Simplifying numerical analyses of Hamilton–Jacobi–Bellman equations
We introduce a simple method for computing value functions. The method is demonstrated by solving for transitional dynamics in the Uzawa and Lucas endogenous growth model. We use the value function approach to solve both the social planner’s optimization problem in the centralized economy and the representative agent’s optimization problem in the decentralized economy. The complexity of the Hamilton–Jacobi–Bellman equations is significantly reduced to an initial value problem for one ordinary differential equation. This approach allows us to find the optimal controls for the non-concave Hamiltonian in the centralized case and to identify the symmetric equilibrium in the decentralized case. Copyright Springer-Verlag 2012
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Benhabib Jess & Perli Roberto, 1994. "Uniqueness and Indeterminacy: On the Dynamics of Endogenous Growth," Journal of Economic Theory, Elsevier, vol. 63(1), pages 113-142, June.
- Erik Canton, 2002. "Business cycles in a two-sector model of endogenous growth," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 19(3), pages 477-492.
- Dirk Bethmann, 2007. "A Closed-form Solution of the Uzawa-Lucas Model of Endogenous Growth," Journal of Economics, Springer, vol. 90(1), pages 87-107, January.
- Bond, Eric W. & Wang, Ping & Yip, Chong K., 1996. "A General Two-Sector Model of Endogenous Growth with Human and Physical Capital: Balanced Growth and Transitional Dynamics," Journal of Economic Theory, Elsevier, vol. 68(1), pages 149-173, January.
- Danyang Xie, 2002.
"Divergence in Economic Performance: Transitional Dynamics with Multiple Equilibria,"
GE, Growth, Math methods
- Xie Danyang, 1994. "Divergence in Economic Performance: Transitional Dynamics with Multiple Equilibria," Journal of Economic Theory, Elsevier, vol. 63(1), pages 97-112, June.
- Caballe, Jordi & Santos, Manuel S, 1993. "On Endogenous Growth with Physical and Human Capital," Journal of Political Economy, University of Chicago Press, vol. 101(6), pages 1042-1067, December.
- Raouf, BOUCEKKINE & JosÃ© R. , RUIZ-TAMARIT, 2004.
"Special functions for the study of economic dynamics : The case of the Lucas-Uzawa model,"
Discussion Papers (IRES - Institut de Recherches Economiques et Sociales)
2004026, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
- Boucekkine, R. & Ruiz-Tamarit, J.R., 2008. "Special functions for the study of economic dynamics: The case of the Lucas-Uzawa model," Journal of Mathematical Economics, Elsevier, vol. 44(1), pages 33-54, January.
- BOUCEKKINE, Raouf & RUIZ-TAMARIT, Ramon, 2004. "Special functions for the study of economic dynamics: The case of the Lucas-Uzawa model," CORE Discussion Papers 2004084, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- BOUCEKKINE, Raouf & RUIZ-TAMARIT, José Ramon, "undated". "Special functions for the study of economic dynamics: The case of the Lucas-Uzawa model," CORE Discussion Papers RP 2003, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Brunner, Martin & Strulik, Holger, 2002.
"Solution of perfect foresight saddlepoint problems: a simple method and applications,"
Journal of Economic Dynamics and Control,
Elsevier, vol. 26(5), pages 737-753, May.
- Martin Brunner & Holger Strulik, 2002. "Code for "Solution of Perfect Foresight Sattlepoint Problems: A Simple Method and Applications"," QM&RBC Codes 93, Quantitative Macroeconomics & Real Business Cycles.
- Chamley, Christophe, 1993.
"Externalities and Dynamics in Models of "Learning or Doing.","
International Economic Review,
Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 34(3), pages 583-609, August.
- Christophe Chamley, 1991. "Externalities and Dynamics in Models of "Learning or Doing"," Boston University - Institute for Economic Development 17, Boston University, Institute for Economic Development.
- Bethmann, Dirk, 2008.
"The open-loop solution of the Uzawa-Lucas model of endogenous growth with N agents,"
Journal of Macroeconomics,
Elsevier, vol. 30(1), pages 396-414, March.
- Bethmann, Dirk, 2004. "The open-loop solution of the Uzawa-Lucas Model of Endogenous Growth with N agents," Papers 2004,42, Humboldt-Universität Berlin, Center for Applied Statistics and Economics (CASE).
- Casey B. Mulligan & Xavier Sala-i-Martin, 1991. "A Note on the Time-Elimination Method For Solving Recursive Dynamic Economic Models," NBER Technical Working Papers 0116, National Bureau of Economic Research, Inc.
- Casey B. Mulligan & Xavier Sala-i-Martin, 1993. "Transitional Dynamics in Two-Sector Models of Endogenous Growth," The Quarterly Journal of Economics, Oxford University Press, vol. 108(3), pages 739-773.
- Lucas, Robert Jr., 1988. "On the mechanics of economic development," Journal of Monetary Economics, Elsevier, vol. 22(1), pages 3-42, July.
When requesting a correction, please mention this item's handle: RePEc:kap:jeczfn:v:107:y:2012:i:2:p:101-128. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Sonal Shukla)or (Rebekah McClure)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.