Answer:
1. All else equal, countries with more natural resources have a higher GDP per capita than those with few natural resources. - True
All else being equal (ceteris paribus), if a country is endowed with more natural resources, it will have a higher GDP per capita than a country with less natural resources, because it will be able to trade and transform those natural resources for a lower cost, allowing it to produce more goods and services.
2. Over the past two hundred years, improvements in productivity have offset lost productivity reduction due to less land being available. - True
This statement is true. In the modern-era, thanks to the green revolution, and other technological improvements, more food can be produced in less land. Many analysts coincide that if the green revolution had not come about, humanity would have been subject to permanent famine.
3. The key to prosperity in the 20th century is an economy rich in natural resources. - False
The key to prosperity in the 20th century is simply producing more goods and services, and human capital has been seen as a more important factor for this than natural resources. For example, countries that are poor in natural resources and are rich such as Japan and South Korea, are so because they have very well-educated populations that produce high quality goods and services.
4. Human and physical capital are only beneficial to an economy when there is an abundance of natural resources in the economy. - False
Human and physical capital can benefit an economy even in the absence of natural resources, because natural resources can be imported. Again, the example of Japan works because the island nation is poor in natural resources, but rich in human capital, and not so deprived of physical capital, and has managed to become a developed nation by highly compex finished goods for natural resources.