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# practice3-answers-fall07 - Note The solution keys to the...

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Note: The solution keys to the practice exams state the °nal answers, but do not include intermediate steps and detailed explanations. They also do not include graphs ± please consult your class notes or the slides or the text book to °nd the relevant graphs. In the exam, you have to show your work and provide the intermediate steps and explanations to obtain full credit. Problem 1 a) MRS = h k = ° 1 if x h < 5 x k 0 if x h > 5 x k p x x h + p k x k ° y b) Utility maximization problem: max f x h ; x k g ° min f x h ; 5 x k g j p x x h + p k x k ° y x h ± 0 , x k ± 0 ± Optimality conditions: x h = 5 x k p x x h + p k x k = y x ° h ( p x ; p k ; y ) = 5 y p k + 5 p h x ° k ( p x ; p k ; y ) = y p k + 5 p h x ° k = y p k +5 p h > 0 for all y , p k , p h > 0 . c) IOC : x h = 5 x k Engel curve: x h ( y ) = 5 y p k +5 p h . 2

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Problem 2 a) MP a = 1 MP b = 1 2 p v b MRTS = MP a MP b = 2 p v b Isoquant: v a = ° y ² p v b b) min f v b g ° w b v b j p v b ± ° y v b ± 0 ± v ° b ( w b ; ° y ; ° v a = 0) = y 2 c ( y ) = w b y 2 AC = c ( y ) y = w b y MC = c 0 ( y ) = 2 w b y c) min f v a ; v b g ° w a v a + w b v b
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