Exam 4: Long-Run Economic Growth

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As China moves along the curve below in a rightward direction, three factors kick in:
i. Diminishing returns.
ii. Depreciation on an ever-larger capital stock takes up a larger share of national savings.
iii. Each new birth requires ever more capital also absorbing more savings.
These factors, then, tend to slow an economy in terms of output. They are related to a key constraint in any economy: the growth of a key input, the labor force. Short of technological progress, labor force growth will act as a bottleneck which slows GDP growth to the same rate as the assumed rate of growth of the population.

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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).

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Here are some things to consider:
$\bullet$ China's labor force growth rate is currently projected to turn negative around 2020 and then relatively quickly move into negative growth of about -5 percent.
$\bullet$ Assume the labor force constitutes people between 18 and 60 years old.
$\bullet$ A bit less than half the labor force lives in urban areas.
$\bullet$ For a population to stabilize (neither gain nor lose) we need about 2.1 births per female.
The first implication is that since the rules apply only to urban residents, the overall labor force birth rate would be .5 x 2 + .5 x 1 = 1.5 kids per labor force urban + rural. Population will still shrink since 1.5 < 2.1. Meanwhile, it would take eighteen years for the new extra kids to enter the labor force (2033 if we start in 2015). So between 2020 and 2033 the same profile will hold as described in the first bullet. After 2033, the labor force growth would still be negative just less so (somewhere between 0 and -5 percent).