lecture5 - Professor Jay Bhattacharya Spring 2001 Demand...

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Professor Jay Bhattacharya Spring 2001 Econ 11--Lecture 5 1 Spring 2001 Econ 11--Lecture 5 1 Demand Part I • Recap: The Consumer’s Optimization Problem • The budget constraint and the tangency condition determine the amount of each good the consumer will purchase. The consumer’s choice of ( X 1 , X 2 ) (i.e. demand for X 1 and X 2 ) depends upon: •p r i c e s( p 1 , p 2 ) •i n c om e( I ) • preferences—U( X 1 , X 2 ) X 1 X 2 Spring 2001 Econ 11--Lecture 5 2 Demand Functions •AM a r s h a l l i a n demand function relates the quantity demanded of a good to prices and income • Demand depends on all prices • Preferences and constraints together determine the shape of demand ) , , ( ) , , ( 2 1 2 2 1 1 I p p g X I p p f X = = Spring 2001 Econ 11--Lecture 5 3 Comparative Statics • What happens to demand when prices or income changes? 1 p I 1 2 p I 2 2 p I 2 p I –e.g., if prices double and income doubles, what happens to demand? Spring 2001 Econ 11--Lecture 5 4 • A function f ( x 1 , x 2 ,… x n ) is homogenous of degree k if • Marshallian demand functions are homogenous of degree zero. This fact is consistent with the absence of “money illusion.” ) 2 , 2 , 2 ( ) , , ( 2 1 1 2 1 1 Ι = p p X I p p X Zero Degree Homogeneity of Demand () ( ) n n k n n x x x f t tx tx tx f ,... , ,... , 1 1 = Spring 2001 Econ 11--Lecture 5 5 What happens to demand when income changes? • Budget constraint shifts in/out. Slope of budget constraint does not change. Increasing income x 1 x 2 Spring 2001 Econ 11--Lecture 5 6 Income Expansion Path (Income-Offer Curve) 1 2 p I 1 1 p I 1 0 p I 2 0 p I 2 1 p I 2 2 p I Prices are fixed along the income expansion path x 1 x 2
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Professor Jay Bhattacharya Spring 2001 Econ 11--Lecture 5 2 Spring 2001 Econ 11--Lecture 5 7 Engel Curves • Engel curve relates income to quantity demanded.
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lecture5 - Professor Jay Bhattacharya Spring 2001 Demand...

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