MECON PS0 sol

MECON PS0 sol - Microeconomics ECON 100A Problem Set 0...

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Unformatted text preview: Microeconomics ECON 100A Problem Set 0 Solutions Due January 13, 2010 (Solutions Posted January 15, 2010) Professor Michael Noel University of California San Diego 1. Find the first and second derivatives for the following functions of x. a. f(x) = a + bx + cx 2 + dx 3 dx c x f dx cx b x f 6 2 ) ( 3 2 ) ( 2 + = + + = b. f(x) = ln(4x 3 ) 2 3 2 3 ) ( 3 4 12 ) ( x x f x x x x f- = = = 2. Let z = 4x 4 y 3 - 5x 2 y + xy 2 a. Derive the first and second partial derivatives for z. What is true about the cross partials? y x y x x y y x z y x z x y x y y x z y x z y x y x y x y x z y x z y y x x y x z y x z xy x y x y y x z y x z y xy y x x y x z y x z yx yy xy xx y x 2 10 48 ) , ( ) , ( 2 24 ) , ( ) , ( 2 10 48 ) , ( ) , ( 10 48 ) , ( ) , ( 2 5 12 ) , ( ) , ( 10 16 ) , ( ) , ( 2 3 2 4 2 2 2 3 2 3 2 2 2 2 2 4 2 3 3 +- = = + = = +- = =- = = +- = = +- = = Note that ) , ( ) , ( y x z y x z yx xy = b. Derive the total differential of z. Derive the total differential of z....
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This note was uploaded on 11/27/2011 for the course ECON 100A taught by Professor Staff during the Winter '08 term at UCSD.

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MECON PS0 sol - Microeconomics ECON 100A Problem Set 0...

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