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HW09-solutions - Suggested Solutions for HW#9 Winter 2006...

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Suggested Solutions for HW #9 Winter 2006 Econ 11 Professor Zame Question 1 (a) Endowment: ( C = 0 , L = 24) Production Function: C out = L in Variables to be determined: Prices: p C , p L Consumer choices: C , L Production choices: C out , L in (b) 5 Equations: L = 2 3 ( 24 p L p L ) C = 1 3 ( 24 p L p C ) C out = L in L in + L = 24 C = C out Solving for the 5 variables: p C p L , C , L , C out , L in L = 2 3 ( 24 p L p L ) = 16 L in + L = 24 L in = 24 16 = 8 C out = L in = 8 C = C out = 8 1
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C = 1 3 ( 24 p L p C ) 8 = 1 3 ( 24 p L p C ) p C p L = 1 Question 2 Country A Consumption goods: F, H Variables to be determined: Prices: p F , p H , p L Individual Consumer choices: F , H Production choices: F out , H out , L F A , L H A Zero-pro fi t condition: π F = p F F p L L F = 0 p F L F p L L F = 0 p L p F = 1 π H = p H H p L L H = 0 4 p H L H p L L H = 0 p L p H = 4 Individual Consumption choices: F = 1 2 ( p L p F ) = 1 2 H = 1 2 ( p L p H ) = 2 Food market clears: MF = F out M 2 = F out 2
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Home appliances market clears: MH = H out 2 M = H out From production functions: F out = L F L F = M 2 H out = 4 L H 2 M = 4 L H L H = M 2 Labor Market clears: L F + L H = M M 2 + M 2 = M Question 3 Country B Consumption goods: F, H Variables to be determined: Prices: p F , p H , p L Individual Consumer choices: F , H Production choices: F out , H out , L F , L H Zero-pro fi t condition: π F = p F F p L L F = 0 6 p F L F p L L F = 0 p L p F = 6 π H = p H H p L L H = 0 2 p H L H p L L H = 0 p L p H = 2 3
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Individual Consumption choices: F = 1 2 ( p L p F ) = 3 H = 1 2 ( p L p H ) = 1 Food market clears: NF = F out 3 N = F out Home appliances market clears: NH = H out N = H out From production functions: F out = 6 L F L F = 3 N 6 = N 2 H out = 2 L H N = 2 L H L H = N 2 Labor Market clears: L F + L H = N N 2 + N 2 = N 4
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Question 4 Case 1: 1 2 < M N < 6 Both countries specialize and trade. Country A will specialize in H, because it has the comparative advantage in H. Country B will specialize in F, because it has the comparative advantage in F.
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