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micro-fall-2007-11

# micro-fall-2007-11 - An Example Labor Supply Notation x...

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Utility maximization with an initial endowment of goods Utility maximization with an initial endowment of goods Choose ( x 1 ; x 2 ) so that u ( x 1 ; x 2 ) is maximized under the constraints p 1 x 1 + p 2 x 2 ° p 1 ω 1 + p 2 ω 2 x 1 ± 0 x 2 ± 0. Interior Solution: MRS ( x 1 ; x 2 ) = p 1 p 2 p 1 x 1 + p 2 x 2 = p 1 ω 1 + p 2 ω 2 . Ani Guerdjikova Fall 2007 122 / 126

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Utility maximization with an initial endowment of goods The O/er Curve De°nition O/er curve The o/er curve is the geometric place of all optimal consumption bundles x = ( x 1 ; x 2 ) of a household for di/erent relative prices p 1 p 2 . 1 At an interior solution MRS ( x 1 ; x 2 ) = p 1 p 2 p 1 x 1 + p 2 x 2 = p 1 ω 1 + p 2 ω 2 . 2 Substituting for p 1 p 2 , we obtain the equation of the o/er curve: x 2 = MRS ( x 1 ; x 2 ) [ ω 1 ² x 1 ] + ω 2 . Ani Guerdjikova Fall 2007 123 / 126
Utility maximization with an initial endowment of goods 6 - S S S S S S S S S S S S S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . l l l l l l l l l l l h h h h h h h h h h h h h h h h h h h h h x 1 ω 1 x 2 ω 2 r p 1 p 2 p 0 1 p 0 2 ? ............. p 00 1 p 00 2 - Ani Guerdjikova Fall 2007 124 / 126

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Utility maximization with an initial endowment of goods
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Unformatted text preview: An Example: Labor Supply Notation: x consumption good l labor p price of consumption good w wage π other income ¯ l total amount of time The household&s problem Choose ( x ; l ; f ) so that u ( x ; f ) is maximized under the constraints: px & wl + π & l & ¯ l , x ± Ani Guerdjikova ECON 313 Fall 2007 125 / 126 Utility maximization with an initial endowment of goods 6-¯ l l x π p & & & & & & & & & & & & . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x & l & Consumption-Labor Decision ............... w p Ani Guerdjikova ECON 313 Fall 2007 126 / 126...
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