How the law helped China progress
All developed countries in the world have effective birth control policies. Conversely, those with loose birth controls are often developing countries.
The one-child policy was introduced in 1979 to curb rampant population growth. Without birth control, China would still have been a recipient of world food aid, whereas today it is a donor.
Currently there are 1.3 billion people on the mainland.
A runaway population growth puts undue strain on resources, such as water, the environment, education, health and welfare. Starvation, drought, a lack of land and services can lead to social upheaval. A government unable to provide for its people lacks resources to pursue other ideals like science.
Parents with only one child will put all their resources into raising that child well, so it will enjoy a higher standard of living.