Q.5 Economic growth (12 points) Consider two countries, Alpha and Beta. 0 In the last 30 years, the average annual growth rate of the real per capita GDP was 1% in Alpha and 2.5% in Beta. 0 In the current year, the real per capita GDP is $10,000 in Alpha and $B in Beta. If the two countries continue to grow at their 30-year-average annual income growth rates given above, then Alpha and Beta would get equal in terms of their real per capita GDP 25 years from now. (a) (3 points) Solve for B, i.e., Beta's real per capita GDP in the current year. (b) (7 points) (i) (2 points) What is the \"catch-up prediction\" of the economic growth model? (ii) (3 points) Explain whether the equalization in real per capita GDPs between Alpha and Beta is consistent with the \"catch-up\" predicted by the growth model. (iii) (2 points) Without the aid of diagrams, explain why the "catch-up prediction" may not hold in reality. (c) (2 points) According to the Rule of 70, how many years would it take for Beta to be twice as rich as Alpha (in terms of real per capita GDP)