Unformatted text preview: income in country B will not be exactly doubled 2 times faster. To see this, note that to calculate the number of years needed to double one’s income, you need to solve the equation Y(t+x)= (1+r) x Y(t) = 2Y(t) or (1+r) x = 2. Taking logs of both parts, you get x*ln(1+r) = ln(2), so x = ln(2)/ln(1+r). Then, in country A x = ln(2)/ln(1+0.06)=11.9, in country B t = ln(2)/ln(1+0.12)=6.12. And 11.9/6.12 = 1.94. So country B will double its income approximately 2 times faster than country A, but not exactly 2 times faster. (Also, “rule of 72” is just an approximation of the method above, so it cannot be used to give the precise answers.) 2. (4 points) Think of two reasons why a country with a lower ratio of capital to labor might grow faster than a country with a higher ratio, and two reasons why it might grow slower....
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 Fall '10
 demidova
 Economics, Approximation, National Income, Household income in the United States

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