Growth and Collapse of Empires: A Dynamic Optimization Model

Yuri Yegorov, Dieter Grass (), Magda Mirescu (), Gustav Feichtinger and Franz Wirl
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Dieter Grass: International Institute for Applied Systems Analysis (IIASA)
Magda Mirescu: University of Vienna

Journal of Optimization Theory and Applications, 2020, vol. 186, issue 2, No 12, 620-643

Abstract: Abstract This paper addresses the spatial evolution of countries accounting for economics, geography and (military) force. Economic activity is spatially distributed following the AK model with the output being split into consumption, investment, transport costs and military (for defense and expansion). The emperor controls the military force subject to the constraints imposed by the economy but also the geography (transport costs, border length) and the necessity to satisfy the needs of the population. The border changes depending on how much pressure the emperor can muster to counter the pressure of neighboring countries. The resulting dynamic process determines a country’s size over time. The model leads to multiple steady states, large empires and small countries being separated by a threshold and collapse. The resulting patterns can be linked to historical observations.

Keywords: Dynamic optimization; Growth model; Empire; Geography; Defense; 49J15; 91B62; 91B72; 91B72; 91D10; 91D20; 91F10 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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Working Paper: Growth and Collapse of Empires: A Dynamic Optimization Model (2019)
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DOI: 10.1007/s10957-020-01719-5

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