Differential equations with advanced and delayed time arguments may arise in the optimality conditions of simple growth models with delays. Models with investment gestation lags (time-to-build), consumption gestation lags (habit formation) or learning by using lie in this category. In this...

In an optimal growth model with a time-to-build delay, the feasibility condition is a delayed-differential equation, and the Euler-type condition is an advanced-differential equation. As in Kalecki's theory of business cycles, the delayed nature of the feasibility constraint naturally induces...