Cover -- Half-title -- Series-title -- Tilte -- Copyright -- Dedication -- Contents -- Introduction -- OVERLAPPING GENERATIONS AND MACRO-ECONOMICS -- OVERLAPPING GENERATIONS IN OTHER FIELDS -- OUTLINE OF THE BOOK -- Acknowledgments -- ONE Competitive Equilibria -- 1.1 THE MODEL -- 1.1.1 Two-period-lived Individuals -- 1.1.2 Neo-classical Technology -- 1.1.3 Firms -- 1.2 MAIN ASSUMPITIONS -- 1.2.1 The Assumptions on the Utility Function -- 1.2.2 The Assumptions on the Production Function -- 1.3 THE BEHAVIOR OF THE AGENTS AT PERIOD t -- 1.3.1 The Young Individuals -- 1.3.2 The Inter-temporal Elasticity of Substitution -- 1.3.3 The Properties of the Savings Function -- 1.3.4 The Old Individuals -- 1.3.5 The Firms -- 1.4 THE TEMPORARY EQUILIBRIUM -- 1.5 THE INTER-TEMPORAL EQUILIBRIUM WITH PERFECT FORESIGHT -- 1.5.1 Existence of Equilibria -- 1.5.2 Uniqueness of the Inter-temporal Equilibrium -- 1.6 CAPITAL DYAMICS AT A RATIONAL INTER-TEMPORAL EQUILIBRIUM -- 1.6.1 Steady States and Stability -- 1.6.2 Dynamics -- 1.6.3 The Behavior Near 0 -- 1.6.4 A Quick Look at the Empirics of Growth -- 1.7 COMPARISON OF MYOPIC AND PERFECT FORESIGHT -- 1.7.1 The Steady States -- 1.7.2 Local Stability -- 1.7.3 Uniqueness of the Steady State -- 1.8 APPLICATIONS AND EXTENSIONS -- 1.8.1 Myopic and Perfect Foresight in an Example -- 1.8.2 A Demographic Shock -- 1.8.3 Non-separable Utility Function -- 1.8.4 Homothetic Preferences -- 1.8.5 Heterogeneous Agents -- 1.8.6 Technical Progress -- 1.8.7 Imperfect Credit Market -- 1.8.8 Three-period-lived Households -- 1.8.9 Borrowing Constraints in the Three-period Model -- 1.9 CONCLUSION -- TWO Optimality -- 2.1 OPTIMALITY OF STATIONARY PATHS -- 2.1.1 Feasible Long-run Capital Stock -- 2.1.2 The Optimal Stationary Path: The Golden Age -- 2.1.3 Under-and Over-accumulation of Capital -- 2.2 OPTIMALITY OF THE DYNAMICS.

2.2.1 Dynamic Efficiency -- 2.2.2 Pareto Optimality of Dynamics -- 2.3 THE PLANNING PROBLEM -- 2.3.1 The Objective Function -- 2.3.2 Properties of the Value Function -- 2.3.3 Existence and Monotonicity of Optimal Paths -- 2.3.4 Limit of the Optimal Path and Optimal Steady State -- 2.4 MARGINAL ANALYSIS OF OPTIMAL SOLUTIONS -- 2.4.1 The Optimality Conditions -- 2.4.2 The Planner's Stationary Solution -- 2.4.3 Local Dynamics -- 2.4.4 A Graphical Exposition -- 2.5 UNBOUNDED OPTIMAL GROWTH -- 2.5.1 Existence of Optimal Paths When sigma >1 -- 2.5.2 Existence of Optimal Paths When sigma 0 -- 2.6.2 Application: The Optimal Speed of Convergence -- 2.6.3 Application: Rise in Beta -- 2.6.4 A Mixed CES-Linear Production Function -- 2.6.5 Optimal Growth in the Ak Model -- 2.7 CONCLUSION -- THREE Policy -- 3.1 LUMP-SUM TRANSFERS AND THE SECOND WELFARE THEOREM -- 3.1.1 Equilibrium with Lump-sum Transfers -- 3.1.2 The Second Welfare Theorem -- 3.1.3 The Direction of Optimal Transfers in the Long Run -- 3.1.4 Reversal of Optimal Transfers Over Time: An Example -- 3.2 PENSIONS -- 3.2.1 Fully Funded System -- 3.2.2 Pay-as-you-go System: Existence of Equilibrium -- 3.2.3 Pay-as-you-go Systems with Constant Pensions -- 3.2.4 Capital Accumulation and Pay-as-you-go Pensions -- 3.2.5 Further Comments -- 3.3 PUBLIC SPENDING -- 3.3.1 Public Spending in the Competitive Economy -- 3.3.2 Public Spending: Optimal Financing -- 3.3.3 Second-best Policies -- 3.4 STUDY OF THE SECOND-BEST PROBLEM -- 3.4.1 Restating the Problem -- 3.4.2 Three Issues -- 3.4.3 A Standard Approach to the Problem -- 3.4.4 An Auxiliary Problem -- 3.5 APPLICATIONS AND EXTENSIONS.

