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Note6 - Demand Curves x = d p x;p y;I y = d p x;p y;I From...

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Unformatted text preview: Demand Curves x = d ( p x ;p y ;I ) y = d ( p x ;p y ;I ) From commodity space ( x and y ) to price-quantity space ( p x and x ). The determinants of the demand of x are p x ; p y ; and I: Demand curves have the following properties. 1. Homogeneity d ( tp x ;tp y ;tI ) = & tx ? x ? (23) If prices and income are doubled, will the quantity demanded be doubled or the same? A function is homogeneous of degree r if f ( &x ) = & r f ( x ) : Examples: (i) f ( x;y ) = p xy (ii) f ( x;y ) = x a y b (iii) f ( x;y ) = x a + y b Demand curves are homogeneous of degree ___. Example: Cobb-Douglas utility 21 2. Movements along the demand curve versus shifts in the de- mand curve Demand curve x = d ( p x ;p y ;I ) & Movements along the demand curve: e.g., a change (decrease/increase) in the quantity demanded for x due to a change in p x : For the Cobb-Douglas utility function u ( x;y ) = x a y b , x & = aI p x ; hence @x & @p x = & aI p 2 x : & Shifts in the demand curve: e.g., a change (decrease/increase) in the demand for x due to a change in p y or I: For the Cobb-Douglas utility function u ( x;y ) = x a y b , x & = aI p x ; hence @x & @I = a p x : & Although mathematically @x & @p x and @x & @I are both partial derivatives, why do we need di¡erent terminologies for the changes? 22 3. Downward sloping A demand curve is downward sloping if @x @p x < : De&nitions: Gi/en Good: @[email protected] x > : Normal Good: @[email protected] > : Inferior Good: @[email protected] < : A Gi/en good has an upward sloping demand curve. There is no empirical evidence of a Gi/en good so far....
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Note6 - Demand Curves x = d p x;p y;I y = d p x;p y;I From...

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