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penn101_09s5 - Market Demand Equilibrium Econ 101...

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Market Demand Equilibrium Econ 101: Intermediate Microeconomics Consumer Theory III: The Market Jing Li Department of Economics University of Pennsylvania February 19, 2009 Jing Li Intermediate Microeconomics
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Market Demand Equilibrium Market Demand Function Elasticity Analysis From individual to market demand There are n individuals on the market, i = 1 , 2 , · · · , n ; Consumer i has preferences u i and income m i ; x 1 i ( p 1 , p 2 , m i ) : consumer i ’s demand function for good 1; x 2 i ( p 1 , p 2 , m i ) : consumer i ’s demand function for good 2. Market demand function for good 1: X 1 ( p 1 , p 2 , M ) = n X i = 1 max { x 1 i ( p 1 , p 2 , m i ) , 0 } , where M = n i = 1 m i denotes the aggregate income. Example: x 1 1 = 50 p 1 , x 1 2 = 10 - p . Note the non-negativity requirement for demand: x 1 i 0 for all i . Jing Li Intermediate Microeconomics
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Market Demand Equilibrium Market Demand Function Elasticity Analysis From individual to market demand There are n individuals on the market, i = 1 , 2 , · · · , n ; Consumer i has preferences u i and income m i ; x 1 i ( p 1 , p 2 , m i ) : consumer i ’s demand function for good 1; x 2 i ( p 1 , p 2 , m i ) : consumer i ’s demand function for good 2. Market demand function for good 1: X 1 ( p 1 , p 2 , M ) = n X i = 1 max { x 1 i ( p 1 , p 2 , m i ) , 0 } , where M = n i = 1 m i denotes the aggregate income. Example: x 1 1 = 50 p 1 , x 1 2 = 10 - p . Note the non-negativity requirement for demand: x 1 i 0 for all i . Jing Li Intermediate Microeconomics
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Market Demand Equilibrium Market Demand Function Elasticity Analysis From individual to market demand There are n individuals on the market, i = 1 , 2 , · · · , n ; Consumer i has preferences u i and income m i ; x 1 i ( p 1 , p 2 , m i ) : consumer i ’s demand function for good 1; x 2 i ( p 1 , p 2 , m i ) : consumer i ’s demand function for good 2. Market demand function for good 1: X 1 ( p 1 , p 2 , M ) = n X i = 1 max { x 1 i ( p 1 , p 2 , m i ) , 0 } , where M = n i = 1 m i denotes the aggregate income. Example: x 1 1 = 50 p 1 , x 1 2 = 10 - p . Note the non-negativity requirement for demand: x 1 i 0 for all i . Jing Li Intermediate Microeconomics
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Market Demand Equilibrium Market Demand Function Elasticity Analysis From individual to market demand There are n individuals on the market, i = 1 , 2 , · · · , n ; Consumer i has preferences u i and income m i ; x 1 i ( p 1 , p 2 , m i ) : consumer i ’s demand function for good 1; x 2 i ( p 1 , p 2 , m i ) : consumer i ’s demand function for good 2. Market demand function for good 1: X 1 ( p 1 , p 2 , M ) = n X i = 1 max { x 1 i ( p 1 , p 2 , m i ) , 0 } , where M = n i = 1 m i denotes the aggregate income. Example: x 1 1 = 50 p 1 , x 1 2 = 10 - p . Note the non-negativity requirement for demand: x 1 i 0 for all i . Jing Li Intermediate Microeconomics
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Market Demand Equilibrium Market Demand Function Elasticity Analysis Inverse demand function Consumer i ’s inverse demand function: p 1 ( x 1 i ) p 1 ( x 1 i ) = p 2 | MRS i | ; Price measures i ’s willingness to pay.
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