What is the most important determinant of a nation's economic growth rate?
Economies evolve and develop on the back of their productive capacity, which is in turn dependent on the available physical and human capital, technology and natural resources. The optimal and efficient utilization of these resources towards production, is what determines a nation's growth rate.
If the income elasticity of demand of good X is less than one, good X is a normal good or an inferior good?
Inferior good. As income rises, demand decreases.
Assume under autarky, the domestic price of good X in country A is lower than the world price of good X. If country A were to open its economy to trade, will it be an exporter or an importer of good X?
Exporter. Country A enjoys a comparative advantage over the rest of the world in producing good X. We know that because the domestic price of good X in country A is lower than the world price.