Kaldor’s non-linear trade cycle theory
In 1940, Kaldor presented an ingenious graphical presentation of his business cycle theory based on Harrod’s principle of instability. By means of S-shaped investment and saving functions, showing that if the investment curve intersects the saving curve three times, the stationary equilibrium might become unstable while, for a wide range of values of capital stock, the economy will stabilize to either a low or a high equilibrium.
These considerations - under the assumption that the speed of quantity adjustment in the goods market is high, while real capital stock moves slowly - result in a self-sustained output and capital stock cycle model in which the economy moves from a stable, to an unstable, to a stable equilibrium. The model, though sufficient to obtain endogenous cycles around a static position does not address the issue of growth-cycle equilibrium values of income and capital. It produced local instability but only in a trendless economy. As Asada (2009) noted, in the 1950s Yasui and Morishima attempted to extend Kaldor’s model through a mathematical formulation that would produce cyclical growth. However, in assuming that growth and cycles were linearly superimposed, their attempts were far from challenging Harrod’s view that trend and cycle were indissolubly mixed.In the 1950s, Goodwin engaged in efforts along similar lines to model Harrod’s insights. With the help of his French Harvard colleague, Philippe Le Corbeiller, he attempted to determine how to exploit the Van der Pol-Raleigh limit-cycle theory of dynamics. In his 1951 pioneering contribution, he showed that this could be achieved within a non-linear formulation of the accelerator interacting with a stabilizing multiplier. However, like his Japanese contemporaries, Goodwin was unable to integrate both growth and cycles, assigning to trend only the role of a benchmark - a role that remained largely unexplained. It was not until the late 1960s that he succeeded in drafting a new approach.