HW_04_Solutions

HW_04_Solutions - 1) If M py px 2p y 2 0, we are on an...

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1) If M u p y px 2 py 2 U 0 , we are on an interior solution and the demands for y and x are: y u px 2 py 2 x u M u p y px 2 py 2 In this case, the elasticity of demand for y is given by: u y , py u ± y ± py py y u u 1 2 p x 2 p y 3 py px 2 py 2 u u 2 However, if M u p y px 2 py 2 U 0 , we are on a corner solution and the demands will be given by: y u M py x u 0 The elasticity will be: u y , py u ± y ± py py y u M p y 2 py M py u u 1 2) a ) 0 1 2 3 4 5 0 1 2 3 4 5 x y b ) The problem the firm has to solve is: min p x x ± p y y
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st x 1 4 y 3 4 u 100 The Lagrangean associated with this problem is L u p x x U p y y U u x 1 4 y 3 4 U 100 . Taking its derivative in respect to the variables and equating them to zero give us: y 3 x u px py To plug this relationship into the restriction gives us: y u 100 3 px py 1 4 x u 100 py 3 px 3 4 When we substitute the prices given in the exercise we get: y u 100 3 px py 1 4 u 100 x u 100 py 3 px 3 4 u 100 c ) Using the same procedure from the previous item, we get that:
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HW_04_Solutions - 1) If M py px 2p y 2 0, we are on an...

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