Decisions in Economics and Finance

, Volume 41, Issue 2, pp 119–143 | Cite as

A piecewise linear model of credit traps and credit cycles: a complete characterization

  • Kiminori Matsuyama
  • Iryna Sushko
  • Laura GardiniEmail author


We reconsider a regime-switching model of credit frictions which has been proposed in a general framework by Matsuyama for the case of Cobb–Douglas production functions. This results in a piecewise linear map with two discontinuity points and all three branches having the same slope. We offer a complete characterization of the bifurcation structure in the parameter space, as well as of the attracting sets and related basins of attraction in the phase space. We also discuss parameter regions associated with overshooting, leapfrogging, poverty traps, reversal of fortune and growth miracle, as well as cycles with any kind of switching between the expansionary and contractionary phases.


Macroeconomic model of credit frictions Poverty traps Growth miracle One-dimensional piecewise linear map Border collision bifurcation 

JEL Classification

E22 E44 O33 C61 



I. Sushko thanks the University of Urbino for the hospitality experienced during her stay there as a Visiting Professor. K. Matsuyama is also grateful to the University of Urbino for the hospitality during his visit.


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Copyright information

© Associazione per la Matematica Applicata alle Scienze Economiche e Sociali (AMASES) 2018

Authors and Affiliations

  • Kiminori Matsuyama
    • 1
  • Iryna Sushko
    • 2
    • 3
  • Laura Gardini
    • 4
    Email author
  1. 1.Department of EconomicsNorthwestern UniversityEvanstonUSA
  2. 2.Kyiv School of EconomicsKyivUkraine
  3. 3.Institute of MathematicsNational Academy of Sciences of UkraineKyivUkraine
  4. 4.Department of Economics, Society and PoliticsUniversity of UrbinoUrbinoItaly

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