Comparison of Closed-Form Solutions for the Lucas-Uzawa Model via the Partial Hamiltonian Approach and the Classical Approach
In this paper we derive the closed-form solutions for the Lucas-Uzawa growth model with the aid of the partial Hamiltonian approach and then compare our results with those derived in literature. The partial Hamiltonian approach provides two first integrals [9] in the case where there are no paramet...
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Vilnius Gediminas Technical University
2017-07-01
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doaj-a86c624f61904d6a89cbacff98bd3d9f2021-07-02T09:50:34ZengVilnius Gediminas Technical UniversityMathematical Modelling and Analysis1392-62921648-35102017-07-0122410.3846/13926292.2017.1323035Comparison of Closed-Form Solutions for the Lucas-Uzawa Model via the Partial Hamiltonian Approach and the Classical ApproachRehana Naz0Azam Chaudhry1Lahore School of Economics, Centre for Mathematics and Statistical Sciences, 53200 Lahore, PakistanLahore School of Economics, Department of Economics, 53200 Lahore, Pakistan In this paper we derive the closed-form solutions for the Lucas-Uzawa growth model with the aid of the partial Hamiltonian approach and then compare our results with those derived in literature. The partial Hamiltonian approach provides two first integrals [9] in the case where there are no parameter restrictions and these two first integrals are utilized to construct three sets of closed form solutions for all the variables in the model. We begin by using the two first integrals to find two closed form solutions, one of which is new to the literature. We then use only one of the first integrals to derive a third solution that is the same as that found in the previous literature. We continue by analyzing the newly derived solution in detail also show that all three solutions converge to the same long run balanced growth path. The special case when the share of capital is equal to the inverse of the intertemporal elasticity of substitution is also investigated in detail. https://journals.vgtu.lt/index.php/MMA/article/view/907economic growthpartial Hamiltonian approachLucas-Uzawa modelcurrentvalue Hamiltonian |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Rehana Naz Azam Chaudhry |
spellingShingle |
Rehana Naz Azam Chaudhry Comparison of Closed-Form Solutions for the Lucas-Uzawa Model via the Partial Hamiltonian Approach and the Classical Approach Mathematical Modelling and Analysis economic growth partial Hamiltonian approach Lucas-Uzawa model currentvalue Hamiltonian |
author_facet |
Rehana Naz Azam Chaudhry |
author_sort |
Rehana Naz |
title |
Comparison of Closed-Form Solutions for the Lucas-Uzawa Model via the Partial Hamiltonian Approach and the Classical Approach |
title_short |
Comparison of Closed-Form Solutions for the Lucas-Uzawa Model via the Partial Hamiltonian Approach and the Classical Approach |
title_full |
Comparison of Closed-Form Solutions for the Lucas-Uzawa Model via the Partial Hamiltonian Approach and the Classical Approach |
title_fullStr |
Comparison of Closed-Form Solutions for the Lucas-Uzawa Model via the Partial Hamiltonian Approach and the Classical Approach |
title_full_unstemmed |
Comparison of Closed-Form Solutions for the Lucas-Uzawa Model via the Partial Hamiltonian Approach and the Classical Approach |
title_sort |
comparison of closed-form solutions for the lucas-uzawa model via the partial hamiltonian approach and the classical approach |
publisher |
Vilnius Gediminas Technical University |
series |
Mathematical Modelling and Analysis |
issn |
1392-6292 1648-3510 |
publishDate |
2017-07-01 |
description |
In this paper we derive the closed-form solutions for the Lucas-Uzawa growth model with the aid of the partial Hamiltonian approach and then compare our results with those derived in literature. The partial Hamiltonian approach provides two first integrals [9] in the case where there are no parameter restrictions and these two first integrals are utilized to construct three sets of closed form solutions for all the variables in the model. We begin by using the two first integrals to find two closed form solutions, one of which is new to the literature. We then use only one of the first integrals to derive a third solution that is the same as that found in the previous literature. We continue by analyzing the newly derived solution in detail also show that all three solutions converge to the same long run balanced growth path. The special case when the share of capital is equal to the inverse of the intertemporal elasticity of substitution is also investigated in detail.
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topic |
economic growth partial Hamiltonian approach Lucas-Uzawa model currentvalue Hamiltonian |
url |
https://journals.vgtu.lt/index.php/MMA/article/view/907 |
work_keys_str_mv |
AT rehananaz comparisonofclosedformsolutionsforthelucasuzawamodelviathepartialhamiltonianapproachandtheclassicalapproach AT azamchaudhry comparisonofclosedformsolutionsforthelucasuzawamodelviathepartialhamiltonianapproachandtheclassicalapproach |
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1721332793674301440 |