400ps6-11 - ECON 400 Winter 2011 Problem Set VI (for...

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E C O N 4 0 0 H a r t m a n Winter 2011 Problem Set VI (for Monday, February 14) 1. Suppose the problem is to find the x and y that either maximize or minimize zx y subject to the constraint 0 mxy  where m is a positive parameter. a. Solve this problem by the method of direct substitution. (The x and y you find will depend on m .) Use the second order condition to determine whether the x and y you have found give a maximum or a minimum. b. Solve this problem using a Lagrange multiplier. Use the second order condition to determine whether the x and y you have found give a maximum or a minimum. c. Let * () x m and * y m denote the solution for x and y from part b, and let * m denote the Lagrange multiplier from part b. Substitute * x xm and * y ym into the expression to be maximized or minimized to get ** * () () zm xmym . Show that * * dz m dm  . 2. Suppose the problem is to find the x and y that either maximize or minimize zxy
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This note was uploaded on 04/04/2011 for the course ECON 400 taught by Professor Ellis,g during the Spring '08 term at University of Washington.

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