4 - Liapunov theory and economic dynamics

Summary

The literature on the stability of the competitive equilibrium that came to fruition in the late 1950s was woven of three specific skeins in earlier work. First, there was the 1930s literature that had attempted to untangle statics from dynamics, and equilibrium from disequilibrium; that analysis had been done by Frisch, Tinbergen, Hicks, and others, though later writers would claim that the issues had finally been framed by Hicks's Value and Capital (1939). That book directed economists to the microfoundations-of-macroeconomics “problem” and suggested that the stable-unstable distinction could make sense of the dissimilar Keynesian and classical positions on unemployment. Second, there was a 1930s literature on equilibrium and stability whose lineage traced back to Pareto, social-systems analysis, and the social application of mechanical ideas. That tradition, with roots in physics, the physical chemistry of Willard Gibbs, and the evolutionary biology/ecology of A. J. Lotka, found expression in Paul Samuelson's writings in the late 1930s and early 1940s and provided the basis for his Foundations of Economic Analysis (1947). Third, the story of the introduction of modern stability theory into economics featured the interrelationship of two disciplines, mathematics and economics, that were linked in serendipitous ways in the 1940s. In this chapter I intend to tell this last story.

The tale is complex, however, and many seemingly peripheral issues take on special meaning. For instance, there have been conflicting priority claims regarding the first uses of certain mathematical techniques in economics.