u-max-demo - OPMT 5701: Calculus for Utility Problems Kevin...

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OPMT 5701: Calculus for Utility Problems Kevin Wainwright October 14, 2003 1 Using Calculus For Utility Maximization Prob- lems 1.1 Review of Some Derivative Rules 1. Partial Derivative Rules: U = xy U/ x = y y = x U = x a y b x = ax a 1 y b y = bx a y b 1 U = x a y b = x a y b x = ax a 1 y b y = bx a y b 1 U = ax + by x = a y = b U = ax 1 / 2 + by 1 / 2 x = a ³ 1 2 ´ x 1 / 2 y = b ³ 1 2 ´ y 1 / 2 2. Logarithm (Natural log) ln x (a) Rules of natural log If Then y = AB ln y =ln( AB )=ln A +ln B y = A/B ln y =ln A ln B y = A b ln y A b )= b ln A NOTE: ln( A + B ) 6 A B (b) derivatives IF THEN y x dy dx = 1 x y f ( x )) dy dx = 1 f ( x ) · f 0 ( x ) (c) Examples y x 2 2 x ) dy/dx = 1 ( x 2 2 x ) (2 x 2) y x 1 / 2 1 2 ln xd y / d x = ³ 1 2 ´³ 1 x ´ = 1 2 x 1
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3. The Number e if y = e x then dy dx = e x if y = e f ( x ) then dy dx = e f ( x ) · f 0 ( x ) (a) Examples y = e 3 x dy dx = e 3 x (3) y = e 7 x 3 dy dx = e 7 x 3 (21 x 2 ) y = e rt dy dt = re rt 1.2 Finding the MRS from Utility functions EXAMPLE: Find the total di f
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This note was uploaded on 03/03/2012 for the course ECON 345 taught by Professor Wendywu during the Fall '11 term at Wilfred Laurier University .

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u-max-demo - OPMT 5701: Calculus for Utility Problems Kevin...

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