Time-to-build and cycles

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 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 differential equations. (C) 1999 Elsevier Science B.V. All rights reserved. JEL classification: E32; C61.