ansas11 - ECON 331 Written Assignment 11 - the answer 1....

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ECON 331 Written Assignment 11 - the answer - 1. The Lagrangian for this problem is L 2 x 2 y 1 x 2 y 2 The FOC satisfied by an extreme point are then L x 4 x 2 x 0 L y 1 2 y 0 L 1 x 2 y 2 0 L x 0 has two solutions: x 0 and 2. If x 0 , then from L 0 , y  1 .From L y 0 , 1/2 y 1/2 . Thus 0,1, 1/2 and 0, 1,1/2 are stationary points. If 2, then from L y 0 , y 1/2 1/4 and from L 0 , x 1 1/16 15 /4 . Thus the other two stationary points are ( 15 /4, 1/4,2 and 15 /4, . The bordered Hessian for this optimization problem is H 4 2 0 2 x 0 2 2 y 2 x 2 y 0 Doing a Laplace expansion by the first column | H | 4 2 2 2 y 2 y 0 2 x 0 2 x 2 2 y 4 2  4 y 2 2 x 4 x
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ansas11 - ECON 331 Written Assignment 11 - the answer 1....

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