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Structural instability and alternative development scenarios

Abstract

Many past societies grew and flourished for several generations, and some for many centuries, prior to experiencing calamities that lowered wealth and/or productivity below some “critical levels.” In some cases, a collapse occurred; in others, the population reductions caused by emigration, plague, or warfare not only extended societies’ survival but induced a growth resurgence. These varied historical development scenarios are captured using a comparative dynamic analysis of structurally unstable variations of the Solow–Swan growth model. These results would seem to be relevant for understanding possibilities in the contemporary world.

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Notes

  1. Recalled from old correspondence.

  2. Braudel (1980), p. 89.

  3. Paraphrased from Grene (1987), p. 14, 18.

  4. This model is commonly referred as the Solow growth model. The contributions to growth theory by Swan (1956) as well as the similarities and differences with the analysis by Solow (1956, 1957) have been examined by Dimand and Spencer (2008).

  5. For instance, papers by Ritschl (1985), Donghan (1998), Fanti and Manfredi (2003), Brida et al. (2006), and Accinelli and Brida (2007) used the Solow–Swan model to analyze how various laws of motion for population affect economic growth.

  6. Thus, the average family size is 2(2 + n).

  7. See Ritschl (1985) in the case in which δ = 0.

  8. For a steady state \(\tilde{k}\) to be preserved following a productivity decline from A to A′, the population growth rate n′ must satisfy the following condition: \(\displaystyle\frac{n^{\prime }+\delta }{sA^{\prime }}=\displaystyle\frac{f(\tilde{k})}{\tilde{k}}=\displaystyle\frac{n+\delta }{sA}\).

  9. If the subsistence consumption level is equal to zero, then the model reduces to the Solow–Swan case with its single possible long-run outcome of perpetual growth for any positive initial wealth level.

  10. Based on Pianigiani and York (1979) and discussed in Day (1994), pp. 167–173.

References

  • Accinelli E, Brida JG (2007) Population growth and the Solow–Swan model. Int J Ecol Econ Stat 8(S07):54–63

    Google Scholar 

  • Azariadis C (1996) The economics of poverty traps, part one: complete markets. J Econ Growth 1(4):449–486

    Article  Google Scholar 

  • Ben-David D (1998) Convergence clubs and subsistence economies. J Dev Econ 55(1):155–171

    Article  Google Scholar 

  • Braudel F (1980) On history. The University of Chicago Press, Chicago

  • Brida JG, Mingari Scarpello G, Ritelli D (2006) The Solow model with logistic manpower: a stability analysis. J World Econ Rev 1(2)

  • Dawid H, Day RH (2007) On sustainable growth and collapse: optimal and adaptive paths. J Econ Dyn Control 31(7):2374–2397

    Article  Google Scholar 

  • Day RH (1994) Complex economic dynamics, vol I, an introduction to dynamical systems and market mechanisms. MIT, Cambridge

    Google Scholar 

  • Diamond J (2005) Collapse: how societies choose to fail or succeed. Viking Books, New York

    Google Scholar 

  • Dimand RW, Spencer BJ (2008) Trevor Swan and the neoclassical growth model. NBER Working Paper 13950

  • Donghan C (1998) An improved Solow–Swan model. Chin Q J Math 13(2):72–78

    Google Scholar 

  • Fanti L, Manfredi P (2003) The Solow’s model with endogenous population: a neoclassical growth cycle model. J Econ Dev 28(2):103–115

    Google Scholar 

  • Gibbon E (1789) The decline and fall of the Roman empire. Strahan & Cadell, London

    Google Scholar 

  • Grene D (1987) Herodotus: the history. University of Chicago Press, Chicago

    Google Scholar 

  • Keynes JM (1930) Essays in persuasion. W.W.Norton, New York

    Google Scholar 

  • King R, Rebelo ST (1993) Transitional dynamics and economic growth in the neoclassical model. Am Econ Rev 83(4):908–931

    Google Scholar 

  • Malthus TR (1798) An essay on the principle of population. Johnson J, London

    Google Scholar 

  • Manzoni A (1827) The betrothed. New edition. McArthur, Toronto

    Google Scholar 

  • McAdam P, Allsopp C (2007) Preface, the 50th anniversary of the Solow growth model. Oxf Rev Econ Policy 23(1):1–2

    Article  Google Scholar 

  • Pianigiani G, York J (1979) Expanding maps in sets which are almost invariant: decay and chaos. Trans Am Math Soc 252:351–360

    Google Scholar 

  • Quigley C (1961) The evolution of civilizations: an introduction to historical analysis, 1st edn. Macmillan, New York

    Google Scholar 

  • Ritschl A (1985) On the stability of the steady state when population is decreasing. J Econ (Wien) 45(2):161–170

    Google Scholar 

  • Solow R (1956) A contribution to the theory of economic growth. Q J Econ 70(1):65–94

    Article  Google Scholar 

  • Solow R (1957) Technical progress and productivity change. Rev Econ Stat 39(3):312–320

    Article  Google Scholar 

  • Swan T (1956) Economic growth and capital accumulation. Econ Rec 32:334–361

    Article  Google Scholar 

  • Tainter JA (1988) The collapse of complex societies. Cambridge University Press, Cambridge

    Google Scholar 

Download references

Acknowledgements

The authors would like to thank two anonymous referees for their valuable comments and suggestions on the preliminary version of this paper.

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Correspondence to Laurent L. Cellarier.

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Responsible editor: Alessandro Cigno

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Cellarier, L.L., Day, R.H. Structural instability and alternative development scenarios. J Popul Econ 24, 1165–1180 (2011). https://doi.org/10.1007/s00148-009-0279-y

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Keywords

  • The Solow–Swan model
  • Minimal consumption level

JEL Classification

  • O41