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
Recalled from old correspondence.
Braudel (1980), p. 89.
Paraphrased from Grene (1987), p. 14, 18.
Thus, the average family size is 2(2 + n).
See Ritschl (1985) in the case in which δ = 0.
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: \(\displaystyle\frac{n^{\prime }+\delta }{sA^{\prime }}=\displaystyle\frac{f(\tilde{k})}{\tilde{k}}=\displaystyle\frac{n+\delta }{sA}\).
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.
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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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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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DOI: https://doi.org/10.1007/s00148-009-0279-y