Lecture1a-2ps - Constrained Optimization Constrained...

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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
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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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