Lecture 4: Constrained Optimization I: Equality Constraints, Lagrange Theorem Lecture 5: Constrained Optimization II: Inequality Constraints, Kuhn-Tucker The-
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obtaining the derivative of TC with respect to 2 and we must set it equals to zero Page 27 CONSTRAINED OPTIMIZATION •
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The nature of the constrained optimization problem facing an airline planner is to minimize maximization and minimization problems in managerial economics
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Most (if not all) economic decisions are the result of an optimization problem subject to one or a series of constraints: • Consumers make decisions on what to
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Lecture 4: Constrained Optimization I: Equality Constraints, Lagrange Theorem Lecture 5: Constrained Optimization II: Inequality Constraints, Kuhn-Tucker The-
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That would be the Lagrangian Method Consider now a constrained optimization problem with equality constraints max x F(x)
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1 Optimization techniques with applications 1 Unconstrained Optimization For a microeconomist, the central assumption is that people, as decision makers, are
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Some important economic functions Slope and its use in economic analysis Derivatives of various functions Optimization techniques Constrained optimization
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Maximization of a function with a constraint is common in economic situations To indicate the dependence on these optimizing points on w, we write x∗(w)
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Constrained Optimization–an intuitive approach Max { f ( x ) b g ( x ) 0 x 0} Economic Interpretation of maximization problem profit maximizing multi-product firm with fixed inputs = vector of outputs 0 f(x) revenue b = vector of inputs (fixed in short run) g(x) inputs needed to produce output vector x Maximization
CONSTRAINED OPTIMIZATION: THEORY AND ECONOMIC EXAMPLES
CONSTRAINED OPTIMIZATION: THEORY AND ECONOMIC EXAMPLES Peter Kennedy These notes provide a brief review of methods for constrained optimization They cover equality-constrained problems only Part 1 outlines the basic theory Part 2 provides a number of economic examples to illustrate the methods
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