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Closed-form solutions for the Lucas-Uzawa growth model with logarithmic utility preferences via the partial Hamiltonian approach
a. | Department of Economics, Lahore School of Economics, Lahore, 53200, Pakistan |
b. | Department of Mathematics and Statistical Sciences, Lahore School of Economics, Lahore, 53200, Pakistan |
In this paper, we present a dynamic picture of the two sector Lucas-Uzawa model with logarithmic utility preferences and homogeneous technology as was proposed by Bethmann [
References:
[1] |
K. J. Arrow,
Applications of Control Theory to Economic Growth, in Veinott, A. F. , & Dantzig, G. B. (Eds. ) Mathematics of the decision sciences, Part 2, American Mathematical scociety 11,1968. |
[2] |
J. Benhabib and R. Perli,
Uniqueness and indeterminacy: On the dynamics of endogenous growth, Journal of Economic Theory, 63 (1994), 113-142.
|
[3] |
D. Bethmann,
Solving macroeconomic models with homogeneous technology and logarithmic preferences, Australian Economic Papers, 52 (2013), 1-18.
|
[4] |
R. Boucekkine and J. R. Ruiz-Tamarit,
Special functions for the study of economic dynamics: The case of the Lucas-Uzawa model, Journal of Mathematical Economics, 44 (2008), 33-54.
doi: 10.1016/j.jmateco.2007.05.001. |
[5] |
J. Caballé and M. S. Santos,
On endogenous growth with physical and human capital, Journal of Political Economy, (1993), 1042-1067.
|
[6] |
A. Chaudhry, H. Tanveer and R. Naz,
Unique and multiple equilibria in a macroeconomic model with environmental quality: An analysis of local stability, Economic Modelling, 63 (2017), 206-214.
|
[7] |
C. Chilarescu,
On the existence and uniqueness of solution to the Lucas-Uzawa model, Economic Modelling, 28 (2011), 109-117.
|
[8] |
C. Chilarescu,
An analytical solutions for a model of endogenous growth, Economic Modelling, 25 (2008), 1175-1182.
|
[9] |
C. Chilarescu and C. Sipos,
Solving macroeconomic models with homogenous technology and logarithmic preferences-A note, Economics Bulletin, 34 (2014), 541-550.
|
[10] |
R. Lucas,
On the mechanics of economic development, Journal of Monetary Economics, 22 (1988), 3-42.
|
[11] |
O. L. Mangasarian,
Sufficient conditions for the optimal control of nonlinear systems, SIAM Journal on Control, 4 (1966), 139-152.
doi: 10.1137/0304013. |
[12] |
C. B. Mulligan and X. Sala-i-Martin,
Transitional dynamics in two-sector models of endogenous growth, The Quaterly Journal of Economics, 108 (1993), 739-773.
|
[13] |
R. Naz, F. M. Mahomed and A. Chaudhry,
A Partial Hamiltonian Approach for Current Value Hamiltonian Systems, Communications in Nonlinear Science and Numerical Simulation, 19 (2014), 3600-3610.
doi: 10.1016/j.cnsns.2014.03.023. |
[14] |
R. Naz,
The applications of the partial Hamiltonian approach to mechanics and other areas, International Journal of Nonlinear Mechanics, 86 (2016), 1-6.
|
[15] |
R. Naz, F. M. Mahomed and A. Chaudhry,
A partial Lagrangian Method for Dynamical Systems, Nonlinear Dynamics, 84 (2016), 1783-1794.
doi: 10.1007/s11071-016-2605-8. |
[16] |
R. Naz, A. Chaudhry and F. M. Mahomed,
Closed-form solutions for the Lucas-Uzawa model of economic growth via the partial Hamiltonian approach, Communications in Nonlinear Science and Numerical Simulation, 30 (2016), 299-306.
doi: 10.1016/j.cnsns.2015.06.033. |
[17] |
R. Naz and A. Chaudhry,
Comparison of closed-form solutions for the Lucas-Uzawa model via the partial Hamiltonian approach and the classical approach, Mathematical Modelling and Analysis, 22 (2017), 464-483.
doi: 10.3846/13926292.2017.1323035. |
[18] |
J. R. Ruiz-Tamarit,
The closed-form solution for a family of four-dimension nonlinear MHDS, Journal of Economic Dynamics and Control, 32 (2008), 1000-1014.
doi: 10.1016/j.jedc.2007.03.008. |
[19] |
H. Uzawa,
Optimum technical change in an aggregative model of economic growth, International Economic Review, 6 (1965), 18-31.
