The Non-linear Accelerator and the Persistence of Business Cycles

Abstract

By taking account of obvious and inescapable limitations on the functioning of the accelerator, we explain some of the chief characteristics of the cycle, notably its failure to die away, along with the fact that capital stock is usually either in excess or in short supply. By a succession of increasingly complex models, the nature and methods of analysing non-linear cycle models is developed. The roles of lags and of secular evolution are illustrated. In each case the system’s equilibrium position is unstable, but there exists a stable limit cycle toward which all motions tend.

This paper, with the exception of a few modifications in the last section, was presented at the 1948 meeting of the Econometric Society in Cleveland, and it was summarised in Econometrica, April 1949 (vol. 17, pp. 184–5). In its various metamorphoses it was followed with great interest and many helpful comments by the late J. A. Schumpeter. His influence on the whole of it is so pervasive, and I hope so evident, that particular acknowledgement would be inadequate.