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Tsinghua Micro Ch6 020927 - Chapter Six Demand What Do We...

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Chapter Six Demand 需需需需需需需需需需需
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What Do We Do in This Chapter? We conduct comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1 ,p 2 ,y) and x 2 *(p 1 ,p 2 ,y) change as prices p 1 , p 2 and income y change. Theoretically, nothing new.
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Own-Price Changes How does x 1 *(p 1 ,p 2 ,y) change as p 1 changes, holding p 2 and y constant? Suppose only p 1 increases, from p 1 to p 1 ’’ and then to p 1 ’’’.
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x 2 x 1 x 1 *(p 1 ’’’) x 1 *(p 1 ’) x 1 *(p 1 ’’) p 1 x 1 *(p 1 ’) x 1 *(p 1 ’’’) x 1 *(p 1 ’’) p 1 p 1 ’’ p 1 ’’’ x 1 * Own-Price Changes Ordinary demand curve for commodity 1 Fixed p 2 and y.
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x 2 x 1 x 1 *(p 1 ’’’) x 1 *(p 1 ’) x 1 *(p 1 ’’) p 1 x 1 *(p 1 ’) x 1 *(p 1 ’’’) x 1 *(p 1 ’’) p 1 p 1 ’’ p 1 ’’’ x 1 * Own-Price Changes Ordinary demand curve for commodity 1 p 1 price offer curve Fixed p 2 and y.
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Own-Price Changes The curve containing all the utility- maximizing bundles traced out as p 1 changes, with p 2 and y constant, is the p 1 - price offer curve . The plot of the x 1 -coordinate of the p 1 - price offer curve against p 1 is the ordinary demand curve for commodity 1.
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The Case of Cobb-Douglas Utility Function Take Then the ordinary demand functions for commodities 1 and 2 are U x x x x a b ( , ) . 1 2 1 2 =
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Own-Price Changes x p p y a a b y p 1 1 2 1 * ( , , ) = + × x p p y b a b y p 2 1 2 2 * ( , , ) . = + × and Notice that x 2 * does not vary with p 1 so the p 1 price offer curve is flat and the ordinary demand curve for commodity 1 is a rectangular hyperbola .
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x 1 *(p 1 ’’’) x 1 *(p 1 ’) x 1 *(p 1 ’’) x 2 x 1 Own-Price Changes Fixed p 2 and y. x by a b p 2 2 * ( ) = + x ay a b p 1 1 * ( ) = +
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x 1 *(p 1 ’’’) x 1 *(p 1 ’) x 1 *(p 1 ’’) x 2 x 1 p 1 x 1 * Own-Price Changes Ordinary demand curve for commodity 1 is Fixed p 2 and y. x by a b p 2 2 * ( ) = + x ay a b p 1 1 * ( ) = + x ay a b p 1 1 * ( ) = +
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The Case of Perfect-Complements Utility Function What does a p 1 price-offer curve look like for a perfect-complements utility function? } { U x x x x ( , ) min , . 1 2 1 2 = Then the ordinary demand functions for commodities 1 and 2 are
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The Case of Perfect-Complements Utility Function x p p y x p p y y p p 1 1 2 2 1 2 1 2 * * ( , , ) ( , , ) . = = +
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Own-Price Changes x p p y x p p y y p p 1 1 2 2 1 2 1 2 * * ( , , ) ( , , ) . = = + With p 2 and y fixed, higher p 1 causes smaller x
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