# PS1Answers - UCLA Economics 11 Fall 2009 Professor Mazzocco...

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UCLA Economics 11 – Fall 2009 Professor Mazzocco Problem Set 1 Due by 1. Unconstrained Optimization (1 exogenous variable) Find the value of x that maximizes y =100−(4−7 x ) 2 . Make sure it is a maximum by checking the Second Order Conditions and plotting the function. Answer F.O.C * 4 14(4 7 ) 0. . 7 y x so x x S.O.C 2 2 98 y x  for any value of x. Therefore, it is a maximum 2. Unconstrained Optimization (2 exogenous variables) Find the values of ( x 1 , x 2) that maximizes the expression y = 9x 1 1/3 x 2 1/3 –3 x 1 – 3x 2 Answer The F.O.C. are now a system of two equations with two unknowns: 2/3 1/3 12 1 2 3 3 0 3 3 0 y xx x y x     Now, we need to solve the system. For example, solve for x 2 in the first equation, and plug that in the second equation to get x 1 =1, then x 2 =1. 3. Constrained Optimization (2 exogenous variables) Find the values of ( x 1 , x 2) that maximizes the expression y=20x 1 1/2 x 2 1/2 subject to the following constraint: x 1

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## This note was uploaded on 04/19/2010 for the course ECON Econ 11 taught by Professor Mcdevitt during the Fall '07 term at UCLA.

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PS1Answers - UCLA Economics 11 Fall 2009 Professor Mazzocco...

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