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Unformatted text preview: Constrained Optimization Constrained Optimization: Almost all of microeconomics can be described as constrained optimization: One definition of economics I’ve heard: Economics is the study of efficient allocations of scarce resources. Efficient means optimal. Scarce means there is a binding constraint. ECG 700 Lecture 1 - Math Review 1/ 34 Constrained Optimization How does a consumer select a consumption bundle from his affordable set to maximize utility? How does a monopolist set prices to maximize profits given demand? How can a manager select inputs so as to minimize costs and achieve a target output? How can stockholders set up an incentive contract so as to induce their CEO to exert the optimal amount of effort? ECG 700 Lecture 1 - Math Review 2/ 34 Constrained Optimization Mathematically, this can be state as follows: Assume there exists a real-valued function f : A → R which characterizes the preferences of the decision-maker. The decision maker solves the problem: max a ∈ A f ( x ) Almost always, A = R n , for some n ....
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This note was uploaded on 10/22/2009 for the course ECG 700 taught by Professor Morrill during the Fall '09 term at N.C. State.
- Fall '09