WeekofFeb02_solns

WeekofFeb02_solns - W3211 Spring 2009 Professor Vogel...

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W3211 Spring 2009 Professor Vogel Recitation for the Week of February 02, 2009 . 1. (a) MRS = MU x =MU y = 1 =x 1 = 1 =x , It is diminishing with x but is independent of y: (b) max L = y + ln x + (12 2 x 3 y ) @ L @x = 1 x 2 = 0 @ L @y = 1 3 = 0 @ L = 12 2 x 3 y = 0 = 1 = 2 x = 1 = 3 ! x = 1 : 5 Substituting x = 1 : 5 into the last FOC, y = 3 2. In order to get elasticities we need demand functions of x and y max L = y + ln x + ( I p x x p y y ) @ L @x = 1 x p x = 0 @ L @y = 1 p y = 0 @ L = I p x x p y y = 0 By solving this maximization problem, we have y = I p y 1 and x = p x p y (a) e y;p y = @y @p y p y y = I p 2 y p y y = I yp y e y;I = @y @I I y = 1 p y I y = I yp y e y;p x = @y @p x p x y = 0 (b) e x;p x = @x @p x p x x = p y xp x e x;I = @x @I I x = 0 e x;p y = @y @p x p x y = p y xp x (c) The optimal consumption of x , x = p x p y , is independent of income I: Ux p x = 1 p x x ; U y p y = 1 p y
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2 3. By MRS = 0 : 4 x & 0 : 6 y 0 : 6 0 : 6 x 0 : 4 y & 0 : 4 = 1
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This note was uploaded on 12/21/2009 for the course ECON 1211 taught by Professor Govel during the Spring '08 term at Columbia.

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WeekofFeb02_solns - W3211 Spring 2009 Professor Vogel...

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