Final answer:
Based on the economic growth model and convergence theory, the growth rate of real GDP per capita will likely be higher in Alpha ($6,000) than Beta ($9,000), as Alpha has more potential for catch-up growth.
Step-by-step explanation:
Based on the economic growth model, economies with lower initial levels of real GDP per capita have greater potential to grow faster than those with higher initial levels of GDP per capita. This concept, known as convergence theory, suggests that poorer economies tend to grow at faster rates than richer ones because they can adopt existing technologies and best practices from wealthier countries. Convergence theory implies that catch-up growth is more rapid for economies starting at a lower base.
In the case of Alpha and Beta, given that Alpha has a real GDP per capita of $6,000 and Beta has $9,000, the economic growth model would predict that the growth rate of real GDP per capita will likely be higher in Alpha than in Beta because Alpha has more room to catch up. Therefore, the answer is 'b) The growth rate of real GDP per capita will be higher in Alpha than it is in Beta.' This pattern of convergence is supported by empirical evidence, though it should be noted that it is not an absolute rule and can be influenced by various factors including government policies, institutional frameworks, and geopolitical conditions.