Necessary conditions for infinite-horizon discounted two-stage optimal control problems

Makris, Miltiadis

doi:10.1016/s0165-1889(00)00009-9

Cited by 56 publications

(64 citation statements)

References 12 publications

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“…In addition to applying this technique to the question of optimal R&D trajectories, we present -to our knowledge -the first application of this technique to a situation characterized by uncertainty over the properties of the next stage of the optimal control problem. This involves a suitable modification of the necessary conditions derived by Makris (2001) and Tomiyama (1985). 1 Our key findings are that in our setting the optimal R&D program is (i) strictly sequential in the sense that at most one technology is developed at any given point in time and (ii) has an endogenous stopping point.…”

Section: Boomerangs and Backstopsmentioning

confidence: 99%

“…The following analysis is based on recent results on multi-stage dynamic optimization techniques derived by Makris (2001) and Tomiyama (1985). The application of the technique to the problem at hand is natural: Here, a stage is defined by reference to the number n of technologies available for production.…”

Section: Setup Of the Optimal Timing Decision For Randdmentioning

confidence: 99%

“…While the necessary conditions derived by Tomiyama (1985) and Makris (2001) are established in the context of a deterministic setting, they are easily modified for the simple discrete probability distribution studied here in order to account for the uncertainty regarding the type of technology developed at the point of switching.…”

Section: Setup Of the Optimal Timing Decision For Randdmentioning

confidence: 99%

“…Given the optimal pollution policies, the applicable necessary conditions for the optimal switching point are essentially those provided by Tomiyama (1985) and Makris (2001), modified however for a setting of two possible outcomes. Two conditions then determine the optimal instant t * n+1 to undertake R&D in order to develop the n + 1 st technology.…”

Section: Setup Of the Optimal Timing Decision For Randdmentioning

confidence: 99%

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On backstops and boomerangs: Environmental R&D under technological uncertainty

Goeschl

Perino

2009

Energy Economics

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may AbstractThe literature on environmental R&D frequently studies innovation as a two-stage process, with a single R&D event leading from a conventional polluting technology to a perfectly clean backstop. We allow for uncertainty in innovation in that the new technology may turn out to generate a new pollution problem. R&D may therefore be optimally undertaken more than once. Using and externding recent results from multi-stage optimal control theory, we provide a full characterization of the optimal pollution and R&D policies. The optimal R&D program is strictly sequential and has an endogenous stopping point. Uncertainty drives total R&D effort and its timing.JEL classification: Q55, Q53, O32, C61

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Section: Boomerangs and Backstopsmentioning

confidence: 99%

Section: Setup Of the Optimal Timing Decision For Randdmentioning

confidence: 99%

Section: Setup Of the Optimal Timing Decision For Randdmentioning

confidence: 99%

Section: Setup Of the Optimal Timing Decision For Randdmentioning

confidence: 99%

See 2 more Smart Citations

On backstops and boomerangs: Environmental R&D under technological uncertainty

Goeschl

Perino

2009

Energy Economics

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“…Second, if the switching cost is a function of the knowledge stock, (T ) = (A(T )), condition (20) is replaced by [see Makris (2001)]…”

Section: Switching Costsmentioning

confidence: 99%

Endogenous Growth, Backstop Technology Adoption, and Optimal Jumps

Valente

2010

Macroecon. Dynam.

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This paper analyzes a two-phase endogenous growth model in which the adoption of a backstop technology (e.g., solar) yields a sustained supply of essential energy inputs previously obtained from exhaustible resources (e.g., oil). Growth is knowledge-driven and the optimal timing of technology switching is determined by welfare maximization. The optimal path exhibits discrete jumps in endogenous variables: technology switching implies sudden reductions in consumption and output, an increase in the growth rate, and instantaneous adjustments in saving rates. Due to the positive growth effect, it is optimal to implement the new technology when its current consumption benefits are substantially lower than those generated by old technologies.

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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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Necessary conditions for infinite-horizon discounted two-stage optimal control problems

Cited by 56 publications

References 12 publications

On backstops and boomerangs: Environmental R&D under technological uncertainty

On backstops and boomerangs: Environmental R&D under technological uncertainty

Endogenous Growth, Backstop Technology Adoption, and Optimal Jumps

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

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