Airy Growth – Was the Take-off Inevitable?

We study the effect of technological knowledge on per-capita income and population in a Malthusian economy. Airy differential equations describe the evolution of knowledge. Consequently, the impact of technological knowledge on aggregate output is feeble before and strong after the Industrial Revolution. The economy exposed to Airy growth of knowledge evolves from a Malthusian regime into a Post-Malthusian phase with rising per-capita income and a growing population. The latter follows the Industrial Revolution, the Malthusian population hypothesis is still in place, and per-capita income grows. This phase is replaced by a modern growth regime when growth rates of per-capita income rise further and population growth declines – giving rise to the demographic transition.