_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 λ (Lagrange multiplier) New function (Lagrangian) L ( x,y,λ ) = F ( x,y ) + λ [ 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,λ ) = xy + λ (6 x + 3 y- 120) 4 y + 6 λ = 0 x + 3 λ = 0 6 x + 3 y- 120 = 0- 18 λ- 18 λ- 120 = 0 → λ =- 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,λ ) = U ( x,y ) + λ (budget line) = x a y b + λ ( 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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