Innovation, Diffusion and the Distribution of Income in a Malthusian Economy

Between 5000 BCE and 1800, the population of the world grew 120-fold despite constraints on the total amount of land available for production. This paper develops a model linking population growth to increasing productivity driven by random innovation and diffusion. People are endowed with a set of skills obtained from their parents or neighbours, but those skills are imperfectly applied during their lifetimes. The resulting variation in productivity leads to a distribution of income and to a process of diffusion whereby high-income activities spread at the expense of low-income activities. An analytic formula is derived for the steady-state distribution of income. The model predicts that the rate of growth of population approaches an asymptotic limit, whereupon there are no scale effects. The model also predicts that if the rate of diffusion of knowledge is increased, the growth rate will increase.