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HW_09_solutions - Economics 11 HW 9 Suggested Solutions...

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Economics 11 HW 9 - Suggested Solutions Question 1 Since the production function of food in country A has the property that it only uses one of unskilled labor and skilled labor, we can guess that only unskilled labor will be used in food production in country A. Otherwise, there would be no place in which unskilled labor could be used. For food industry to hire only unskilled workers, p A l should be lower than p A L : We will verify that this is true in the equlibrium. Competitive Equilibrium Variables ° prices p C ; p F ; p A l ; p A L (normalization p C = 1) ° consumption choices C ° 1 ; F ° 1 ; l ° ; C ° 2 ; F ° 2 ; L ° ° production plans ( C out ; L in ) ; ( F out ; l in ) Competitive Equilibrium Equations ° Consumption Consumer demands of unskilled workers are C ° 1 = (1 = 10) p A l 1 F ° 1 = (6 = 10) p A l p F l ° = (3 = 10) p A l p A l = 3 10 ; and consumer demands of skilled workers are C ° 2 = (1 = 10) p A L 1 F ° 2 = (6 = 10) p A L p F L ° = (3 = 10) p A L p A L = 3 10 : ° Production 1
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From °rm C±s zero pro°t condition together with feasibility condition C out = L in ° = C out ± 1 ² L in p A L = 0 ; we get p A L = 1 : Similarly, for °rm F F out = 2 l in ° = F out p F ² l in p A l = 0 ; we get p A l p F = 2 : ° Market clearing for good C and L N 1 C ° 1 + N 2 C ° 2 = C out N 2 L ° + L in = N 2 = ) N 1 ( 1 10 ) p A l + N 2 ( 1 10 )(1) = 7 10 N 2 = ) p A l = 6 N 2 N 1 = ) p F = 3 N 2 N 1 2
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Hence the CE is p C = 1 p F = 3 N 2 N 1 p A l = 6 N 2 N 1 p A L = 1 C ° 1 = 3 N 2 5 N 1 F ° 1 = 6 5 l ° = 3 10 C ° 2 = 1 10 F ° 2 = N 1 5 N 2 L ° = 3 10 ( C out ; L in ) = ° 7 10 N 2 ; 7 10 N 2 ± ( F
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