An infinite-horizon multistage dynamic optimization problem

Babad, H. R.

doi:10.1007/bf02192158

Cited by 3 publications

(2 citation statements)

References 19 publications

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“…Kamien and Schwartz, in the second edition of their book (1991), point out that such problems are analogous to the existence of discrete jumps in the state variables of the system. An extension to multi-stage switching problems is carried out by Babad (1995), using multiprocess theory. Hertzler (1990) considered a similar problem in an agricultural setting.…”

Section: Previous Investigationsmentioning

confidence: 99%

The dynamics of phase farming in dryland salinity abatement

Mueller

Schilizzi

Tran

1999

Aus J Agri & Res Econ

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In Australia, soil salinisation has become a major concern. One way to deal with the problem is for farmers to plant trees or regenerate native bush. However, doing so raises several questions which involve optimal switching times, when switching involves a cost in the form of up‐front investments. Optimality conditions are derived for the three‐stage problem, and applied to dryland salinity control in Western Australia. Optimal management practices are found to be very sensitive to farmers’ discount rates and to the speed at which the watertable rises or falls.

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Section: Previous Investigationsmentioning

confidence: 99%

The dynamics of phase farming in dryland salinity abatement

Mueller

Schilizzi

Tran

1999

Aus J Agri & Res Econ

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“…More generally, two‐stage (or multistage) control problems are concerned with switching between alternative and consecutive regimes, where the switching times are endogenously determined. Such problems have been studied by in the context of maximum principle , or multiprocess maximum principle, see . In particular, applied this technique to investigate technology adoption .…”

Section: Introductionmentioning

confidence: 99%

When can it be not optimal to adopt a new technology? A viability theory solution to a two‐stage optimal control problem of new technology adoption

Krawczyk

Serea

2011

Optim Control Appl Methods

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SUMMARYPoliticians often deplore economic agents' behaviour when they do not accept new technologies. For a new technology to be adopted, the new technology value function needs to dominate the old technology value function. If this is the case, a technology switch will occur. We characterise the value functions, without computing them, using the fact that their hypographs are viability kernels of some auxiliary control problems and study whether the graphs intersect. If they do not, the corresponding value functions do not dominate each other, and the switch cannot occur at a positive time. Using this characterisation, we analyse a technology adoption problem and show how to recognise the models, for which the switch will occur at time zero or never, without solving an optimal control problem. We conclude that the current control regime may not change if the economic agents' preferences are modelled as an integral of discounted differences between a reward from the flow variable (control) and a penalty from the stock variable (state). Copyright

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Ecosystem Shifts: Implications for Groundwater Management

Esteban

Calvo

Albiac

2021

Environ Resource Econ

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Freshwater ecosystems provide a large number of benefits to society. However, extensive human activities threat the viability of these ecosystems, their habitats, and their dynamics and interactions. One of the main risks facing these systems is the overexploitation of groundwater resources that hinders the survival of several freshwater habitats. In this paper, we study optimal groundwater paths when considering freshwater ecosystems. We contribute to existing groundwater literature by including the possibility of regime shifts in freshwater ecosystems into a groundwater management problem. The health of the freshwater habitat, which depends on the groundwater level, presents a switch in its status that occurs when a critical water level (‘tipping point’) is reached. Our results highlight important differences in optimal extraction paths and optimal groundwater levels compared with traditional models. The outcomes suggest that optimal groundwater withdrawals are non-linear and depend on the critical threshold and the ecosystem’s health function. Our results show that the inclusion of regime shifts in water management calls for a reformulation of water policies to incorporate the structure of ecosystems and their interactions with the habitat.

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An infinite-horizon multistage dynamic optimization problem

Cited by 3 publications

References 19 publications

The dynamics of phase farming in dryland salinity abatement

The dynamics of phase farming in dryland salinity abatement

When can it be not optimal to adopt a new technology? A viability theory solution to a two‐stage optimal control problem of new technology adoption

Ecosystem Shifts: Implications for Groundwater Management

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