To show how the estimate of 5 per cent involves a linear approximation, we expand theexpression for real GDP at the end of the year.(?+±?)(²+±²)=?²+?±²+²±?+±?±²Dividing by?²(?+±?)(²+±²)?²=1+±²²+±??+±?±²?²The growth rate of nominal GDP is(?+±?)(²+±²)−?²?²=(?+±?)(²+±²)?²−1=±²²+±?±?+±?±²?²= Growth rate of output+ Inﬂation rate+ Error termFor small changes, the error term±?±²/?²is insigni±cant, and we can approximate thegrowth rate of output according to the sumGrowth rate of nominal GDP = Growth rate of output + Inﬂation rateThis is alinearapproximation since it approximates the function (?+±?)(²+±²)bythe linear function?²+?±²+²±?. In e²ect, we are evaluating the change output atthe old prices, and the change in prices at the old output, and ignoring in interaction
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