Competitive Agents in Certain and Uncertain Markets

✍ Scribed by Robert G. Chambers

• Publisher: Oxford University Press
• Year: 2021
• Tongue: English
• Leaves: 390
• Category: Library

✦ Synopsis

For all its elaborate theories and models, economics always reduces to comparisons. Should we build A rather than B? Will I be better off if I eat D rather than C? How much will it cost me to produce F instead of E? At root, the ultimate goal of economics is simple: assessing the alternatives
and finding the best possible outcome. This basic mathematical concept underlies all introductions to the field of economics, yet as advanced students progress through the discipline, they often lose track of this foundational idea when presented with real-world complications and uncertainty.

In Competitive Agents in Certain and Uncertain Markets, Robert G. Chambers develops an integrated analytic framework for treating consumer, producer, and market equilibrium analyses as special cases of a generic optimization problem. He builds on lessons learned by all beginning students of
economics to show how basic concepts can still be applied even in complex and highly uncertain conditions. Drawing from optimization theory, Chambers demonstrates how the same unified mathematical framework applies to both stochastic and non-stochastic decision settings. The book borrows from both
convex and variational analysis and gives special emphasis to differentiability, conjugacy theory, and Fenchel's Duality Theorem. Throughout, Chambers includes practical examples, problems, and exercises to make abstract material accessible.

Bringing together essential theoretical tools for understanding decision-making under uncertainty, Competitive Agents in Certain and Uncertain Markets provides a unified framework for analyzing a broad range of microeconomic decisions. This book will be an invaluable resource for advanced graduate
students and scholars of microeconomic theory.

✦ Table of Contents

Cover
Competitive Agents in Certain and Uncertain Markets
Copyright
Dedication
Contents
Preface
Acknowledgments
Chapter 1: What’s Covered
Chapter 2: Differentials and Convex Analysis
1 Correspondences
2 Differentiability?
3 Do You Prefer to Be Constrained or Penalized?
4 Convex Structures
4.1 Concave (Convex) Functions.
4.2 Differential Properties of Concave Functions and Directional Derivatives.
5 Conjugate Duality
5.1 A Brief Word about Dual Spaces
5.2 Concave Conjugates
5.2.1 Intuition and Sketch of a Demonstration
5.3 A More Formal Argument
5.4 And for Nonconcave Structures?
5.5 Two Economically Important Concave–Conjugate Pairs
5.6 Convex Conjugates
5.7 Fenchel’s Duality Theorem
6 Chapter Commentary
Chapter 3: Orders and Their Representations
1 What Is an Order?
2 Some Structure (Assumptions)
3 Cardinal Representations of Orders
4 Properties of d (x, y; g)
5 Superdifferentiability and d ( x, y; g)
5.1 A Basic Result on Internal (Shadow) Prices
6 Turning the Bowl Over
7 Three Types of Convexity Restrictions
8 Why Three Types of Convexity?
9 Chapter Commentary
Chapter 4: Squiggly Economics
1 A Standard Problem: Expenditure Minimization
2 Expenditure Minimization without Lagrangians
2.1 McKenzie Expenditure from an Indicator Function
2.2 McKenzie Expenditure Function from a Distance Function
2.3 d and E as Concave Conjugates
2.4 Why Is Conjugacy (Duality) Important?
2.5 E (q; y)′s Behavior in y
3 A Standard Problem: Revenue Maximization
4 A Standard Problem: Profit Maximization
5 Superdifferentials, Subdifferentials, and Economic Behavior
6 Chapter Commentary
Chapter 5: The Consumer Problem
1 The Budget Correspondence
2 Rational Demand
3 Price-Dependent Rational Demand
4 What’s Rational?
5 A Utility Function?
6 Marshallian Demand and the Slutsky–Hicks Equation
7 Profit Maximization and Utility Maximization
8 Revealed Preference
9 Constructing a Utility Function from E(p; y) or R(p; x)
10 A Structural Restriction
11 Chapter Commentary
Chapter 6: The (Nonstochastic) Producer Problem
1 The Canonical Problem
2 Defining the Technology
2.1 Properties of Output Sets
2.1.1 No Fixed Costs and No Free Lunch (No Land of Cockaigne)
2.1.2 Disposability of Outputs
2.1.3 Input Disposability and Input Congestion
2.1.4 Bounds on Output Sets
2.1.5 Curvature Properties of Output Sets
2.1.6 Y ∶ ℝN ⇉ ℝM a closed correspondence
3 Function Representations of the Technology
3.1 The directional input distance function
3.2 Properties of d (x, y; g)
4 Structure of Technology
4.1 Homotheticity
4.1.1 Output homotheticity
4.1.2 Quasi-input homotheticity
4.1.3 Quasi-output homotheticity
4.2 Nonjointness
4.2.1 Input nonjointness
4.2.2 Output nonjoint
4.2.3 Input-price-nonjoint
4.2.4 Output-price-nonjoint
5 A Closer Look at the Canonical Problem
6 Comparative Statics and the LeChatelier Principle for the Canonical Problem
7 Revealed Preference and Producers
8 Chapter Commentary
Chapter 7: Equilibrium, Efficiency, and Welfare
1 Partial Equilibrium
2 Consumer Surplus, Producer Surplus, and Equilibrium
3 General Equilibrium and the First and Second Welfare Theorems
4 Kinks and Equilibrium
5 It’s Obvious, Right?
6 Chapter Commentary
Chapter 8: Preferences and Production under Uncertainty
1 The Economic Environment
2 Preferences
2.1 Choosing a Numeraire
2.2 The Cardinal Representation
2.3 Structural Restrictions
3 Production
3.1 The Cardinal Measure
3.2 Structure
4 Chapter Commentary
Chapter 9: Decision Making and Equilibrium under Uncertainty
1 The Portfolio Problem
1.1 The Budget Correspondence
1.2 Arbitrages and the Land of Cockaigne
1.3 Rational Behavior
2 The Producer Problem
3 Production and Portfolio Decisions
3.1 The Budget Constraints and Arbitrage
3.2 Rational Production Decisions
4 Complete Ordering and Production–Portfolio Decisions
5 Equilibrium
6 A Closing Word on Uncertainty in Economics
7 Chapter Commentary
Chapter 10: Quality, Valuation, and Welfare
1 Quality-Differentiated Production
2 Household Production
3 Welfare, Real Benefits, and Valuation
3.0.1 Real Benefit Measures
3.1 From Observed Behavior to Practical Measures
3.2 Benefits and the Kaldor Compensation Criterion
3.3 Nontraded Goods and Services
3.3.1 Marketed Goods Fixed
3.3.2 Marketed Goods Variable
3.4 Willingness-to-Pay and Willingness-to-Accept Discrepancies: Anomaly or Artifact?
4 Valuation under Uncertainty
5 Chapter Commentary
Bibliography
Notation
Index