Non-Linear Dynamics and Chaos in Optimal Growth: A Constructive Exposition

In the recent literature, it has been demonstrated that optimal capital accumulation may be chaotic; see Boldrin and Montrucchio (1986) , and Deneckere and Pelikan (1986). 1 This finding indicates, as Scheinkman (1990) discusses, that the deterministic equilibrium model of a dynamic economy may explain various complex dynamic behaviors of economic variables, and, in fact, search for such explanations has already begun (see Brock, 1986, and Scheinkman and LeBaron, 1989, for example) . In the existing literature, however, not much has yet been revealed with respect to the circumstances under which optimal accumulation exhibits complex non-linear dynamics. In particular, it has not yet been known whether or not chaotic optimal accumulation may appear in the case in which future utilities are discounted not so strongly.2