An Optimal Growth Model with Time Lags

El-Hodiri, Mohamed; Loehman, Edna T.; Whinston, Andrew B.

doi:10.2307/1913860

Cited by 22 publications

(14 citation statements)

References 3 publications

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“…To solve problem (1), we apply the generalized Maximum principle derived in El-Hodiri et al (1972) for delayed optimal control problems and derive the following present-value Hamiltonian H:…”

Section: A Generic Pollution Control Model With Delayed Stock Accumulmentioning

confidence: 99%

Optimal Control of Pollutants with Delayed Stock Accumulation

Winkler

2008

SSRN Journal

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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. Abstract: We study the optimal control of a pollutant that accumulates with a delay. We find that optimal paths are, in general, non-monotonic and oscillatory, but monotonic if the objective function is additively separable. Hence, using additively separable objective functions as an approximation to a general objective function may be a misspecification. Terms of use: Documents in EconStor mayWith a numerical example we illustrate that an additively separable approximation performs considerably worse in delayed compared to instantaneous stock accumulation.

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Section: A Generic Pollution Control Model With Delayed Stock Accumulmentioning

confidence: 99%

Optimal Control of Pollutants with Delayed Stock Accumulation

Winkler

2008

SSRN Journal

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“…To solve the optimization problem (8), we apply the generalized maximum principle derived in El-Hodiri et al (1972) for time-lagged optimal control problems. One obtains the following present-value Hamiltonian H:…”

Section: Necessary and Sufficient Conditions For The Social Optimummentioning

confidence: 99%

The Role of Environmental and Technology Policies in the Transition to a Low-Carbon Energy Industry

Heinzel¹,

Winkler

2007

SSRN Journal

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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. Abstract: In a dynamic general equilibrium model we study the interplay between gradual and structural change in the transition to a low-carbon energy industry. We focus on the welfare-theoretic consequences of diverging social and private rates of time preference and a time-to-build feature in capital accumulation. Both features are particularly important in the transformation of energy systems. We show that only a combination of environmental and technology policies can achieve a socially optimal transition. We thus provide a new reason for environmental regulation to be complemented by technology policy such as a non-distortionary investment subsidy. Terms of use: Documents in EconStor may

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“…To derive necessary and sufficient conditions for the optimal solution of the optimization problem (1), we apply the generalized maximum principle derived in El-Hodiri et al (1972) for delayed optimal control problems. This is possible, as the equation of motion (1b) is additively separable 1 in the time-lagged control variable u(t−σ) and the stock variable x(t).…”

Section: Necessary and Sufficient Conditions Of The Optimal Solutionmentioning

confidence: 99%

“…El-Hodiri et al (1972) derived a generalized maximum principle for a growth model with heterogeneous capital goods and exogenously given and constant delays of control and state variables. Production lags have been discussed in the macroeconomic real business cycle theory.…”

Section: Introductionmentioning

confidence: 99%

Numerical Solution of Optimal Control Problems With Constant Control Delays

et al. 2006

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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. Abstract: We investigate a class of optimal control problems that exhibit constant exogenously given delays in the control in the equation of motion of the differential states. Therefore, we formulate an exemplary optimal control problem with one stock and one control variable and review some analytic properties of an optimal solution. However, analytical considerations are quite limited in case of delayed optimal control problems. In order to overcome these limits, we reformulate the problem and apply direct numerical methods to calculate approximate solutions that give a better understanding of this class of optimization problems. In particular, we present two possibilities to reformulate the delayed optimal control problem into an instantaneous optimal control problem and show how these can be solved numerically with a state-of-the-art direct method by applying Bock's direct multiple shooting algorithm. We further demonstrate the strength of our approach by two economic examples. Terms of use: Documents in

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An Optimal Growth Model with Time Lags

Cited by 22 publications

References 3 publications

Optimal Control of Pollutants with Delayed Stock Accumulation

Optimal Control of Pollutants with Delayed Stock Accumulation

The Role of Environmental and Technology Policies in the Transition to a Low-Carbon Energy Industry

Numerical Solution of Optimal Control Problems With Constant Control Delays

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