_Lecture_04

_Lecture_04 - HW # 01 due 3:15 today 1 Lecture 4 1-minute...

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Unformatted text preview: HW # 01 due 3:15 today 1 Lecture 4 1-minute review Consumer Problem: maximize utility subject to budget con- straint Substitution Method Geometric Method/Marginal Utility per Dollar Cobb-Douglas Lagrangian 2 Lagrangian Method Maximize F ( x,y ) Subject to G ( x,y ) = c New variable (Lagrange multiplier) New function (Lagrangian) L ( x,y, ) = F ( x,y ) + [ G ( x,y )- c ] Solutions to original problem are critical points of L all partial derivatives = 0 3 Maximize U ( x,y ) = xy Subject to 6 x + 3 y = 120 L ( x,y, ) = xy + (6 x + 3 y- 120) 4 y + 6 = 0 x + 3 = 0 6 x + 3 y- 120 = 0- 18 - 18 - 120 = 0 =- 10 / 3 x = 10 y = 20 5 Demand function Solution to choice problem as function of income prices What happens to demand for a good when income changes? its own price changes? price(s) of other good(s) change 6 General Cobb-Douglas (two goods) U ( x,y ) = x a y b income = M prices = p x ,p y Lagrangian L ( x,y, ) = U ( x,y ) + (budget line) = x a y b + ( p x x + p y y- M ) 7 Three equations...
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_Lecture_04 - HW # 01 due 3:15 today 1 Lecture 4 1-minute...

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