|
[20] |
D. Xie,
Divergence in economic performance: Transitional dynamics with multiple equilibria, Journal of Economic Theory, 63 (1994), 97-112.
|
show all references
References:
[1] |
K. J. Arrow,
Applications of Control Theory to Economic Growth, in Veinott, A. F. , & Dantzig, G. B. (Eds. ) Mathematics of the decision sciences, Part 2, American Mathematical scociety 11,1968. |
[2] |
J. Benhabib and R. Perli,
Uniqueness and indeterminacy: On the dynamics of endogenous growth, Journal of Economic Theory, 63 (1994), 113-142.
|
[3] |
D. Bethmann,
Solving macroeconomic models with homogeneous technology and logarithmic preferences, Australian Economic Papers, 52 (2013), 1-18.
|
[4] |
R. Boucekkine and J. R. Ruiz-Tamarit,
Special functions for the study of economic dynamics: The case of the Lucas-Uzawa model, Journal of Mathematical Economics, 44 (2008), 33-54.
doi: 10.1016/j.jmateco.2007.05.001. |
[5] |
J. Caballé and M. S. Santos,
On endogenous growth with physical and human capital, Journal of Political Economy, (1993), 1042-1067.
|
[6] |
A. Chaudhry, H. Tanveer and R. Naz,
Unique and multiple equilibria in a macroeconomic model with environmental quality: An analysis of local stability, Economic Modelling, 63 (2017), 206-214.
|
[7] |
C. Chilarescu,
On the existence and uniqueness of solution to the Lucas-Uzawa model, Economic Modelling, 28 (2011), 109-117.
|
[8] |
C. Chilarescu,
An analytical solutions for a model of endogenous growth, Economic Modelling, 25 (2008), 1175-1182.
|
[9] |
C. Chilarescu and C. Sipos,
Solving macroeconomic models with homogenous technology and logarithmic preferences-A note, Economics Bulletin, 34 (2014), 541-550.
|
[10] |
R. Lucas,
On the mechanics of economic development, Journal of Monetary Economics, 22 (1988), 3-42.
|
[11] |
O. L. Mangasarian,
Sufficient conditions for the optimal control of nonlinear systems, SIAM Journal on Control, 4 (1966), 139-152.
doi: 10.1137/0304013. |
[12] |
C. B. Mulligan and X. Sala-i-Martin,
Transitional dynamics in two-sector models of endogenous growth, The Quaterly Journal of Economics, 108 (1993), 739-773.
|
[13] |
R. Naz, F. M. Mahomed and A. Chaudhry,
A Partial Hamiltonian Approach for Current Value Hamiltonian Systems, Communications in Nonlinear Science and Numerical Simulation, 19 (2014), 3600-3610.
doi: 10.1016/j.cnsns.2014.03.023. |
[14] |
R. Naz,
The applications of the partial Hamiltonian approach to mechanics and other areas, International Journal of Nonlinear Mechanics, 86 (2016), 1-6.
|
[15] |
R. Naz, F. M. Mahomed and A. Chaudhry,
A partial Lagrangian Method for Dynamical Systems, Nonlinear Dynamics, 84 (2016), 1783-1794.
doi: 10.1007/s11071-016-2605-8. |
[16] |
R. Naz, A. Chaudhry and F. M. Mahomed,
Closed-form solutions for the Lucas-Uzawa model of economic growth via the partial Hamiltonian approach, Communications in Nonlinear Science and Numerical Simulation, 30 (2016), 299-306.
doi: 10.1016/j.cnsns.2015.06.033. |
[17] |
R. Naz and A. Chaudhry,
Comparison of closed-form solutions for the Lucas-Uzawa model via the partial Hamiltonian approach and the classical approach, Mathematical Modelling and Analysis, 22 (2017), 464-483.
doi: 10.3846/13926292.2017.1323035. |
[18] |
J. R. Ruiz-Tamarit,
The closed-form solution for a family of four-dimension nonlinear MHDS, Journal of Economic Dynamics and Control, 32 (2008), 1000-1014.
doi: 10.1016/j.jedc.2007.03.008. |
[19] |
H. Uzawa,
Optimum technical change in an aggregative model of economic growth, International Economic Review, 6 (1965), 18-31.
|
[20] |
D. Xie,
Divergence in economic performance: Transitional dynamics with multiple equilibria, Journal of Economic Theory, 63 (1994), 97-112.
|
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