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Solving Macroeconomic Models with Homogenous Technology and Logarithmic Preferences - A Note


  • Constantin Chilarescu

    () (Laboratory CLERSE, University of Lille 1)

  • Ciprian Sipos

    () (Department of Economics, West University of Timisoara)


In a recent published paper, Bethmann analyzed a stylised Robinson Crusoe economy, defining the state-like and control-like variables and then introducing the value-function-like function. He claims in the final section, that even if the model can be solved explicitly, but with complicated numerical analyses, he focuses instead on illustrating some dynamic programing techniques. In our opinion there are no complicated mathematical procedures to solve explicitly the model and we present here a closed-form solution of the model, only for the continuous case.

Suggested Citation

  • Constantin Chilarescu & Ciprian Sipos, 2014. "Solving Macroeconomic Models with Homogenous Technology and Logarithmic Preferences - A Note," Economics Bulletin, AccessEcon, vol. 34(1), pages 541-550.
  • Handle: RePEc:ebl:ecbull:eb-13-00811

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    References listed on IDEAS

    1. Cysne, Rubens Penha, 2006. "A note on the non-convexity problem in some shopping-time and human-capital models," Journal of Banking & Finance, Elsevier, vol. 30(10), pages 2737-2745, October.
    2. 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.
    3. Chilarescu, Constantin, 2011. "On the existence and uniqueness of solution to the Lucas–Uzawa model," Economic Modelling, Elsevier, vol. 28(1), pages 109-117.
    4. 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.
    5. Xie Danyang, 1994. "Divergence in Economic Performance: Transitional Dynamics with Multiple Equilibria," Journal of Economic Theory, Elsevier, vol. 63(1), pages 97-112, June.
    6. Dirk Bethmann, 2013. "Solving Macroeconomic Models with Homogeneous Technology and Logarithmic Preferences," Australian Economic Papers, Wiley Blackwell, vol. 52(1), pages 1-18, March.
    7. Chilarescu, Constantin, 2011. "On the existence and uniqueness of solution to the Lucas-Uzawa model," Economic Modelling, Elsevier, vol. 28(1-2), pages 109-117, January.
    8. Lucas, Robert Jr., 1988. "On the mechanics of economic development," Journal of Monetary Economics, Elsevier, vol. 22(1), pages 3-42, July.
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    Cited by:

    1. Rehana Naz, 2017. "Closed-form Solutions for the Lucas-Uzawa model: Unique or Multiple," Papers 1712.08654,

    More about this item


    Robinson Crusoe economy; Hamiltonian function; uniqueness of solution;

    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • O4 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity


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