Contents. Preface... Part I Single-Objective Optimization
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1 Preface... xi Part I Single-Objective Optimization 1 Scarcity and Efficiency The Mathematical Programming Problem Mathematical Programming Models in Economics The Diet Problem The Neoclassical Theory of the Household The Neoclassical Theory of the Firm The Theory of Comparative Advantage The Giffen Paradox The Transportation Problem Portfolio Selection Model Input Output Analysis and Mathematical Programming Data Envelopment Analysis Classification of Mathematical Programming Problems References and Further Reading Kuhn Tucker Conditions The Kuhn Tucker Theorem Rationale of the Kuhn Tucker Conditions Kuhn Tucker Conditions and a Saddle Point of the Lagrange Function Kuhn Tucker Conditions for the General Mathematical Programming Problem The Kuhn Tucker Conditions and Economic Analysis Peak Load Pricing Revenue Maximization under a Profit Constraint... 39
2 viii Behavior of the Firm under Regulatory Constraint Environmental Regulation: The Effects of Different Restrictions References and Further Reading Convex Programming Basic Definitions and Properties Kuhn Tucker Conditions for a Convex Programming Problem Duality Theory Economic Interpretation of Duality in Convex Programming References and Further Reading Linear Programming The General Linear Programming Problem Implications of Linearity Assumption for Economic Analysis Duality in Linear Programming The More-for-Less Paradox Computational Procedure: The Simplex Method Some Applications of Linear Programming in Economics The Theory of Comparative Advantage The Giffen Paradox Leontief Pollution Model References and Further Reading Data Envelopment Analysis Productivity and Technical and Allocative Efficiency Basic DEA Models The Input-Oriented Model under a Constant Returns-to- Scale Assumption The Output-Oriented Model under a Constant Returns-to-Scale Assumption The Additive Model under a Constant Returns-to-Scale Assumption DEA Models under a Variable Returns-to-Scale Assumption Production Technologies and Efficiency Measurement Technical versus Environmental Efficiency, or How to Measure Ecoefficiency Composition of Technical and Environmental Efficiency Comprehensive Measurement of Ecoefficiency References and Further Reading Geometric Programming The Principle of Geometric Programming The Theory of Geometric Programming
3 ix 6.3 Models of Geometric Programming in Economics The Economic Lot Size Problem The Minimization of Cost The Economic Interpretation of Dual Variables as Elasticity Coefficients An Open Input Output Model with Continuous Substitution between Primary Factors Transformation of Some Optimization Problems into Standard Geometric Programming Models References and Further Reading Part II Multiobjective Optimization 7 Fundamentals of Multiobjective Optimization Examples of Multiobjective Programming Models in Economics Welfare Economics Quantitative Economic Policy Optimal Monetary Policy Optimal Behavior of a Monopolist Facing a Bicriteria Objective Function Leontief Pollution Model with Multiple Objectives A Nonlinear Model of Environmental Control Kuhn Tucker Conditions for the Multiobjective Programming Problem Duality for Multiobjective Optimization Problems Duality for Multiobjective Optimization Problems in Parametric Form Duality Theory for Convex Lexicographic Programming Behavior of the Firm Facing a Bicriteria Objective Function under Regulatory Constraint References and Further Reading Multiobjective Linear Programming Linear Vector Optimization Problems Duality in Multiple-Objective Linear Programming Interactive Procedures and the Zionts Wallenius Method The Leontief Pollution Model with Multiple Objectives References and Further Reading Multiobjective Geometric Programming Vector Minimization Problems in Geometric Programming Duality for Multiobjective Geometric Programming in Parametric Form
4 x 9.3 A Nonlinear Model of Environmental Control Optimal Behavior of a Monopolist Facing a Bicriteria Objective Function References and Further Reading Index
5
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