Using the standard Solow framework, explain how China's one child policy of the past affects per capita incomes in the short run and the long run. Explain how it will affect economic growth in the long run.

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The Answer is In fact the one child policy has had two related effects: slower labor force growth and an aging population. Both act as constraints to economic growth in the long run in a Solow framework where labor force growth determines steady-state (long run) growth.
Recall, in the steady state:

\Delta Y / Y=\eta=\Delta K / K

where η is population growth. The aging population has another effect-it increases the dependency ratio which in turn is a force that would lower national savings. This will also have a negative impact on long run per capita income. In the short run and the long run, the one child policy shifts the uses line down and to the right (see below)-this has the effect of increasing per capita income. Since the uses line is everywhere lower than before: Sources (Savings) - Uses (Pop. growth + Depreciation) is higher in the short run implying faster accumulation of capital and higher short run per capita incomes in the transition (in the earlier years of the short run).
$In fact the one child policy has had two related effects: slower labor force growth and an aging population. Both act as constraints to economic growth in the long run in a Solow framework where labor force growth determines steady-state (long run) growth. Recall, in the steady state: \Delta Y / Y=\eta=\Delta K / K where η is population growth. The aging population has another effect-it increases the dependency ratio which in turn is a force that would lower national savings. This will also have a negative impact on long run per capita income. In the short run and the long run, the one child policy shifts the uses line down and to the right (see below)-this has the effect of increasing per capita income. Since the uses line is everywhere lower than before: Sources (Savings) - Uses (Pop. growth + Depreciation) is higher in the short run implying faster accumulation of capital and higher short run per capita incomes in the transition (in the earlier years of the short run).$

Using the Standard Solow Framework, Explain How China's One Child