Optimal Chaos, Nonlinearity and Feasibility Conditions

This chapter presents a new characterization of chaotic optimal capital accumulation by which a chaotic optimal path can be constructed in a simple systematic manner. In the existing literature, it has been demonstrated that optimal capital accumulation may be chaotic in the sense of Li and Yorke (1975); see Boldrin and Montrucchio (1986b) and Deneckere and Pelikan (1986).1 As Scheinkman’s survey (1990) discusses, this finding indicates that the deterministic equilibrium model of a dynamic economy may explain various complex dynamic behaviors of economic variables. And, in fact, the search for such explanations has already begun.2 In the existing literature, however, not much as been revealed with respect to the circumstances under which optimal accumulation exhibits complex nonlinear dynamics.3