HomeAs3 - Fall 2010 - Answer Key

# HomeAs3 - Fall 2010 - Answer Key - Econ 3T03 Home...

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Econ 3T03 Fall 2010 Home Assignment #3: Answer Key 1. (6 points) Consider country A with a growth rate of 6% and country B with a growth rate of 12%. Both countries have the same initial national income of \$1,000,000. What will be the national income in each country in 5 years? Will it be correct to say that country B will double its income 2 times faster than country A? If no, then what is the correct answer? Answer: Note that Y(t+1)=(1+r)Y(t), and Y(t+2)=(1+r)Y(t+1)=(1+r) 2 Y(t), where r is the growth rate. Using this logic again and again, it can be shown that the national income in A years can be calculated as Y(t+A)=(1+r) A Y(t). Thus, in 5 years Country A: Y A (t+5)=(1+r A ) 5 Y(t)=(1+0.06) 5 1,000,000=1,338,225.56. Country A: Y B (t+5)=(1+r B ) 5 Y(t)=(1+0.12) 5 1,000,000=1,762,341.68. Although the growth rate of country B is twice as large as that in country A, the national
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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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