Contents
9.4 Stationary Discounted Optima and Equilibria
Acknowledgments
1 Why Study General Equilibrium?
2 The General Equilibrium Model
2.1 Commodities
2.3 Utility Functions
2.4 Economies
3.1 Definition of Pareto Optimality
3.2 Existence of Pareto Optimal Allocations; The Bolzano-Weierstrass Theorem
3.3 The Utility Possibility Frontier
3.4 The Calculation of Pareto Optima; Homogeneous Functions
3.5 Pareto Optimality and Optimality: Minkowski’s SeparationTheorem
3.6 The Structure of the Utility Possibility Frontier
3.7 Compactness of the Set of Feasible Allocations
4.1 The Definition of Competitive Equilibrium
4.2 Properties of Market Excess Demand and Equilibrium
4.3 Offer Curves
4.4 Equilibrium with Constant Returns to Scale
4.5 Computation of Competitive Equilibrium in SimpleExamples
4.6 Aggregate Input-Output Possibility Sets
4.7 An Incomplete Theorem on the Existence of Equilibrium
4.8 A Complete Theorem on the Existence of Equilibrium
4.9 An Example of Discontinuous Behavior of Equilibria
5.1 The FirstWelfare Theorem
5.2 The SecondWelfare Theorem
5.3 Another Complete Theorem on the Existence of Equilibrium
6.1 Kuhn-Tucker Theorem
6.2 Kuhn-Tucker Coefficients
6.3 The Kuhn-Tucker Interpretation of Competitive Equilibrium
6.4 The Differentiable Case
6.5 Proof of the Kuhn-Tucker Theorem
7.1 The Arrow-Debreu Model
7.2 Arrow Equilibrium
7.3 Insurance
7.4 Incomplete Markets and the Definition of Profit Maximization
8 Rational Expectations Equilibrium and the Permanent Income Hypothesis
8.1 The Permanent Income Hypothesis
8.2 Rational Expectations Equilibrium
8.3 Short-Run Equilibrium
8.4 Consumer Surplus
8.5 The Stability of Short-Run Equilibrium
9 Samuelson’s Overlapping Generations Model
9.1 Overlapping Generations with a Finite Time Horizon
9.2 Inefficiency with an Infinite Horizon
9.3 Pareto Optimal Equilibria
9.5 Nonuniqueness of Equilibrium
9.6 Discounted Optimality and Equilibrium
9.7 Undiscounted Optimality and Equilibrium
9.8 Uniqueness of Optimal Allocations
9.9 Existence of Optimal Allocations
10.1 The One-Sector Diamond and Optimal Growth Models
10.2 Inefficiency
10.3 Pareto Optimal Equilibria
10.4 Stationary Discounted Optima and Equilibria
10.5 Social Security
10.6 Population Growth
10.7 Discounted Optimal and Equilibrium Allocations
10.8 Discounted Optimal and Equilibrium Programs
10.9 Program Efficiency and the Hahn Problem
10.10 Euler’s Equation
10.11 Policy Functions and the Value Function
10.12 The Turnpike Theorem
10.13 Equilibrium, Optimality, and the Turnpike Theorem in the Undiscounted Case
10.14 Existence of Optimal Allocations and Programs
11 A Critical Assessment
References
Index