Macroeconomics Exam Review 199

Macroeconomics Exam Review 199 - Solutions for Foundations...

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