HW10-REV-solutions

HW10-REV-solutions - Suggested Solutions for HW#10 Winter...

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Suggested Solutions for HW #10 Winter 2006 Econ 11 Professor Zame Question 1 (a) Variables Prices: p L , p B , p G Consumption goods: B , G Production Choices: B out , G out , L B , L G (b) Equations Consumer’s optimize: B = 4 5 ( p L p B ) G = 1 5 ( p L p G ) Zero-pro fi t conditions: π B = p B B out p L L B = 0 = 5 p B L B p L L B = 0 5 p B = p L p L p B = 5 π G = p G G out p L L G = 0 = 5 p G L G p L L G = 0 5 p G = p L p L p G = 5 Production Functions: B out = 5 L B G out = 5 L G 1
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Market Clearing: B out = B G out = G L B + L G = 1 (c) Equilibrium Normalize prices such that p B = / 1 . Then from the zero-pro fi t conditions, we have p L = 5 and p G = 1 . From the consumer’s optimization equations, we get B = 4 and G = 1 . Then from the fi rst two market clearing conditions, we get B out = 4 and G out = 1 . From the production functions, we get L B = 4 5 and L B = 1 5 . It is easy to verify that the labor market also clears. Question 2 (a) Variables Prices: p L , p B , p G Consumption goods: B , G Production Choices: B out , G out , L B , L G (b) Equations Consumer’s optimize: B = 3 5 ( p L p B ) G = 2 5 ( p L p G ) Zero-pro fi t conditions: π B = p B B out p L L B = 0 = 10 p B L B p L L B = 0 10 p B = p L p L p B = 10 2
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π G = p G G out p L L G = 0 = 2 p G L G p L L G = 0 2 p G = p L p L p G = 2 Production Functions: B out = 10 L B G out = 2 L G Market Clearing: B out = B G out = G L B + L G = 1 (c) Equilibrium Normalize prices such that p B = / 1 . Then from the zero-pro fi t conditions, we have p L = 10 and p G = 5 . From the consumer’s optimization equations, we get B = 6 and G = 4 5 . Then from the fi rst two market clearing conditions, we get B out = 6 and G out = 4 5 . From the production functions, we get L B = 3 5 and L B = 2 5 . It is easy to verify that the labor market also clears. Question 3 (a) PPF of Country A: Production Functions: B = 5 L B L B = B 5 G = 5 L G L G = G 5 Total Labor Supply is 1 . 3
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L B + L G = 1 B 5 + G 5 = 1 B + G = 5 PPF of Country A: B + G = 5 PPF of Country B: Production Functions: B = 10 L B L B = B 10 G = 2 L G L G = G 2 Total Labor Supply is 1 .
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