of the increase in height, and it is the marginal cost of height decrease.…”

Section: Optimal Urban Groundwater Managementmentioning

confidence: 99%

The economics of optimal urban groundwater management in southwestern USA

Hansen

2012

Hydrogeol J

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Groundwater serves as the primary water source for approximately 80% of public water systems in the United States, and for many more as a secondary source. Traditionally management relies on groundwater to meet rising demand by increasing supply, but climate uncertainty and population growth require more judicious management to achieve efficiency and sustainability. Over-pumping leads to groundwater overdraft and jeopardizes the ability of future users to depend on the resource. Optimal urban groundwater pumping can play a role in solving this conundrum. This paper investigates to what extent and under what circumstances controlled pumping improves social welfare. It considers management in a hydro-economic framework and finds the optimal pumping path and the optimal price path. These allow for the identification of the social benefit of controlled pumping, and the scarcity rent, which is one tool to sustainably manage groundwater resources. The model is numerically illustrated with a case study from Albuquerque, New Mexico (USA). The Albuquerque results indicate that, in the presence of strong demand growth, controlled pumping improves social welfare by 22%, extends use of the resource, and provides planners with a mechanism to advance the economic sustainability of groundwater.

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The Costate Variable in Natural Resource Optimal Control Problems

Cited by 17 publications

References 1 publication

Optimal Discounting of Benefits From Cleanup at Waste Sites

Optimal Discounting of Benefits From Cleanup at Waste Sites

Optimal Discounting in Control Problems That Span Multiple Generations

The economics of optimal urban groundwater management in southwestern USA

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