At the beginning of 1950, John moved from country A to country B. That year, income per capita was 75 in country A and 100 in country B. John died at the end of 2000. Although country A was poorer than country B when John emigrated, country A had a better growth performance. Specifically, between 1950 and2000 income per capita grew at 2 percent per year in country A and at 1 percent per year in country B. Taking the sum of all incomes between 1950 and 2000 as a measure of well being, did John commit a mistake by moving from A to B in 1950? Show your work. Hint: You might find useful the relationship Y + Y (1 + x) + Y (1 + x)2 + . . . + Y (1 + x)T = Y 1 + x (1 + x)T 1 , xx for T = 0, 1, 2