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1
Essential Mathematics for ECON2003
INDICES
1.
a
b
a b
x x
x
2.
a
ab
b
x
x
x
3.
()
a b
ab
xx
4.
1
a
a
x
x
similarly
1
a
a
x
x
5.
1
n
n
6.
m
n
m
n
7.
a
a
a
xy
x y
8.
a
a
a
yy
SURDS
1.
xy
x y
2.
y
y
3.
n
n
n
y
y
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LOGARITHMS
Economists often find it more convenient to use natural logarithms to discuss
growth
rates.
Logarithms,
written
either
as
log
or
ln
in
this
course,
are
transformations of variables. The definition of the natural logarithm of a variable
ln(x) is the log to the base e = 2.71828.
.. In other words,
ln( )
( )
e
x
log x
.
There is nothing very mysterious about logarithms; they are simply a convenient
way of rescaling data series. A logarithm is just a function, like others we use in
economics, but with some very useful properties:
1.
log(
)
log
log
xy
x
y
2.
log( )
log
log
x
xy
y
3.
log(
)
log
a
x
a
x
4.
11
log(
)
log
log
t
t
t
t
t
t
tt
x
x
x
x
x
x
xx
This says that the difference in the log of a variable is approximately
equal to the percentage change in that variable.
GROWTH RATES
The growth of a variable is represented by the percentage change in that variable:
t
t
t
x
x
x
When we are interested in the growth of a combination of variables, we can
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This note was uploaded on 11/12/2011 for the course ECON 2003 taught by Professor Macoeconomics2 during the Spring '10 term at University of the West Indies at Mona.
 Spring '10
 MacoEconomics2

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