A growth model with endogenous technological revolutions and cycles

We propose a new approach to deal with continuous time dynamic model with discontinuity, by which we incorporate gradual innovations and technological leaps, as well as endogenous cycles and long-run growth into one framework. We show that the optimal or equilibrium growth path is a cyclic growth path (CGP) and we develop the mathematical technique to prove the existence and uniqueness of the solution. We provide two basic setups to include the technological leaps in the R&D sector or goods production sector respectively. The growth paths under these two setups show different cyclic features and abundant economic dynamics. Our approach can be easily utilized to evaluate the optimality of the timing of the technological revolution. In the decentralized economy, the technological breakthrough is exogenous to families and always happens too late. The social planner’s problem clarifies two fundamental effects on the optimal growth path, i.e., the “dividend effect” and the “swot-up effect”, induced by discontinuous technological change. Our framework can also serve as a workhorse to address dynamic economic problems with discontinuity.