We find that by endogenizing the population growth rate, a growth model under the productive consumption hypothesis is more tractable than models in previous studies and has interesting implications for population dynamics. In the zero-saving phase, multiple saddle point stable steady states may exist, and the population growth rate may rise or decline along a transition path. In the positive-saving phase, such a steady state may exist uniquely, and the population growth rate may decline. With phase switching, the population growth rate may follow an inverted U-shaped curve. Human development aid may help an economy escape from an underdevelopment trap.
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