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Optimal growth with investment enhancing labor

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  • Crettez, Bertrand
  • Hayek, Naila
  • Morhaim, Lisa

Abstract

We study a non-convex optimal growth problem with investment enhancing labor. We prove that there exists an optimal growth path, that all optimal paths are interior and we provide a condition under which at least one of them is monotonic. We also study the existence and uniqueness of the steady state. We show in particular that a rise in the efficiency of the investment enhancing labor does not necessarily lead to an increase in the steady state value of this labor. Furthermore we provide a complete study of the dynamics of the optimal solution in the special case of a logarithmic utility function and a Cobb–Douglas production function.

Suggested Citation

  • Crettez, Bertrand & Hayek, Naila & Morhaim, Lisa, 2017. "Optimal growth with investment enhancing labor," Mathematical Social Sciences, Elsevier, vol. 86(C), pages 23-36.
    • Handle: RePEc:eee:matsoc:v:86:y:2017:i:c:p:23-36
    DOI: 10.1016/j.mathsocsci.2016.12.002
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    2. Ha-Huy, Thai & Tran, Nhat-Thien, 2019. "A simple characterization for sustained growth," MPRA Paper 94576, University Library of Munich, Germany.

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