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Lecture 9

Econ 105 Lecture 9 Feb 4th.doc

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ECON 105
Brian Krauth

Econ 105 Lecture 9 Feb 4th Chapter 7: Production and Growth Measurement of growth rates: -Suppose we have variable X measured at different points in time. (also known as a time series) -X(t) = value of X and time t -ex. X = GDP -X(2006) = GDP in 2006 -X(2007) = GDP in 2007 -etc. ***** where "t" is involved, its just X (sub t) -The percentage change or growth rate of X is: -g = (X(t+1) - X(t)) / X(t) ->measured in proportions = [(X(t+1) - X(t)) / X(t)] x 100% ->measured in percentage -Now, if we do a little algebra: -gX(t) = X(t+1) - X(t) gX(t) + X(t) = X(t+1) X(t+1) = X(t) x (1+g) ........................................................ (ask jeanne for notes) - => (X(t+k) - X(t)) / X(t) = ((1+g)^k) - 1 Compounding: Supposed GDP grows by 5% a year for 10 years. Does it increase by 50%? No. It increases by: -((1+0.05)^10) - 1 =(aprox.) 63% The log approximation: Let X(t), Y(t), and Z(t) be three time series variables. Growth rates g(X), g(Y), g(Z) Then the following approximations hold: -(1) Z(t) =
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