Revisiting Samuelson’s models, linear and nonlinear, stability conditions and oscillating dynamics

Fabio Tramontana, Laura Gardini

Risultato della ricerca: Contributo in rivistaArticolo in rivista


In this work, we reconsider the dynamics of a few versions of the classical Samuelson’s multiplier–accelerator model for national economy. First we recall that the classical one with constant governmental expenditure, represented by a linear second-order difference equation, is able to generate oscillations converging to the equilibrium for a wide range of values of the parameters, and give its analytic solution for all the possible cases. A delayed version proposed in the recent literature, represented by a linear third-order difference equation, is also considered. We show that also this model is able to produce converging oscillations, and give a complete analysis of the stability region of the equilibrium. A new simple nonlinear model is proposed, showing that it keeps oscillatory behavior, although coupled with other dynamics related to global effects. Our analysis confirms that the seminal work of Samuelson and simple modifications of it, may give powerful tools in the study of the business cycles.
Lingua originaleEnglish
pagine (da-a)1-15
Numero di pagine15
RivistaJournal of Economic Structures
Stato di pubblicazionePubblicato - 2021


  • Difference equations
  • Economic modelling
  • Linear and nonlinear models
  • Oscillatory dynamics
  • Samuelson model
  • Stability of the equilibrium


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