practice3

practice3 - Practice Problem from Lecture 3 A consumer has...

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Practice Problem from Lecture 3 A consumer has the following utility function: U = x 1 4 y 3 4 1. Find the uncompensated demand functions for x and y . ANSWER: The constrained utility maximization problem L = x 1 4 y 3 4 + ( M p x x p y y ) @L @x : 1 4 x 3 4 y 3 4 x = 0 @L @y : 3 4 x 1 4 y 1 4 y = 0 @L : M p x x ± p y y ± = 0 which in turn provide two conditions that must hold at the optimum: (a) the MRS must equal the price ratio: 1 4 x 3 4 y 3 4 3 4 x 1 4 y 1 4 = p x p y y ± 3 x ± = p x p y y ± = 3 p x p y x ± (b) the budget constraint must hold with equality: M = p x x ± + p y y ± functions: M = p x x ± + p y 3 p x p y x ± ± = 4 p x x ± x ( p x ;p y ;M ) = M 4 p x y ( p x ;p y ;M ) = 3 p x p y M 4 p x ± = 3 M 4 p y 1
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2. Find the indirect utility function. ANSWER: The indirect utility function is found by plugging our uncom-
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practice3 - Practice Problem from Lecture 3 A consumer has...

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