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HW2_SOL - Economics 314 Suggested Solutions to HW 2 TA...

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Economics 314: Suggested Solutions to HW 2 TA: Romita Mukherjee September 21, 2008 1 [Page 5, 3, NQ 1] (a) If real GDP=$7 trillion, then real GDP after 10 years=($7 trillion) * (1 . 025) 10 =$8.96 trillion. (b) If real GDP grows by $0.175 trillion per year: real GDP=$7 trillion + (0.175)*10=$8.75. The answer in part (a) is greater than $8.75 trillion since the growth is compounded over time. 2 [page 5, 3, NQ 3] (a) Initial output is given by: Y = AK β L 1 - β = 5 * (400) 0 . 3 (100) 0 . 7 = 758 . (b) Total Compensation to Employees=(1 - β ) Y = (0 . 7) * 758 = 531 . (c) Increase labor and capital by 50%, we get changed Y as Y = 5 * (600) 0 . 3 * (150) 0 . 7 = 1137 , which is 50% greater than 758. 3 [page 5, 3, (NQ 4)] (a) Using Cobb Douglas production function with K = 200, L = 100, A = 2, and β = 0 . 4, we have: Intensive form: y = Ak β = 2 * (200 / 100) 0 . 4 = 2 . 64 (b) With k = 4 , y = 2 * (4) 0 . 4 = 3 . 48 1
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(c) The answer to part (b) does not depend on how the value of k changed since y is a function of k itself. 4 [page 6, 3, NQ 5] (a) Y 1988 = (10)(1000) 0 . 3 (500) 0 . 7 = 6165 . Y 1998 = (11)(1100) 0 . 3 (600) 0 . 7 = 7916 . Δ Y Y = 7916 - 6156 6156 = 29% . (b) Using growth accounting equation: Δ Y Y = Δ A A + β Δ K K + (1 - β ) Δ L L Δ Y Y 10 + (0 . 3)(10) + (0 . 7)(20) = 27% .
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