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Structural instability and alternative development scenarios


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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  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.


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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).

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  • The Solow–Swan model
  • Minimal consumption level

JEL Classification

  • O41