How to Sow and Reap as You Go: a Simple Model of Cyclical Endogenous Growth

In this paper, we present a simple endogenous growth model that allows for the occurrence of innovations that can develop into General Purpose Technologies (GPTs), which are the result of basic R&D. The model incorporates the main features of the Romer (1990) model and the Aghion and Howitt (1992) model by using multi-level Ethier functions on the one hand, and Poisson processes to describe the arrival of innovations produced by performing basic R&D and applied R&D. Through basic R&D the core of a potentially new GPT enters the economic system. This core offers the possibility for further expansion of the potential GPT through applied R&D by adding peripherals to this core. The characteristics of the new potential GPT that is represented by the core are randomly distributed. These characteristics include intrinsic profitability, scope for expansion, as well as R&D opportunities and efficiency of the corresponding applied R&D process. By using some illustrative simulations with the model, we show that the arrival of a successful GPT does indeed bring about a reallocation of R&D activities towards applied R&D, thus postponing the moment of arrival of the next GPT. Meanwhile, applied R&D raises the productivity of the GPT as a whole. But the profitability of finding the next/marginal peripheral falls in the process. This fall in marginal profits diminishes the incentives to engage in further applied R&D and increases the incentives to move into basic R&D activities again. Thus, we obtain a cyclical pattern in output growth that is not only partly driven by the arrival of the new potential GPTs but also by the continuing development of existing GPTs in the absence of the arrival of new ones. In periods that do not give rise to the arrival of new successful GPTs we find instances of alternating expansions of existing GPTs that have the character of a GPT-race.