Malthusian Trap and Endogenous Population

In this paper, we develop a model in which human being constitutes the sole asset and is a production factor which can be combined with a fixed factor, say land, to produce a homogeneous commodity. Saving, so to speak, can only be made through having children, the number of which is an endogenous decision to the household. We show that the economy will run into the Malthusian equilibrium with high population and subsistent per capita consumption only when the initial population is large enough. Otherwise, the steady state equilibrium with lower population and higher per capita consumption than the Malthusian outcome will prevail. Also, we have identified the persistent Malthusian equilibrium--or Malthusian trap--and demonstrate that the economy can escape from this unappealing long-run situation either through a suitable technological shift or an appropriate subsidy of the child-rearing cost. Our results are then extended to the stochastic framework where the time rate of population change undergoes a process of Brownian motion. The probability distribution of the steady state is well determined, and saving via the number of offspring, as with the standard capital model, incorporates a precautionary component