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Topic_0_-_Essential_Math_for_ECON2003

# Topic_0_-_Essential_Math_for_ECON2003 - Essential...

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1 Essential Mathematics for ECON2003 INDICES 1. a b a b x x x 2. a a b b x x x 3. ( ) a b ab x x 4. 1 a a x x similarly 1 a a x x 5. 1 n n x x 6. m n m n x x 7. ( ) a a a xy x y 8. a a a x x y y SURDS 1. xy x y 2. x x y y 3. n n n x x y y

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2 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 x y y 3. log( ) log a x a x 4. 1 1 1 1 log( ) log log t t t t t t t t x x x x x x x x 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: 1 1 t t t t t x x x x x When we are interested in the growth of a combination of variables, we can
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