A Stability Result on a Reformulated Samuelson Economical Model

Ioannis K. Dassios, Charalambos P. Kontzalis, and Grigoris I. Kalogeropoulos


Mathematical Modelling, Samuelson model, Difference Equations, Ruth criterion, control


This paper extends the classical Samuelson's multiplier-accelerator model for national economy. Under this new approach, we introduce some kind of memory into the system. Actually, we assume that total consumption and private investment depend upon the national income values. Then, delayed difference equations of third order are employed to describe the model, while the respective solutions of third order polynomial, correspond to the typical observed business cycles of real economy. Stability conditions are investigated while numerical examples provide further insight and better understanding.

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