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Constant population growth rate and time to build: the Solow model case

Author

Listed:
  • Luca Guerrini

    (University of Bologna)

Abstract

We analyze the Solow model with constant population growth rate, where production occurs with a time delay while new capital is installed (time to build). Taking time delay as a bifurcation parameter, we discuss the stability and the existence of the Hopf bifurcation occurring at the equilibrium. It is proved that the equilibrium is locally asymptotically stable for any delay if population is increasing, whereas there are stability switches if population is decreasing. In this case, a steady state bifurcation and a Hopf bifurcation occur. Contrary to the Solow model, a different scenario arises.

Suggested Citation

  • Luca Guerrini, 2012. "Constant population growth rate and time to build: the Solow model case," Economics Bulletin, AccessEcon, vol. 32(4), pages 3260-3265.
    • Handle: RePEc:ebl:ecbull:eb-12-00652
    as

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    References listed on IDEAS

    as
    1. Asea, Patrick K. & Zak, Paul J., 1999. "Time-to-build and cycles," Journal of Economic Dynamics and Control, Elsevier, vol. 23(8), pages 1155-1175, August.
    2. Kydland, Finn E & Prescott, Edward C, 1982. "Time to Build and Aggregate Fluctuations," Econometrica, Econometric Society, vol. 50(6), pages 1345-1370, November.
    3. Thomas Christiaans, 2011. "Semi-endogenous growth when population is decreasing," Economics Bulletin, AccessEcon, vol. 31(3), pages 2667-2673.
    4. Rebelo, Sergio, 1991. "Long-Run Policy Analysis and Long-Run Growth," Journal of Political Economy, University of Chicago Press, vol. 99(3), pages 500-521, June.
    5. Paul Zak, 1999. "Kaleckian Lags in General Equilibrium," Review of Political Economy, Taylor & Francis Journals, vol. 11(3), pages 321-330.
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    More about this item

    Keywords

    Solow model; time to build; negative population growth;
    All these keywords.

    JEL classification:

    • O4 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity

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