Cyclical Fluctuations in Continuous Time Dynamic Optimization Models: Survey of General Theory and an Application to Dynamic Limit Pricing

Abstract

In this chapter, we reconsider the analytical results on the existence of cyclical fluctuations in continuous time dynamic optimization models with two state variables and their applications to dynamic economic theory. In the first part, we survey the useful analytical results which were obtained by Dockner and Feichtinger (J Econom 53–1:31–50, 1991), Liu (J Math Anal Appl 182:250–256, 1994) and Asada and Yoshida (Chaos, Solitons and Fractals 18:525–536, 2003) on the general theory of cyclical fluctuations in continuous time dynamic optimizing and non-optimizing models. In the second part, we provide an application of these analytical results to a particular continuous time dynamic optimizing economic model, that is, a model of dynamic limit pricing with two state variables, which is an extension of Gaskins (J Econom Theor 3:306–322, 1971) prototype model.