# 06s - 6 2010 W W Norton Company Inc Demand Outline...

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6 Demand

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2 Outline Own-price changes Price offer curve Ordinary demand curve Inverse demand curve Income changes Income offer curve Engel curve Cross-price effects
3 Properties of Demand Functions 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.

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4 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 ’’’.
5 Own-Price Changes x 1 x 2 p 1 = p 1 ’’ p 1 = p 1 ’’’ Fixed p 2 and y. p 1 = p 1 p 1 x 1 + p 2 x 2 = y

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6 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.
7 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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8 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.
9 Own-Price Changes What does a p 1 price-offer curve look like for Cobb-Douglas preferences?

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10 Own-Price Changes What does a p 1 price-offer curve look like for Cobb-Douglas preferences? Take Then the ordinary demand functions for commodities 1 and 2 are U x x x x a b ( , ) . 1 2 1 2
11 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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12 x 1 *(p 1 ’’’) x 1 *(p 1 ’) x 1 *(p 1 ’’) x 2 x 1 Fixed p 2 and y. x by a b p 2 2 * ( ) x ay a b p 1 1 * ( )
13 p 1 x 1 * Ordinary demand curve for commodity 1 is x ay a b p 1 1 * ( )

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## This note was uploaded on 06/12/2011 for the course ECON 101 taught by Professor Dee during the Spring '10 term at Andhra University.

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06s - 6 2010 W W Norton Company Inc Demand Outline...

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