ECO 3145 Lecture 6: Lecture 6.pdf

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13. 1, 13. 4: structure of the problem single constraint: Notation: example consumption problem: subject to. , for all i, and subject to and. Unlike the case of equality constraints, there is no need for. , since any number of inequality constraints can still leave a non-trivial range of variation for the choice variables. Kuhn-tucker (first-order necessary) conditions for a maximum: and with complementary slackness. , for all sign direction: diagram complementary slackness conditions. Minimizing a function f is equivalent to maximizing. Kuhn-tucker conditions compare the value of the objective function obtained under different combinations choose the combination/ solution with the highest value of the objective function. Tricks in theoretical papers in practice, it can be very tedious to check all the cases which arise in a kuhn-tucker optimization problem. Fortunately, economic intuition can often help us to narrow down the choices theoretical papers often assume away corner solutions e. g. the famous inada conditions have.

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