Conjugate Duality in Economic Analysis

Erscheinungsjahr 2026
ISBN: 978-3-032-21395-2
Verlag: Springer

Buch, Englisch, 530 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 1019 g

Reihe: Contributions to Economics

An original contribution to economics, this book demonstrates how convex optimization via duality provides a unified methodology for discovering and developing economic and econometric theory. It presents diverse applications in microeconomics, econometrics, finance, and mathematical programming. A central theme is that conjugate duality enables the discovery of new economic relationships. One sets up a minimization problem (the "primal") to embody an economic condition. From the primal, one derives an equivalent but different problem (the "dual"). By solving the dual, one both discovers and proves a new economic result. The primal and the dual are solved simultaneously by setting them equal and factoring. The requirement that each factor must be zero at the solution yields necessary and sufficient conditions for the solution. Taking a subtle and sophisticated approach to optimization, this book will interest academic economists in many fields—microeconomics, international trade, finance, econometrics, and mathematical economics—as well as scholars in other disciplines such as operations research, statistics, mathematics, and electrical engineering.

Zielgruppe

Research

Autoren/Hrsg.

Dieffenbach, Bruce C.

Fachgebiete

• Wirtschaftswissenschaften Volkswirtschaftslehre Volkswirtschaftslehre Allgemein Mikroökonomie
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Wirtschaftswissenschaften Wirtschaftswissenschaften Wirtschaftswissenschaften: Allgemeines
• Wirtschaftswissenschaften Volkswirtschaftslehre Volkswirtschaftslehre Allgemein Wirtschaftstheorie, Wirtschaftsphilosophie
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Optimierung

Inhaltsverzeichnis

Part I – Optimization by Duality: Chapter 1: Discovery and Proof via Duality.- Chapter 2: No Duality Gap.- Chapter 3: Fenchel Factors.- Chapter 4: Conjugate Duality.- Chapter 5: Support.- Chapter 6: Epigraph.- Chapter 7: Subdifferential.- Chapter 8: Lagrangian.- Chapter 9: Karush-Kuhn-Tucker.- Part II – Linear Algebra: Chapter 10: Linear Transformation.- Chapter 11: Decomposition.- Chapter 12: Linear Equation.- Part III – Economic Applications: Chapter 13: Benefit and Cost.- Chapter 14: Diet.- Chapter 15: Activity Analysis.- Chapter 16: Zero-Sum Game.- Chapter 17: Assignment.- Chapter 18: Constant Elasticity of Substitution.- Part IV – Cone Representation: Chapter 19: Cone Representation of a Convex Set.- Chapter 20: Cone Representation of a Convex Function.- Part V – Local Analysis: Chapter 21: Directional Derivative and Subdifferential.- Chapter 22: Normal Cone.- Chapter 23: Subdifferential Calculus.- Chapter 24: Polyhedra.- Part VI – Euclidean Jordan Algebra: Chapter 25: Euclidean Jordan Algebra.- Chapter 26: Spectral Decomposition.- Chapter 27: Spectral Conjugate.- Chapter 28: Quadratic Function.- Chapter 29: Lorentz Euclidean Jordan Algebra.- Chapter 30: Hermitian Euclidean Jordan Algebra.- Part VII – Mathematical Programming: Chapter 31: Hahn-Banach.- Chapter 32: Ekeland Variational Principle.- Chapter 33: Homogeneous Fractional Programming.- Chapter 34: Fractional Programming.- Chapter 35: The Alternative.- Part VIII – Efficiency: Chapter 36: Efficiency Duality.- Chapter 37: Weak Efficiency.- Chapter 38: Efficiency.- Part IX – Production: Chapter 39: Domestic Product and Income.- Chapter 40: Shephard Duality.- Chapter 41: Heckscher-Ohlin via Shephard Duality.- Chapter 42: Factor-Intensive Production Function.- Chapter 43: Heckscher-Ohlin via Factor-Intensive Production Function.- Part X – Consumption: Chapter 44: Hicks and Marshall Decompositions.- Chapter 45: Consumption Demand.- Chapter 46: Indirect Utility.- Chapter 47: Benefit.- Part XI: Welfare Economics: Chapter 48: Resource Utilization.- Chapter 49: Welfare and Equilibrium.- Part XII: Core: Chapter 50: Core and Equilibrium.- Chapter 51: Bondareva-Shapley.- Part XIII – Econometrics: Chapter 52: Moment Space.- Chapter 53: Least-Squares Linear Regression.- Chapter 54: Multivariate Least-Squares Linear Regression.- Chapter 55: Instrumental Variables.- Chapter 56: Likelihood Statistical Inference.- Chapter 57: Conjugate Maximum Likelihood.- Chapter 58: Maximum-Likelihood Estimation of Linear Regression.- Part XIV: Finance: Chapter 59: Stochastic Discount Factor.- Chapter 60: Expected Utility.- Chapter 61: Price Bounds.- Chapter 62: Sharpe Ratio.- Chapter 63: Efficient-Portfolios Risk-Free Asset.- Chapter 64: Efficient Portfolios No Risk-Free Asset.- Chapter 65: Capital-Asset Pricing.- Chapter 66: Arbitrage Pricing Theory.- Part XV – Dynamics: Chapter 67: Stability.- Chapter 68: Balanced Growth.

Über Autor(innen)

Bruce C. Dieffenbach received his PhD in Economics from Harvard University, where he studied under Nobel laureate Kenneth Arrow. He has taught economics at the University of Pennsylvania and at the University at Albany, State University of New York and has published in , , and . His research spans finance, macroeconomics, and monetary economics.