Haunschmied, J. (2003). Discontinuous optimal policy rules : accumulate or exploit? - starting from the same initial conditions both can be optimal [Dissertation, Technische Universität Wien]. reposiTUm. https://resolver.obvsg.at/urn:nbn:at:at-ubtuw:1-9075
E105 - Institut für Ökonometrie, Operations Research und Systemtheorie
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Date (published):
2003
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Number of Pages:
71
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Abstract:
Let us assume that a single decision maker controls a deterministic dynamic system to optimize a measured output of this system. For a chosen control path the resulting initial value problem has a unique solution, but it may happen, that for given initial values different optimal controls lead to different long run outcomes. The indeterminacy arises here from the possibility to choose different optimal controls. In this work I deal with initial states, at which such discontinous policy rules arise. In the studied capital accumulation model a DNS-curve separates two steady states, whereas in the studied technology accumulation model a DNS-curve separates an optimal steady state and an optimal limit cycle. Especially, a threshold behavior separating a steady state and a limit cycle is an innovative feature in an economic model. In both models, the existence of DNS-curves are not only the features of the investigated models, but also their occurrence and shapes can be suggestively and economically interpreted. Other interesting features are a sub-critical Hopf-bifurcation and a limit point bifurcation, where a stable and an unstable limit cycle coincide and disappear. Finally, I describe the used numerical algorithms in order to compute the DNS-sets.