General Equilibrium, Overlapping Generations Models, and Optimal Growth Theory

Truman F. Bewley

    • Acknowledgments

    1. Why Study General Equilibrium?

    2. The General Equilibrium Model

    • Commodities
    • Allocations
    • Utility Functions
    • Economies

    3. Economic Efficiency

    • Definition of Pareto Optimality
    • Existence of Pareto Optimal Allocations; The Bolzano-Weierstrass Theorem
    • The Utility Possibility Frontier
    • The Calculation of Pareto Optima; Homogeneous Functions
    • Pareto Optimality and Optimality: Minkowski’s Separation Theorem
    • The Structure of the Utility Possibility Frontier
    • Compactness of the Set of Feasible Allocations
    • Problem Set

    4. Competitive Equilibrium

    • The Definition of Competitive Equilibrium
    • Properties of Market Excess Demand and Equilibrium
    • Offer Curves
    • Equilibrium with Constant Returns to Scale
    • Computation of Competitive Equilibrium in Simple Examples
    • Aggregate Input-Output Possibility Sets
    • An Incomplete Theorem on the Existence of Equilibrium
    • A Complete Theorem on the Existence of Equilibrium
    • An Example of Discontinuous Behavior of Equilibria
    • Problem Set

    5. The Welfare Theorems

    • The FirstWelfare Theorem
    • The SecondWelfare Theorem
    • Another Complete Theorem on the Existence of Equilibrium
    • Problem Set

    6. The Kuhn-Tucker Approach to General Equilibrium Theory

    • Kuhn-Tucker Theorem
    • Kuhn-Tucker Coefficients
    • The Kuhn-Tucker Interpretation of Competitive Equilibrium
    • The Differentiable Case
    • Proof of the Kuhn-Tucker Theorem
    • Problem Set

    7. Arrow-Debreu Equilibrium

    • The Arrow-Debreu Model
    • Arrow Equilibrium
    • Insurance
    • Incomplete Markets and the Definition of Profit Maximization
    • Problem Set

    8. Rational Expectations Equilibrium and the Permanent Income Hypothesis

    • The Permanent Income Hypothesis
    • Rational Expectations Equilibrium
    • Short-Run Equilibrium
    • Consumer Surplus
    • The Stability of Short-Run Equilibrium
    • Problem Set

    9. Samuelson’s Overlapping Generations Model

    • Overlapping Generations with a Finite Time Horizon
    • Inefficiency with an Infinite Horizon
    • Pareto Optimal Equilibria
    • Stationary Discounted Optima and Equilibria
    • Nonuniqueness of Equilibrium
    • Discounted Optimality and Equilibrium
    • Undiscounted Optimality and Equilibrium
    • Uniqueness of Optimal Allocations
    • Existence of Optimal Allocations
    • Problem Set

    10. The One-Sector Growth and Diamond Overlapping Generations Models

    • The One-Sector Diamond and Optimal Growth Models
    • Inefficiency
    • Pareto Optimal Equilibria
    • Stationary Discounted Optima and Equilibria
    • Social Security
    • Population Growth
    • Discounted Optimal and Equilibrium Allocations
    • Discounted Optimal and Equilibrium Programs
    • Program Efficiency and the Hahn Problem
    • Euler’s Equation
    • Policy Functions and the Value Function
    • The Turnpike Theorem
    • Equilibrium, Optimality, and the Turnpike Theorem in the Undiscounted Case
    • Existence of Optimal Allocations and Programs
    • Problem Set

    11. A Critical Assessment

    • References
    • Index
  • Cover: General Equilibrium, Overlapping Generations Models, and Optimal Growth Theory
  • A photo of the author

Truman F. Bewley is Alfred Cowles Professor of Economics at Yale University.