The long-run evolution of per-capita income exhibits a structural break often associated with the Industrial Revolution. We follow Mokyr (2002) and embed the idea that this structural break reflects a regime switch in the evolution of technological knowledge into a dynamic framework, using Airy differential equations to describe this evolution. We show that under a non-monotonous income-population equation, the economy evolves from a Malthusian to a Post-Malthusian Regime, with rising per-capita income and a growing population. The switch is brought about by an acceleration in the growth of technological knowledge. The demographic transition marks the switch into the Modern Growth Regime, with higher levels of per-capita income and declining population growth.