# Note7 - Figure 7 x is a substitute for y does not imply...

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Figure 7 x is a substitute for y does not imply that y is a substitute for x original budget line = MN original optimum = A When p y " , hence y # and x " , thus x and y are substitutes ( x is a substitute for y ). TE = total e/ect = x 2 ± x 0 > 0 SE = substitution e/ect = x 1 ± x 0 > 0 IE = income e/ect = x 2 ± x 1 < 0 SE dominates IE (SE > j IE j ), hence TE > 0 When p x " , the optimum moves from A to C±, hence x # and y # , thus x and y are complements ( y is a complement for x ). TE = total e/ect = y 2 ± y 0 < 0 SE = substitution e/ect = y 1 ± y 0 > 0 IE = income e/ect = y 2 ± y 1 < 0 IE dominates SE ( j IE j > SE), hence TE < 0 34

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3. Net Substitutes and Complements x and y are net substitutes if @x @p y U = constant > 0 x and y are net complements if @x @p y U = constant < 0 @x @p y U = constant > 0 implies that @y @p x U = constant > 0 (proof not required) Example: U ( x;y;z ) = 1 x 1 y 1 z : Then x = I p x + p p x p y + p p x p z , y = I p
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Note7 - Figure 7 x is a substitute for y does not imply...

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