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Fifty years of mathematical growth theory: Classical topics and new trends

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Abstract

We present an overview of selected contributions of the Journal of Mathematical Economics' authors in the last half century. We start with the classical optimal growth theory within a benchmark multisector model and outline the successive developments in the analysis of this model, including the turnpike theory. Different refinements of the benchmark are considered along the way. We after survey the abundant literature on endogenous fluctuations in two-sector models. We conclude with two strong trends in the recent growth literature: green growth and infinite-dimensional growth models.

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  • Emmanuelle Augeraud-Véron & Raouf Boucekkine & Fausto Gozzi & Alain Venditti, 2024. "Fifty years of mathematical growth theory: Classical topics and new trends," AMSE Working Papers 2406, Aix-Marseille School of Economics, France.
    • Handle: RePEc:aim:wpaimx:2406
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    1. Daron Acemoglu (ed.), 2004. "Recent Developments in Growth Theory," Books, Edward Elgar Publishing, volume 0, number 2981.
    2. Llavador, Humberto & Roemer, John E. & Silvestre, Joaquim, 2010. "Intergenerational justice when future worlds are uncertain," Journal of Mathematical Economics, Elsevier, vol. 46(5), pages 728-761, September.
    3. Hori, Hajime, 1987. "A turnpike theorem for rolling plans," Journal of Mathematical Economics, Elsevier, vol. 16(3), pages 223-235, May.
    4. Ali Khan, M. & Mitra, Tapan, 2008. "Growth in the Robinson-Solow-Srinivasan model: Undiscounted optimal policy with a strictly concave welfare function," Journal of Mathematical Economics, Elsevier, vol. 44(7-8), pages 707-732, July.
    5. Takekuma, Shin-Ichi, 1980. "A sensitivity analysis on optimal economic growth," Journal of Mathematical Economics, Elsevier, vol. 7(2), pages 193-208, July.
    6. W. Davis Dechert & Kazuo Nishimura, 2012. "A Complete Characterization of Optimal Growth Paths in an Aggregated Model with a Non-Concave Production Function," Springer Books, in: John Stachurski & Alain Venditti & Makoto Yano (ed.), Nonlinear Dynamics in Equilibrium Models, edition 127, chapter 0, pages 237-257, Springer.
    7. Ha-Huy, Thai & Tran, Nhat Thien, 2020. "A simple characterisation for sustained growth," Journal of Mathematical Economics, Elsevier, vol. 91(C), pages 141-147.
    8. Le Van, Cuong & Nguyen, Manh-Hung & Vailakis, Yiannis, 2007. "Equilibrium dynamics in an aggregative model of capital accumulation with heterogeneous agents and elastic labor," Journal of Mathematical Economics, Elsevier, vol. 43(3-4), pages 287-317, April.
    9. Amir, Rabah & Mirman, Leonard J & Perkins, William R, 1991. "One-Sector Nonclassical Optimal Growth: Optimality Conditions and Comparative Dynamics," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 32(3), pages 625-644, August.
    10. Barro, Robert J, 1974. "Are Government Bonds Net Wealth?," Journal of Political Economy, University of Chicago Press, vol. 82(6), pages 1095-1117, Nov.-Dec..
    11. Amir, Rabah, 1996. "Sensitivity analysis of multisector optimal economic dynamics," Journal of Mathematical Economics, Elsevier, vol. 25(1), pages 123-141.
    12. d’Albis, Hippolyte & Augeraud-Veron, Emmanuelle & Venditti, Alain, 2012. "Business cycle fluctuations and learning-by-doing externalities in a one-sector model," Journal of Mathematical Economics, Elsevier, vol. 48(5), pages 295-308.
    13. Borissov, Kirill & Dubey, Ram Sewak, 2015. "A characterization of Ramsey equilibrium in a model with limited borrowing," Journal of Mathematical Economics, Elsevier, vol. 56(C), pages 67-78.
    14. Hartl, Richard F. & Kort, Peter M., 2003. "History dependence without unstable steady state: a non-differentiable framework," Journal of Mathematical Economics, Elsevier, vol. 39(8), pages 891-900, November.
    15. Bewley, Truman, 1982. "An integration of equilibrium theory and turnpike theory," Journal of Mathematical Economics, Elsevier, vol. 10(2-3), pages 233-267, September.
    16. Morimoto,Hiroaki, 2010. "Stochastic Control and Mathematical Modeling," Cambridge Books, Cambridge University Press, number 9780521195034.
    17. Le Van, Cuong & Nguyen, Manh-Hung & Vailakis, Yiannis, 2007. "Equilibrium dynamics in an aggregative model of capital accumulation with heterogeneous agents and elastic labor," Journal of Mathematical Economics, Elsevier, vol. 43(3-4), pages 287-317, April.
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    More about this item

    Keywords

    Growth theory; multisector models; turnpike theory; green growth; infinite-dimensional growth models; optimization;
    All these keywords.

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • O41 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models

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