A Reconsideration of Samuelson’s Multiplier-Accelerator Model

The year 2009 marks the 70th anniversery of the publication of Samuelson’s Multiplier-Accelerator model, which laid out a rigorous mathematical formulation of the theory of Business Cycles. It is interesting to note that today’s economic climate is reminiscent of the historical context of Samuelson’s Multiplier-Accelrator paper. The global response to the present crisis in the form of fiscal stimulus motivated us to reconsider Samuelson’s model with the benefit of hindsight from the vast inspiring literature that followed his paper. Our aim in the paper is to reconsider the original Samuelson’s multiplier-accelerator model from the point of view of the recent fiscal stimulus programs by governments to combat the global recession. The fiscal stimulus program adopted by various governments lends naturally to model such a stabilization policy as a discontinuity in the government expenditure variable in the multiplier-accelerator model. The investigation of the effects of the discontinuity in the government expenditure is pertinent not only from the point of view the dynamics of the theoretical model, but also for furthering the discussion on the potential implications of the fiscual stimulus programs. We show that this simple modification yields some interesting dynamics in terms of periodic orbits and chaotic fluctuations in the original Samuelson’s model. We also note with particular interest that our model is able to generate new dynamics in the region where both the multiplier and accelerator coefficients are less than one or in Region A of Samuelson’s model and in contrast to the most of the models discussed in the literature.