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A NOTE ON THE ANALYTICAL SOLUTION TO THE NEOCLASSICAL GROWTH MODEL WITH LEISURE

Published online by Cambridge University Press:  13 June 2012

Ryoji Hiraguchi
Ryoji Hiraguchi*
Affiliation:
Ritsumeikan University
*
Address correspondence to: Ryoji Hiraguchi, Faculty of Economics, Ritsumeikan University. 1-1-1, Noji-higashi, Kusatsu, Shiga, Japan; e-mail: [email protected].
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Abstract

In this note, we study the basic Ramsey models with labor–leisure choice. We first study the deterministic model and find that a closed-form solution exists and is represented by the Gauss hypergeometric functions. We next incorporate stochastic productivity shocks into the model. We prove that the analytical solution path still exists if the coefficient of relative risk aversion is equal to the capital share.

Keywords

Optimal GrowthClosed-Form SolutionRamsey Model
Type
Notes
Information
Macroeconomic Dynamics , Volume 18 , Issue 2 , March 2014 , pp. 473 - 479
Copyright
Copyright © Cambridge University Press 2012 

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References

REFERENCES

Benchekroun, Hasssan and Withagen, Cees (2011) The optimal depletion of exhaustible resources: A complete characterization. Resource and Energy Economics 33, 612–636.Google Scholar
Boucekkine, Raouf, Martínez, Blanca, and Ruiz-Tamarit, Jose (2008) Note on global dynamics and imbalance effects in the Lucas–Uzawa model. International Journal of Economic Theory 4, 503–518.Google Scholar
Boucekkine, Raouf and Ruiz-Tamarit, Jose (2008) Special functions for the study of economic dynamics: The case of the Lucas–Uzawa model. Journal of Mathematical Economics 44, 33–54.Google Scholar
Guerrini, Luca (2010) Transitional dynamics in the Ramsey model with AK technology and logistic population change. Economics Letters 109, 17–19.Google Scholar
Hiraguchi, Ryoji (2009) A note on the closed-form solution to the Lucas–Uzawa model with externality. Journal of Economic Dynamics and Control 33, 1757–1760.Google Scholar
Robert, Lucas (1988) On the mechanics of economic development. Journal of Monetary Economics 22, 3–42.Google Scholar
Nagata, Hisao (2008) On the Closed-Form Solution of the Ramsey Model: The Cases of Inelastic and Elastic Labor Supply. Working paper, Niigata University.Google Scholar
Pérez-Barahona, Agustin (2011) Nonrenewable energy resources as input for physical capital accumulation: A new approach. Macroeconomic Dynamics 15, 1–30.Google Scholar
Ruiz-Tamarit, Jose (2008) The closed-form solution for a family of four-dimension nonlinear MHDS. Journal of Economic Dynamics and Control 32, 1000–1014.Google Scholar
William, Smith (2006) An analytical solution to the Ramsey model. Contributions to Macroeconomics 6 (1), Art (3). 1–28.Google Scholar
Smith, William (2007) Inspecting the mechanism exactly: A closed-form solution to a stochastic growth model. Contributions to Macroeconomics 7 (1), Art. 30.Google Scholar
Wälde, Klaus (2011) Production technologies in stochastic continuous time models. Journal of Economic Dynamics and Control 35, 616–622.Google Scholar