This paper describes a two-sector demo-economic model (agricultural and non-agricultural sectors) applied to Europe and spanning the period from the neolithic agricultural revolution to the Industrial Revolution. The model describes the "incessant contest" between population growth and food production. As long as per capita agricultural output is above a critical minimum, the population is assumed to grow at a constant rate. When this output drops below the minimum, the population is subjected to random mortality "shocks" which lower the population until the production grows above the minimum. Society is thus in a "Malthusian trap". The average magnitude of the mortality crises is assumed to decrease as capital increases, which captures an increased "resistance" that comes with increased knowledge and technology. The slow accumulation of capital thus diminishes the severity of the mortality shocks; as a result both the population of the non-agricultural sector and capital grow sufficiently to bring about a permanent escape from the Malthusian trap, i.e. the Industrial Revolution.