ECON
PracticeQuestion5.pdf

# PracticeQuestion5.pdf - Econ 326 Practice Question...

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Econ 326 Practice Question 5 (Chapter 11) Heejeong Kim 1. Find the extreme values (maxima or minima) of each of the following functions (a) z = x 2 + xy + 2 y 2 + 3 (b) z = - x 2 - y 2 + 6 x + 2 y (c) z = e 2 x - 2 x + 2 y 2 + 3 2. Express each of the following quadratic forms as a matrix product involving a sym- metric coeﬃcient matrix (form of X AX ) and determine whether the quadratic forms are positive or negative definite. (a) q = 3 u 2 - 4 uv + 7 v 2 (b) q = 6 xy - 5 y 2 - 2 x 2 (c) q = u 2 + 7 uv + 3 v 2 (d) q = 3 u 2 1 - 2 u 1 u 2 + 4 u 1 u 3 + 5 u 2 2 + 4 u 2 3 - 2 u 2 u 3 (e) q = 8 uv - u 2 - 31 v 2 (f) q = - u 2 + 4 uv - 6 uw - 4 v 2 - 7 w 2 3. Find the extreme values, if any, of the following functions. Check whether they are maxima or minima by the determinantal test. Also, find the Hessian matrix for each of the functions. (a) z = x 2 1 + 3 x 2 2 - 3 x 1 x 2 + 4 x 2 x 3 + 6 x 2 3 (b) z = 29 - ( x 2 1 + x 2 2 + x 2 3 ) (c) z = e 2 x + e - y + e w 2 - (2 x + 2 e w - y ) 4. Suppose that a perfectly competitive firm has a production function given by Q = L α K β where 0 < α < 1, 0 < β < 1, and α + β < 1. A firm pays W

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• Fall '15
• michaelsampson
• Economics, Marginal product, perfectly competitive firm, following functions

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