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PS3 Answer Key - Econ 3140 Fall 2009 Problem Set 3 Answer...

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Econ 3140 Fall 2009 Problem Set 3 Answer Key 1. Calculating chain-weighted indexes is not too hard and you can use the computer- bicycle example in Table 2.4 to illustrate how to do so, as suggested in Box 2.2. De°ne the Laspeyres quantity index (using year 1 prices) for year 1 as the value of year 1 output at year 1 prices: L 1 = $46 ; 000 ; the Laspeyres quantity index of year 2 output is L 2 = $62 ; 000 . De°ne the Paasche quantity index (using year 2 prices) for year 1 as the value of year 1 output at year 2 prices: P 1 = $51 ; 000 ; the Paasche quantity index of year 2 output is P 2 = $66 ; 000 . (These amounts are all calculated in Table 2.4, they just are not labeled this way.) The chain-weighted index is just the geometric mean of the Laspeyres and Paasche indexes: C 1 = ( L 1 ° P 1 ) 1 2 = (46 ; 000 ° 51 ; 000) 1 2 = $48 ; 400 ; C 2 = ( L 2 ° P 2 ) 1 2 = (62 ; 000 ° 66 ; 000) 1 2 = $63 ; 970 : Note that the growth rate of real GDP in this case is ($63 ; 970 ± $48 ; 400) = $48 ; 400 = 32 : 06% , which is close to the average growth rate calculated by the Laspeyres ( 34 : 8% ) and Paasche ( 29 : 4% ) indexes, which is 32 : 095% : 2. 12 : 87% 3. Recall that, to calculate the Marginal Product of any factor (labor, N; capital, K, or any
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