A simple model of growth cycles with technology choice

Yosuke Umezuki, Masanori Yokoo

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


In this study, we develop a simple, computable overlapping generations model that exhibits endogenous fluctuations. The key assumption is that a firm can choose from multiple technologies of production. Since the model reduces to a piecewise linear map on the unit interval, it allows us to conduct an in-depth analysis of its dynamic properties. Particularly, this piecewise linearization reveals the ability of the model to exhibit periodic attracting cycles of an arbitrarily large period as well as non-periodic attractors. Furthermore, it is demonstrated that the occurrence of periodic patterns is completely characterized by the rotation number or the “devil's staircase.”

Original languageEnglish
Pages (from-to)164-175
Number of pages12
JournalJournal of Economic Dynamics and Control
Publication statusPublished - Mar 2019


  • Devil's staircase
  • Endogenous fluctuations
  • Overlapping generations model
  • Piecewise linearity
  • Rotation number
  • Technology choice

ASJC Scopus subject areas

  • Economics and Econometrics
  • Control and Optimization
  • Applied Mathematics


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