# PS1Answers - UCLA Economics 11 Fall 2010 Professor Mazzocco...

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Economics 11 – Fall 2010 Professor Mazzocco Problem Set 1 1. Unconstrained Optimization (2 exogenous variables) Find the values of ( x , z ) that maximizes the expression y = 24x 1/4 z 1/4 – 3x – 3z The F.O.C. are now a system of two equations with two unknowns: Eq 1: y x 6 x 3 / 4 z 1/ 4 3 0 Eq 2 : y z 6 x 1/ 4 z 3 / 4 3 0 Now, we need to solve the system. For example, solve for x in the first equation (Eq1): x 2 4 / 3 z 1/3 and then plug that in the second equation (Eq2) and solve for z: 6(2 4 / 3 z 1/ 3 ) 1/ 4 z 3 / 4 3 0 2 1/ 3 z 1/12 z 9 /12 1 2 z 8 /12 2 16/12 z 4 then get x=4 from Eq1 or Eq2. 2. Unconstrained Optimization (1 exogenous variable) a. Find the value of x that maximizes y =500−(10−2 x ) 2 F.O.C y x 4(10 2 x ) 0 So x*=5. b. Make sure it is a maximum by checking the Second Order Conditions and plotting the function. S.O.C

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## This note was uploaded on 10/18/2010 for the course ECON 11 taught by Professor Cunningham during the Spring '08 term at UCLA.

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PS1Answers - UCLA Economics 11 Fall 2010 Professor Mazzocco...

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