Problem Set 7 - Solution - Econ 313-1 TA: Tian Liang...

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Unformatted text preview: Econ 313-1 TA: Tian Liang Solutions to Problem Set 7 1. (a) i. max x 1 ;x 2 x 3 1 x 2 s.t. x 1 > ; x 2 > p 1 x 1 + p 2 x 2 = m ii. If x 1 = 0 or x 2 = 0 , then u ( x 1 ;x 2 ) = 0 . But for any m > , the comsumer can have a strictly positive utility level by consuming a bundle with positive amounts of both goods. iii. & 3 x 2 x 1 = p 1 p 2 p 1 x 1 + p 2 x 2 = m = ) & x 1 ( p 1 ;p 2 ;m ) = 3 m 4 p 1 x 2 ( p 1 ;p 2 ;m ) = m 4 p 2 (b) v ( p 1 ;p 2 ;m ) = u ( x 1 ( p 1 ;p 2 ;m ) ;x 2 ( p 1 ;p 2 ;m )) = 3 m 4 p 1 3 m 4 p 2 = 27 m 4 256 p 3 1 p 2 2. (a) max x 1 ;x 2 p x 1 x 2 s.t. x 1 > ; x 2 > p 1 x 1 + p 2 x 2 = m & x 2 x 1 = p 1 p 2 p 1 x 1 + p 2 x 2 = m = ) & x 1 ( p 1 ;p 2 ;m ) = m 2 p 1 x 2 ( p 1 ;p 2 ;m ) = m 2 p 2 (b) v ( p 1 ;p 2 ;m ) = u ( x 1 ( p 1 ;p 2 ;m ) ;x 2 ( p 1 ;p 2 ;m )) = r m 2 p 1 & m 2 p 2 = m 2 p p 1 p 2 1 (c) x 1 (1 ; 1 ; 100) = 100 = (2 & 1) = 50 , x 2 (1 ; 1 ; 100) = 50 , v (1 ; 1 ; 100) = 50 ....
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This note was uploaded on 06/27/2008 for the course ECON 3130 taught by Professor Masson during the Spring '06 term at Cornell University (Engineering School).

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Problem Set 7 - Solution - Econ 313-1 TA: Tian Liang...

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