Population density and economic development

We describe formally the relationship between population density and per capita income along the two growth regimes put forward by KUZNETS (1960), BOSERUP (1965) and TAMURA (2002). We consider a spatial economy where an undifferentiated consumer good is produced by a continuum of competitive agents. Each agent requires one unit of a capital good to produce the final good and the two goods are assumed to be perfect substitutes in production. Under the first growth regime (called “classical” or “Malthusian”), each agent self-produces the capital good by shifting resources that would otherwise produce one unit of the final good. This economy shows marginal decreasing returns of labour. Population growth brings about congestion and the elasticity of output per worker (and income per capita) is negative. A structural change takes place following a sufficient increase in population density and decrease in transport costs. Then, the supply of capital goods is outsourced to a specialized industry, operating in spatial monopolistic competition in line with SALOP (1979). Under this “modern” growth regime, the specialization of the capital goods production is a source of increasing returns in the aggregate economy. The elasticity of per capita income with respect to population density becomes positive just after the structural transition, but this effect may not persist in the long run. If the outsourcing of capital goods is matched by a rising importance in final production of activities which are not land-based, then aggregate increasing returns can be sustained in the long run. Otherwise, the positive sign of elasticity will be transitory and a further increase in population density will revert the economy to a situation where the use of increasing amounts of labour with non-reproducible resources determines mainly a congestion effect.