โ Scribed by Patrick K Asea; Paul J Zak
No coin nor oath required. For personal study only.
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) di!erential 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 counterexample 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 di!erential equations.
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