On Demographic Transition, Structural Change, and Economic Growth and Stagnation

The paper analyzes an economy with an agrarian and an industrial sector. Demand is determined by Engel's Law. Population growth follows a non--linear income dependent path according to the theory of demographic transition. In case of decreasing returns to scale in the agrarian sector the existence of a stable low--income equilibrium with high population growth can be shown. If this equilibrium is globally unstable, the system evolves towards a steady--state of perpetual economic growth and low population growth. The path of demographic transition coincides with a path of structural change from an economy specialized in agriculture to a fully industrialized economy. The introduction of an income dependent savings rate allows the interpretation of the low--income equilibrium as a limit cycle and, therefore, the explanation of high fluctuations in population growth and per capita income in least developed economies.