The present paper discusses the long-run effects of two interdependent relations between economic and population growth. According to a frequently used formulation of the population-push hypothesis, learning-by-doing effects in production lead to increasing returns to scale and, therefore, to a positive correlation between economic and population growth. In accordance to the theory of demographic transition the population growth rate initially increases with rising income levels and then declines. Regarding this relationship, the existence and stability of a low-income equilibrium and a high-income equilibrium will be shown in a neoclassical growth model. Under plausible conditions a demo-economic transition from the first to the second steady-state takes place. The result yields a meaningful interpretation of the population-push hypothesis, which is consistent with the empirical findings on the correlation between economic and population growth.