Handbook of Mathematical Economics Volume 1 1st Edition by Kenneth Arrow, Intriligator ISBN 0444861262 9780444861269

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Product details:
ISBN 10: 0444861262
ISBN 13: 9780444861269
Author: Kenneth Arrow, Intriligator

The Handbook of Mathematical Economics aims to provide a definitive source, reference, and teaching supplement for the field of mathematical economics. It surveys, as of the late 1970’s the state of the art of mathematical economics. This is a constantly developing field and all authors were invited to review and to appraise the current status and recent developments in their presentations. In addition to its use as a reference, it is intended that this Handbook will assist researchers and students working in one branch of mathematical economics to become acquainted with other branches of this field. Volume 1 deals with Mathematical Methods in Economics, including reviews of the concepts and techniques that have been most useful for the mathematical development of economic theory.

Handbook of Mathematical Economics Volume 1 1st Edition Table of contents:

Part I: General Equilibrium and Welfare Economics

1. Introduction to Mathematical Economics

   • The Role of Mathematics in Economic Theory
   • History of Mathematical Economics
   • Mathematical Methods and Tools in Economics

2. General Equilibrium Theory

   • The Walrasian General Equilibrium Model
   • Existence and Uniqueness of Equilibria
   • Comparative Statics in General Equilibrium
   • Welfare Theorems and Efficiency Criteria

3. Pareto Optimality and Welfare Economics

   • The Concept of Pareto Efficiency
   • Social Welfare Functions
   • Market Failures and Externalities
   • Public Goods and Their Provision

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Part II: Consumer and Producer Theory

4. Consumer Theory

   • Utility Functions and Indifference Curves
   • The Budget Constraint and Consumer Choice
   • Demand Functions and Price Effects
   • The Slutsky Equation and Expenditure Functions

5. Producer Theory

   • Production Functions and Returns to Scale
   • Cost Minimization and Profit Maximization
   • Duality in Production Theory
   • Market Supply Curves and Firm Behavior

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Part III: Game Theory and Strategic Behavior

6. Introduction to Game Theory

   • The Nash Equilibrium Concept
   • Static vs Dynamic Games
   • Dominant Strategies and Rationalizability
   • Mixed Strategies and Probabilistic Choices

7. Applications of Game Theory in Economics

   • Oligopoly and Market Structure
   • Auctions and Bidding Strategies
   • Bargaining Theory
   • Mechanism Design and Market Design

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Part IV: Mathematical Methods in Economics

8. Optimization Techniques

   • Unconstrained and Constrained Optimization
   • The Lagrange Multiplier Method
   • Kuhn-Tucker Conditions
   • Applications to Consumer and Producer Theory

9. Differential Equations and Dynamic Systems

   • First and Second Order Differential Equations
   • Stability Analysis and Equilibrium Paths
   • Dynamic Models in Economics
   • Applications in Growth Theory and Economic Cycles

10. Mathematical Programming

    • Linear Programming: Theory and Applications
    • Nonlinear Programming Techniques
    • Integer and Mixed-Integer Programming
    • Applications to Resource Allocation and Planning

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Part V: Economic Applications and Extensions

11. Public Economics and Taxation

    • Optimal Taxation Theory
    • The Theory of Public Goods and Externalities
    • Redistribution and Income Inequality
    • Social Choice and Voting Systems

12. Monetary and Fiscal Policy

    • The Role of Money and Credit in the Economy
    • Central Banking and Interest Rates
    • Fiscal Policy and Government Spending
    • Models of Economic Fluctuations and Policy Responses

13. International Trade and Development Economics

    • Comparative Advantage and Trade Theory
    • Trade Policies and Welfare Effects
    • Economic Development Models
    • Growth Models for Developing Economies

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