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midterm_ans_w09

midterm_ans_w09 - Macroeconomics Econ 202 Midterm Answers...

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Macroeconomics, Econ 202, Midterm: Answers February 12, 2009 Instructions. Answer all 4 questions . 1. Suppose data on output and prices are available for years 1 and 2. Using year 1 prices, GDP is 100 in year 1 and 110 in year 2, a 10% increase. Suppose using year 2 prices, GDP in year 1 was 5% lower than in year 2 GDP. Setting year 1 real GDP at 100, what is the chain-weighted value of year 2 real GDP? The expression for the chain-weighted index would take an average of the growth rates obtained using the two di/erent sets of prices. This would be p (1 + 0 : 1)(1 + 0 : 05) ° 1 = 0 : 0747 so real chain-weighted GDP in year 2 would be 107 : 47 . However, since you were not required to have a calculator, recall that if p (1 + x )(1 + y ) = 1 + z , for some unknown z , then (1 + x )(1 + y ) = 1 + x + y + xy = 1 + 2 z + z 2 , or x + y + xy = 2 z + z 2 . But to °rst order, this means x + y = 2 z , or z = ( x + y ) = 2 . So the growth rate of chain-weighted real GDP in the question was approximately (0 : 10 + 0 : 05) = 2 = 0 : 075 , yielded a value of 107 : 5 for year 2 real chain-weighted GDP. 2. The basic short run model of the text book takes the form ~ Y t = ° a ° ° b ( R t ° ° r ) R t ° ° r = ° m ( ° t ° ° ) ° t = ° t ° 1 + ° v ~ Y t (a) Brie°y explain in words what each equation represents. The °rst equation is the IS relationship, showing aggregate spending (relative to potential) as a negative function of the real rate of interest. The second relationship is the monetary policy rule, showing the way the central bank raises real interest rates when in±ation increases. The third equation is the Phillips curve relating current
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