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Time-to-build and cycles. (English) Zbl 1016.91068
Summary: 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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