ABSTRACT
Most early post-war contributions to non-linear business cycle theory are credited to authors adopting a certain form of Keynesianism. Indeed, the approach initiated by Kaldor, Hicks and Goodwin contributed to the development of Keynesian macrodynamics within a non-linear perspective. Kaldor, Hicks and Goodwin’s original approach is well-known and has been extensively studied following the renewed interest in non-linear dynamics in the 1980s (see e.g. Lorenz 1989). The pioneering mathematical formulations proposed by Yasui, Morishima and Ichimura are less known but are examined in detail in Velupillai (2008), which is dedicated to Japanese advances in non-linear dynamics in the 1950s. Therefore, we do not elaborate this approach further. We simply highlight that these contributions were the first to investigate closely the question of the existence and uniqueness of a limit cycle in the business cycle models of Kaldor, Hicks and Goodwin with Lienard or van der Pol equations and Levinson and Smith (1942) criteria resorting to controversial ad hoc assumptions (see Velupillai 2008). These findings were synthesised by Ichimura (1955) in his classical attempt to develop a general non-linear macrodynamic theory of economic fluctuations along Keynesian lines. However, it would be misleading to attribute the pioneering research in
the field of non-linear cycle theory exclusively to this first tradition. This paper attempts to shed light on the existence of another view expressed by Allais who published a less well-known but impressive number of contributions to non-linear cycle theory in the 1950s.
