The Goodwin growth cycle model as solution to a variational problem

Abstract

R. M. Goodwin modelled economic cycles of income and employment with dynamical features formally similar to the predator-prey model of V. Volterra. The present model generates similar dynamics. It features antagonistic preferences of workers and capitalists as well as economic fluctuations as proxy for associated costs. On this basis it presents optimality conditions in a-temporal and inter-temporal context. Formal aspects of the present version of predator-prey dynamics are discussed by P. A. Samuelson in more general terms. But whilst Samuelson saw no economic contents in his variational dynamic set-up, the present contribution claims plausibility for income-employment cycles which are derived in a model of class conflict with antagonistic target functions of the two opposing actors.