Time-Delayed Dynamic Model of Renewable Resource and Population

Akio Matsumoto, Mami Suzuki and Yasuhisa Saito
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Akio Matsumoto: Chuo University
Mami Suzuki: Aichi Gakusen University
Yasuhisa Saito: Shizuoka University

Chapter 8. in Time and Space in Economics, 2007, pp 145-159 from Springer

Abstract: Summary This chapter reconsiders the “Ricardo-Malthus” dynamic model of population and renewable resource developed by Brander and Taylor. To this end, it sheds light on a delay in production, which is a key feature of long-run evolution in a preindustrial economic society. It is clear that the delay has a considerable effect on the long-run dynamics of natural resources and population. This notwithstanding, much previous work relates to a case in which production is instantaneous. As such, the purpose of this chapter is to investigate the effect caused by the delay in production. Our analysis shows that there is a critical value of the delay with which a delayed version of an otherwise stable system becomes unstable. In addition, it shows numerically that the critical value is negatively related to the size of the carrying capacity and the exogenous net birth rate.

Keywords: Delayed differential equation; Easter Island; Economic dynamics model; Environmental degradation; Population growth (search for similar items in EconPapers)
Date: 2007
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-4-431-45978-1_8

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DOI: 10.1007/978-4-431-45978-1_8

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