In China, why may a lower birth rate lead to slower growth in real GDP per capita? Why might high levels of spending on investment in China lead to high rates of growth in the short run but not in the long run?

When considering the economics of a lower birth rate, it is essential to understand its potential impact on a country's growth trajectory. A declining birth rate can substantially influence the labor market, which is a critical component of any economy. Fewer births over time result in a smaller younger population, ultimately leading to a reduced workforce in the future.
As the population ages, the proportion of retirees grows relative to the number of working-age individuals. With a shrinking workforce, the economy may struggle with fewer workers available to produce goods and services, and to innovate. Moreover, fewer workers also mean potentially less tax revenue and higher public spending on healthcare and pensions, straining government budgets.
This demographic shift leads to changes in consumption patterns and might diminish the demand for certain goods and services. Consequently, it could slow down the growth in real GDP per capita because with fewer people contributing to the economy and a simultaneous increase in dependency ratio, the productivity per capita may decline.

Investment spending is a powerful engine for economic growth, particularly in the short run. When businesses invest in new capital goods, such as machinery, buildings, or technology, it often leads to the creation of new jobs, boosts productivity, and stimulates demand within the economy. This injection of capital usually results in an increase in output and, as corporations expand to accommodate new capacities, a rise in real GDP ensues.
However, investment is not just about the quantity but also the quality. Effective investment spending that focuses on productive capacity and technological advancement can foster sustainable long-term growth. Conversely, if investments are made into less productive areas or become excessive, it may lead to inefficiencies or asset bubbles—situations where the actual economic value is not reflective of the investment made. In the context of education, it's crucial to underline that the return on investment spending is contingent on wise allocation and the capacity of the economy to absorb and efficiently utilize the investment.

Economic growth can be considered in two different timelines: the short run and the long run. In the short run, growth is mainly driven by increases in demand and utilization of existing resources. It is during this period that investments and spending can quickly ramp up production and GDP. The effects of new policies or changes in spending behaviors are more visible and tend to have immediate impacts on the economy. However, this rapid expansion is not always sustainable.
In the long run, growth is more about the expansion of an economy's productive potential. This is achieved through technological innovation, investments in human capital, and increases in efficiency and productivity. Here, economic principles such as the law of diminishing returns come into play, indicating that adding more of one input, such as labor or capital, while holding others constant will eventually yield lower incremental outputs. Thus, for sustainable long-term growth, economies need to ensure that investments are not merely increasing the amount of capital but are also improving the quality and productivity of that capital.