Discuss the convergence hypothesis and do you believe that in the long run there will be a narrowing of the differences in real GDP per capita in all countries.

I believe that there are people who want to create a one world government. And there aim is to bring all economies to the same level. This is what is happening in our country the USA. It is a deliberate attempt to bring us down.

Explain why savings must equal investment spending. What government policy could be used to increase the national savings rate and how this would impact investment spending?

With respect to the convergence hypothesis:

http://econc10.bu.edu/economic_systems/Lecture_notes/Introduction/intro_types_convergence_lg.htm

with respect to S=I,
GNP is the value of everything we produce GNP=C+I. (Ignore government expenditures or net exports for now). GNP is also the value income of a country. With income, you can either consume it or save it. So, GNP=C+S.
Thus, you have C+I=GNP=C+S. Ergo, I=S.

The convergence hypothesis suggests that in the long run, there will be a narrowing of the differences in real GDP per capita across countries. It is based on the idea that poor countries have the potential to grow at a faster pace than richer countries, leading to catch-up effects and ultimately convergence in living standards.

There are several factors that support the convergence hypothesis. Firstly, poorer countries may have more opportunities for economic growth due to their lower initial levels of development. They can adopt technologies and practices already used by more developed countries, which can lead to faster productivity growth. Additionally, poorer countries may also benefit from foreign direct investment and technological spillovers from more advanced economies.

Furthermore, the convergence hypothesis suggests that capital should flow from richer to poorer countries. In theory, this should equalize returns on investment across countries, as investors seek higher returns in countries with lower levels of capital. This capital flow can facilitate investment, enhance productivity, and contribute to economic growth in poorer countries.

However, it is important to note that the convergence hypothesis does not guarantee convergence in real GDP per capita across all countries. There are several challenges and factors that can hinder convergence. Some of these factors include differences in institutional quality, governance, political stability, access to education, health care, and infrastructure. These factors can significantly impact a country's ability to take advantage of catch-up effects and achieve sustained economic growth.

Moreover, there are instances where countries have experienced growth divergence rather than convergence. This can be attributed to various reasons, such as economic policies that hinder growth, income inequality, natural disasters, conflicts, and global economic shocks.

In conclusion, while the convergence hypothesis provides a theoretical framework for the narrowing of GDP per capita differences across countries in the long run, it is not a guaranteed outcome. It relies on various factors and conditions, and the reality is that some countries may experience convergence while others may not.