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

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Unformatted text preview: Economics 314 Suggested Solutions to HW 2 February 6, 2009 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. (a) Initial output is given by: Y = AK & L 1 & & = 5 & (400) : 3 (100) : 7 = 758 : (b) Total Compensation to Employees = (1 ¡ & ) Y = (0 : 7) & 758 = 531 : (see labor income on p.11 of L2) (c) Increase labor and capital by 50%, we change Y to Y = 5 & (600) : 3 & (150) : 7 = 1137 ; which is 50% greater than 758. The reason is that the exponents of all factors of production add up to 1. Contrast with increasing returns to scale (sum of exponents > 1) and dimin- ishing returns to scale (sum of exponents < 1) for Cobb-Douglas production functions. 3. (a) Using Cobb-Douglas production function with K = 200 , L = 100 , A = 2 , and & = 0 : 4 , which means the capital-to-labor ratio is...
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HW2_SOL - Economics 314 Suggested Solutions to HW 2...

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