# practice4-answers-fall07 - Note The solution keys to the...

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intermediate steps and detailed explanations. They also do not include graphs ± please exam, you have to show your work and provide the intermediate steps and explanations to obtain full credit. Problem 1 a) Indifference curve: x s u 1 2 p x d Budget constraint: p s x s + p d x d ± y b) Optimization problem: max f x s ; x d g x s + 1 2 p x d j p s x s + p d x d ± y x s ² 0 , x d ² 0 ± Optimality conditions: MRS = s d = p x d = p s p d p s x s + p d x d = y Optimal demand: x s ( p s ; p d ; y ) = y p s p s p d if p s p d ± y p s 0 else x d ( p s ; p d ; y ) = ( p 2 s p 2 d if p s p d ± y p s y p d else x s = 0 for p s p d ² y p s . c) Demand for x s : x s ( p s ) = y p s p s p d To draw the function note that x 0 s ( p s ) < 0 ; x 00 s ( p s ) = ² y p 2 s ³ 0 = 2 y p 3 s > 0 so the function is decreasing and convex in

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practice4-answers-fall07 - Note The solution keys to the...

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