Problem_Set_3_Solution

Problem_Set_3_Solution - Economic Growth and Development...

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Economic Growth and Development Professor Olivier de La Grandville Problem Set 3 Solutions 1. (50 points) We know from Chapter 13: s * = ± δ i ² σ ( n + g ) (1) V * = 1 - ( δ i ) σ ( n + g ) i - ( n + g ) " δ 1 - δ ( δ i ) 1 - σ - δ + 1 - δ # σ 1 - (2) e V * ,g = log V * log g = g " ( δ i ) σ ( δ i ) σ ( n + g ) - 1 + 1 i - ( n + g ) # (3) e V * = log V * log σ = - σ ( δ i ) σ ( n + g ) log ( δ i ) 1 - ( δ i ) σ ( n + g ) - σ ( σ - 1) 2 log " δ 1 - δ ( δ i ) 1 - σ - δ + 1 - δ # + σ 2 δ σ - 1 · 1 - δ h ( δ i ) 1 - σ - δ i 2 · ± δ i ² 1 - σ · log ± δ i ² · " δ 1 - δ ( δ i ) 1 - σ - δ + 1 - δ # - 1 (4) Using these formulas we can calculate the values of s * , V * , and e V * e V * ,g , as shown in tables 1, 2, and 3, respectively. Table 1. Calculated percentage s * for δ = 0 . 25, g = 1%, n = 1%, and various values of i and σ i 4% 5% 6% 7% 8% 9% σ 0 . 70 7 . 21 6 . 17 5 . 43 4 . 88 4 . 44 4 . 09 0 . 75 7 . 91 6 . 69 5 . 83 5 . 20 4 . 70 4 . 30 0 . 80

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This note was uploaded on 06/16/2010 for the course MS&E 249 taught by Professor Olivierdelagrandville during the Fall '08 term at Stanford.

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Problem_Set_3_Solution - Economic Growth and Development...

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