Quiz 4 Examples
1. Suppose the ratio of China’s GDP to U.S. GDP is rising 4% a year.
How long will it
take to double?
Use the “rule of 70,” or rt=0.70, where r is a rate of growth and t is the
number of years required to double.
Then r = 4% = 0.04 and t = 0.70/0.04 = 18.5 years.
The rule of 70 is an approximation from Xt/X0 = e
rt
, and e
0.693
= 2.
The text uses a looser approximation, the “rule of 72,” from banking.
It’s easier to
apply to monthly data, since 72 is divisible by 12.
2. Suppose the nominal debt grows 6% a year and nominal GDP grows 2% a year.
How
long will it take the ratio of the debt to GDP to double?
Let z = x/y.
Then for low rates of growth, z* = x*  y* is an okay approximation,
where * indicates rate of growth.
Let ratio = debt/GDP.
Then ratio* = debt*  GDP* =
6%  2% = 4%.
If something is growing at 4% a year, it will double in 18.5 years, by the
rule of 70.
3. If India’s GDP quadruples in 24 years, what is its rate of growth?
To quadruple, something had to double two times.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '05
 Denslow
 Macroeconomics, Deficit, Inflation, Supply And Demand, Interest, Public Finance, total government deficit

Click to edit the document details