3.5.1 Optimal Growth Rate of Population -- 3.5.2 Application: The Tax on the First Old Generation -- 3.5.3 Application: Financing Future Spending -- 3.5.4 Proportional Government Spending -- 3.6 CONCLUSION -- FOUR Debt -- 4.1 DIAMOND'S MODEL WITH DEBT -- 4.1.1 The Model -- 4.1.2 The Temporary Equilibrium -- 4.1.3 The Inter-temporal Equilibrium with Perfect Foresight -- 4.2 THE INTER-TEMPORAL BUDGET CONSTRAINT OF THE GOVERNMENT -- 4.2.1 Debt with the Two Types of Lump-sum Taxes -- 4.2.2 Debt with a Restriction of Only One Type of Lump-sum Tax -- 4.2.3 Ponzi Games -- 4.3 CONSTANT DEFICIT POLICIES -- 4.3.1 Balanced Budget Policies: Local Analysis -- 4.3.2 Balanced Budget Policies: Graphical Illustration -- 4.3.3 Non-zero Deficit: Local Analysis -- 4.3.4 Non-zero Deficit: Graphical Illustration -- 4.3.5 Ponzi Debt, Money, and Bubbles -- 4.4 CONSTANT DEBT POLICIES -- 4.4.1 Sustainability in the Short Run -- 4.4.2 Sustainability in the Long Run -- 4.4.3 Characteristics of Inter-temporal Equilibria -- 4.4.4 Policy Implications -- 4.5 APPLICATIONS AND EXTENSIONS -- 4.5.1 Constant Debt-Output Ratio -- 4.5.2 Deficits and Cycles -- 4.6 CONCLUSION -- Five Further Issues -- 5.1 DYNASTIC ALTRUISM: A BEQUEST MOTIVE -- 5.1.1 Modeling Voluntary Bequests -- 5.1.2 Marginal Analysis of Bequests -- 5.1.3 Altruism and the Neutrality of Economic Policy -- 5.1.4 When are Bequests Positive? -- 5.2 HUMAN CAPITAL AND EDUCATION -- 5.2.1 Modeling Education -- 5.2.2 Parental Funding: Private vs Public Education -- 5.2.3 Market Funding -- 5.2.4 The Tradeoff between Studying and Working -- 5.3 INTER-GENERATIONAL EXTERNALITIES -- 5.3.1 Inter-generational Taste Externalities in the Competitive Economy -- 5.3.2 The Optimal Allocation -- 5.3.3 Extensions -- 5.3.4 Conclusion -- 5.4 MACRO-ECONOMICS AND GENERAL EQUILIBRIUM -- 5.4.1 Modeling Arrow-Debreu Market Equilibria.

5.4.2 Arrow-Debreu Market Equilibria from… -- 5.4.3 Sequence Equilibrium from… -- 5.4.4 Arrow -Debreu Equilibria from… -- 5.4.5 Example -- 5.4.6 Conclusion -- Technical Appendices -- A.1 production functions -- A.1.1 Homogeneity -- A.1.2 Limits of f(k)and f(k) -- A.1.3 The Marginal Productivity of Labor -- A.1.4 The Limit of ω(k)/k -- A.1.5 The Cobb-Douglas Function as a Limit Case -- A.2 CALCULUS -- A 2.1 The Mean Value Theorem for Derivatives -- A.2.2 The Implicit Function Theorem -- A.2.3 Limits, lim sup, and lim inf -- A.2.4 Limit Points of Multi-dimensional Sequences -- A.3 DYNAMICAL ANALYSIS -- A.3.1 Monotonic Dynamics -- A.3.2 Local Stability (Dimension One) -- A.3.3 Linear Dynamics in the Plane -- A.3.4 Local Stability of Non-linear Dynamics (Dimension 2) -- A.3.5 Bifurcations of Monotonic Dynamics -- A.4 DYNAMIC OPTIMIZATION -- A.4.1 The Value Function -- A.4.2 Necessary and Sufficient Conditions for Optimality -- A.5 CALIBRATION AND SIMULATION -- A.5.1 The Cobb-Douglas Model -- A.5.2 The Model with a CES Production Function -- A.5.3 Introduction of Policies in the Model with CES Production -- A.5.4 Numerical Solution to Non-linear Forward-looking Models -- A.6 STATISTICS -- A.6.1 Dynamics of Distributions -- A.6.2 Normal and Log-normal Distributions -- A.1 PRODUCTION FUNCTIONS -- A.1.1 Homogeneity -- A.1.2 Limits off f(k) and f(k) -- A.1.3 The Marginal Productivity of Labor -- A.1.4 The Limit of omega (k)/k -- A.1.5 The Cobb-Douglas Function as a Limit Case -- List of Definitions -- List of Propositions -- List of Assumptions -- Bibliography -- Author Index -- Subject Index.