Mathematical Analysis of Income Per Capita in the United Kingdom

Industrial Revolution did not boost economic growth and the growth of population even in the United Kingdom, the centre of this revolution. On the contrary, from around 1850, economic growth and the growth of population started to be diverted to slower trajectories. The new trend describing the growth of income per capita (Gross Domestic Product per capita, i.e. GDP/cap) is now analysed using Maddison’s data. Two numerical solutions and two analytical solutions of the differential equation describing the growth rate of income per capita are presented. It is demonstrated yet again that even strong fluctuations in the growth rate do not change the shape of growth trajectories. Thus, contrary to the common misconception, even strong fluctuations in the growth rate cannot be used as the evidence of the existence of Malthusian stagnation because they do not change the mechanism of growth. Such strong fluctuations can at best produce only small and negligible ripples in growth trajectories. Our analysis shows also that the current growth of income per capita in the UK follows an unsustainable trajectory.