1) Use the Lagrange-multiplier method to find the stationary values of z: a) z=xy, subject to x+2y=2 b) z=x(y+4), subject to x+y=8 2) Use the bordered Hessian to determine whether the stationary value of z obtained in each part of the previous Exercise is a maximum or a minimum

1) Use the Lagrange-multiplier method to find the stationary values of z: a) z=xy, subject to x+2y=2 b) z=x(y+4), subject to x+y=8 2) Use the bordered Hessian to determine whether the stationary value of z obtained in each part of the previous Exercise is a maximum or a minimum

MACROECONOMICS FOR TODAY

10th Edition

ISBN:9781337613057

Author:Tucker

Publisher:Tucker

Chapter2: Productions Possibilities, Opportunity Costs, And Economic Growth

Section: Chapter Questions

Problem 3SQ

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Question

1) Use the Lagrange-multiplier method to find the stationary values of z:
a) z=xy, subject tox+2y=2
b) z=x(y+4), subject to x+y=8
2) Use the bordered Hessian to determine whether the stationary value of z obtained in each part of the previous Exercise is a maximum or a
minimum

Explain the effects of imposing a constraint in an optimization problem. Give at least one economic
example.

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