HW04-solutionsREV

HW04-solutionsREV - Suggested Solutions for HW #4 Winter...

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Suggested Solutions for HW #4 Winter 2006 Econ 11 Professor Zame Question 1 (a) u ( x, y )= x 1 / 3 y 2 / 3 MU x y = p x p y y 2 x = p x p y Budget line : p x x + p y y = I Solving for the demand functions: x = I 3 p x and y = 2 I 3 p y Plugging in I = 5000 and p y = 100 , the demand functions become x = 5000 3 p x and y = 100 3 (b) v ( x, y x 2 / 3 y 1 / 3 x y = p x p y 2 y x = p x p y Budget line : p x x + p y y = I Solving for the demand functions: x = 2 I 3 p x and y = I 3 p y Plugging in I = 5000 and p y = 100 , the demand functions become x = 10000 3 p x and y = 50 3 1
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Graph The di f erence between the two demand curves arises from the fact that we like the x goodbetterinpartbthaninparta . Th isisre f ected in the demand function. Notice that the part b demand function is greater than the part a demand function. Question 2 (a) u ( x, y )= x +log y MU x y = p x p y y = p x p y Budget line : p x x + p y y = I Solving for the demand functions: 2
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p x x + p y ( p x p y )= I x = I p x p x S incewecannothavenegat iveva lueso f x , the demand functions are: If I p x ,x = I p x p x ,y = p x p y If I<p x =0 = I p y Plugging in I =50 and p x =1 x =4 9 y = 1 p y (b) u ( x, y x 1 y MU x y = p x p y y 2 = p x p y Budget line : p x x + p y y = I Solving for the demand functions: y = r p x p y p x x + p y r p x p y = I p x x + p y p x = I x = I p y p x p x S f x , the demand functions are: If I p y p x , then x = I p y p x p x = r p x p y If I< p y p x , then x = I p y 3
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Plugging in I =50 and p x =1 If 50 p y ,then x p y ,y = s 1 p y If 50 < p y x =0 = 50 p y If 2500 p y x p y = s 1 p y If 2500 <p y x = 50 p y Graph 4
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Question 3 u ( x, y )= x 1 / 4 + y 1 / 4 MU x y = p x p y ( y x ) 3 / 4 = p x p y Budget line : p x x + p y y = I Solving for the demand function of just x as a functions of prices and income: y x =( p x p y ) 4 / 3 y = x ( p x p y ) 4 / 3 p x x + p y y = I p x x + p y x ( p x p y ) 4 / 3 = I p x x + xp 4 / 3 x p 1 / 3 y = I x ( p x + p 4 / 3 x p 1 / 3 y I x = I ( p x + p 4 / 3 x p 1 / 3 y ) x = I p x [1 + ( p x p
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HW04-solutionsREV - Suggested Solutions for HW #4 Winter...

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