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Exact solutions for a Solow-Swan model with non-constant returns to scale

Author

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  • Nicolò Cangiotti

    (Politecnico di Milano)

  • Mattia Sensi

    (Inria Sophia Antipolis - Méditerranée Research Centre)

Abstract

The Solow-Swan model is shortly reviewed from a mathematical point of view. By considering non-constant returns to scale, we obtain a general solution strategy. We then compute the exact solution for the Cobb-Douglas production function, for both the classical model and the von Bertalanffy model. Numerical results are eventually provided.

Suggested Citation

  • Nicolò Cangiotti & Mattia Sensi, 2023. "Exact solutions for a Solow-Swan model with non-constant returns to scale," Indian Journal of Pure and Applied Mathematics, Springer, vol. 54(4), pages 1278-1285, December.
  • Handle: RePEc:spr:indpam:v:54:y:2023:i:4:d:10.1007_s13226-022-00341-7
    DOI: 10.1007/s13226-022-00341-7
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    References listed on IDEAS

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    1. Bajo-Rubio, Oscar, 2000. "A further generalization of the Solow growth model: the role of the public sector," Economics Letters, Elsevier, vol. 68(1), pages 79-84, July.
    2. Litina, Anastasia & Palivos, Theodore, 2008. "Do Inada conditions imply that production function must be asymptotically Cobb-Douglas? A comment," Economics Letters, Elsevier, vol. 99(3), pages 498-499, June.
    3. Robert M. Solow, 1956. "A Contribution to the Theory of Economic Growth," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 70(1), pages 65-94.
    4. Luc Everaert & Francisco Simone, 2007. "Improving the estimation of total factor productivity growth: capital operating time in a latent variable approach," Empirical Economics, Springer, vol. 33(3), pages 449-468, November.
    5. Luis A. Quezada-Téllez & Guillermo Fernández-Anaya & Dominique Brun-Battistini & Benjamín Nuñez-Zavala & Jorge E. Macías-Díaz, 2021. "An Economic Model for OECD Economies with Truncated M -Derivatives: Exact Solutions and Simulations," Mathematics, MDPI, vol. 9(15), pages 1-14, July.
    6. Jungsoo Park & Hang Ryu, 2006. "Accumulation, Technical Progress, and Increasing Returns in the Economic Growth of East Asia," Journal of Productivity Analysis, Springer, vol. 25(3), pages 243-255, June.
    7. Barelli, Paulo & de Abreu Pessoa, Samuel, 2003. "Inada conditions imply that production function must be asymptotically Cobb-Douglas," Economics Letters, Elsevier, vol. 81(3), pages 361-363, December.
    8. Titus J. Galama & Patrick Hullegie & Erik Meijer & Sarah Outcault, 2012. "Is There Empirical Evidence For Decreasing Returns To Scale In A Health Capital Model?," Health Economics, John Wiley & Sons, Ltd., vol. 21(9), pages 1080-1100, September.
    9. T. W. Swan, 1956. "ECONOMIC GROWTH and CAPITAL ACCUMULATION," The Economic Record, The Economic Society of Australia, vol. 32(2), pages 334-361, November.
    10. Jensen Christian, 2014. "Replication and Returns to Scale in Production," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 14(1), pages 127-148, February.
    11. Ding, Sai & Knight, John, 2009. "Can the augmented Solow model explain China's remarkable economic growth? A cross-country panel data analysis," Journal of Comparative Economics, Elsevier, vol. 37(3), pages 432-452, September.
    12. John Conlisk, 1971. "Nonconstant Returns to Scale and the Technical Change Frontier," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 85(3), pages 483-493.
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