The project will analyze the effect of the One Child Policy on the population of China. The One Child Policy was implemented to prevent social and economic problems of rapid population growth by barring most families from having more than one child. Since it came up into effect three decades ago, the policy has reduced the Chinese population by at least 250 million. However, recent studies have shown that the One Child Policy may have been the cause of a worsening demographic problem with an aging population and a dwindling work force. TIME magazine reported that there were six adults of working age for every retiree. The ratio is expected to continue to decline. The National Committee of Ageing estimated that 52 percent of the work force in 2053 will have to support one-third of the Chinese seniors as well as 16 percent of the children.

In order to investigate the consequences of the policy, we will predict and compare the long term population of China with and without the One Child Policy. We will first construct a transition matrix that models the current population growth of different age groups in China by using current birth rate and mortality rate. Three equations will used to indicate the number of minors(0-18), adults(18-65), and the elderly(65+). Then we will construct a transition matrix of the Chinese population without the effects of the One Child Policy. The transition matrix without the effect of the One Child Policy will be applied to the population of when the policy was first implemented. We will assume that all births prevented will be added to the minors age group and the birth rate and mortality rate are constant. Furthermore, we will assume that every adult will be in the workforce for later analysis. With the given assumptions, the eigenvalues of the matrices will show us the ratio of the age groups in both scenarios.

The long term population growth of both cases can be studied from the data collected. We are mostly interested in the ratio between the working force and elderly. We will compare our derived ratio and the ratio projected by experts. This difference will be taken account and show us the validity of our data when studying the projected ratio of the working force and the elderly in the case where the One Child Policy was not implemented. The result of this study will show us whether removing the One Child Policy would alleviate the burden of future generations.

Citation:

Republic of China. Information Office of the State Council Of the People's Republic of China. *Family Planning in China*. Beijing: , 1995. Web. <http://www.fmprc.gov.cn/ce/celt/eng/zt/zfbps/t125241.htm>.

A BRIEF HISTORY OF-China's One-Child Policy

<http://content.time.com/time/world/article/0,8599,1912861,00.html>