Time-to-build and cycles.

*(English)*Zbl 1016.91068Summary: We analyze the dynamics of a simple growth model in which production occurs with a delay while new capital is installed (time-to-build). The time-to-build technology is shown to yield a system of functional (delay) differential equations with a unique steady state. We demonstrate that the steady state, though typically a saddle, may exhibit Hopf cycles. Furthermore, the optimal path to the steady state is oscillatory. A counter-example to the claim that ‘models with a time-to-build technology are not intrinsically oscillatory’ is provided. We also provide a primer on the central technical apparatus – the mathematics of functional differential equations.

##### MSC:

91B38 | Production theory, theory of the firm |

91B62 | Economic growth models |

34K60 | Qualitative investigation and simulation of models involving functional-differential equations |

90C90 | Applications of mathematical programming |

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\textit{P. K. Asea} and \textit{P. J. Zak}, J. Econ. Dyn. Control 23, No. 8, 1155--1174 (1999; Zbl 1016.91068)

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