A theory of economic growth

Cover......Page 1
Half-title......Page 3
Series-title......Page 4
Tilte......Page 5
Copyright......Page 6
Dedication......Page 7
Contents......Page 9
OVERLAPPING GENERATIONS AND MACRO-ECONOMICS......Page 15
OVERLAPPING GENERATIONS IN OTHER FIELDS......Page 17
OUTLINE OF THE BOOK......Page 18
Acknowledgments......Page 19
1.1 THE MODEL......Page 21
1.1.1 Two-period-lived Individuals......Page 22
1.1.2 Neo-classical Technology......Page 23
1.2.1 The Assumptions on the Utility Function......Page 24
1.2.2 The Assumptions on the Production Function......Page 26
1.3.1 The Young Individuals......Page 30
1.3.2 The Inter-temporal Elasticity of Substitution......Page 31
1.3.3 The Properties of the Savings Function......Page 32
1.3.5 The Firms......Page 35
1.4 THE TEMPORARY EQUILIBRIUM......Page 36
1.5 THE INTER-TEMPORAL EQUILIBRIUM WITH PERFECT FORESIGHT......Page 39
1.5.1 Existence of Equilibria......Page 40
1.5.2 Uniqueness of the Inter-temporal Equilibrium......Page 42
1.6.1 Steady States and Stability......Page 47
1.6.2 Dynamics......Page 49
1.6.3 The Behavior Near 0......Page 54
1.6.4 A Quick Look at the Empirics of Growth......Page 57
1.7 COMPARISON OF MYOPIC AND PERFECT FORESIGHT......Page 59
1.7.1 The Steady States......Page 61
1.7.2 Local Stability......Page 62
1.7.3 Uniqueness of the Steady State......Page 63
1.8.1 Myopic and Perfect Foresight in an Example......Page 65
1.8.2 A Demographic Shock......Page 70
1.8.3 Non-separable Utility Function......Page 71
1.8.4 Homothetic Preferences......Page 73
1.8.5 Heterogeneous Agents......Page 74
1.8.6 Technical Progress......Page 76
1.8.7 Imperfect Credit Market......Page 77
1.8.8 Three-period-lived Households......Page 84
1.8.9 Borrowing Constraints in the Three-period Model......Page 86
1.9 CONCLUSION......Page 90
TWO Optimality......Page 92
2.1 OPTIMALITY OF STATIONARY PATHS......Page 93
2.1.1 Feasible Long-run Capital Stock......Page 94
2.1.2 The Optimal Stationary Path: The Golden Age......Page 97
2.1.3 Under-and Over-accumulation of Capital......Page 100
2.2.1 Dynamic Efficiency......Page 102
2.2.2 Pareto Optimality of Dynamics......Page 106
2.3 THE PLANNING PROBLEM......Page 110
2.3.1 The Objective Function......Page 111
2.3.2 Properties of the Value Function......Page 112
2.3.3 Existence and Monotonicity of Optimal Paths......Page 115
2.3.4 Limit of the Optimal Path and Optimal Steady State......Page 119
2.4 MARGINAL ANALYSIS OF OPTIMAL SOLUTIONS......Page 121
2.4.1 The Optimality Conditions......Page 122
2.4.3 Local Dynamics......Page 126
2.4.4 A Graphical Exposition......Page 128
2.5.1 Existence of Optimal Paths When sigma >1......Page 132
2.5.2 Existence of Optimal Paths When sigma < 1 (and y…......Page 134
2.5.3 Existence of Optimal Paths When  sigma = 1......Page 135
2.5.5 The Long-run Growth Rate......Page 136
2.6 APPLICATIONS AND EXTENSIONS......Page 137
2.6.1 Properties of the Policy Functions When f (0) > 0......Page 138
2.6.2 Application: The Optimal Speed of Convergence......Page 140
2.6.3 Application: Rise in Beta......Page 141
2.6.4 A Mixed CES–Linear Production Function......Page 142
2.6.5 Optimal Growth in the Ak Model......Page 144
2.7 CONCLUSION......Page 147
3.1.1 Equilibrium with Lump-sum Transfers......Page 149
3.1.2 The Second Welfare Theorem......Page 156
3.1.3 The Direction of Optimal Transfers in the Long Run......Page 158
3.1.4 Reversal of Optimal Transfers Over Time: An Example......Page 159
3.2 PENSIONS......Page 160
3.2.1 Fully Funded System......Page 161
3.2.2 Pay-as-you-go System: Existence of Equilibrium......Page 163
3.2.3 Pay-as-you-go Systems with Constant Pensions......Page 164
3.2.4 Capital Accumulation and Pay-as-you-go Pensions......Page 170
3.2.5 Further Comments......Page 172
3.3.1 Public Spending in the Competitive Economy......Page 175
3.3.2 Public Spending: Optimal Financing......Page 178
3.3.3 Second-best Policies......Page 179
3.4.1 Restating the Problem......Page 181
3.4.2 Three Issues......Page 182
3.4.3 A Standard Approach to the Problem......Page 185
3.4.4 An Auxiliary Problem......Page 187
3.5 APPLICATIONS AND EXTENSIONS......Page 191
3.5.1 Optimal Growth Rate of Population......Page 192
3.5.2 Application: The Tax on the First Old Generation......Page 193
3.5.3 Application: Financing Future Spending......Page 194
3.5.4 Proportional Government Spending......Page 195
3.6 CONCLUSION......Page 198
FOUR Debt......Page 199
4.1.1 The Model......Page 201
4.1.2 The Temporary Equilibrium......Page 202
4.1.3 The Inter-temporal Equilibrium with Perfect Foresight......Page 203
4.2 THE INTER-TEMPORAL BUDGET CONSTRAINT OF THE GOVERNMENT......Page 204
4.2.1 Debt with the Two Types of Lump-sum Taxes......Page 206
4.2.2 Debt with a Restriction of Only One Type of Lump-sum Tax......Page 210
4.2.3 Ponzi Games......Page 212
4.3 CONSTANT DEFICIT POLICIES......Page 213
4.3.1 Balanced Budget Policies: Local Analysis......Page 215
4.3.2 Balanced Budget Policies: Graphical Illustration......Page 218
4.3.3 Non-zero Deficit: Local Analysis......Page 223
4.3.4 Non-zero Deficit: Graphical Illustration......Page 228
4.3.5 Ponzi Debt, Money, and Bubbles......Page 231
4.4.1 Sustainability in the Short Run......Page 236
4.4.2 Sustainability in the Long Run......Page 239
4.4.3 Characteristics of Inter-temporal Equilibria......Page 243
4.4.4 Policy Implications......Page 246
4.5.1 Constant Debt–Output Ratio......Page 250
4.5.2 Deficits and Cycles......Page 253
4.6 CONCLUSION......Page 256
Five Further Issues......Page 258
5.1.1 Modeling Voluntary Bequests......Page 259
5.1.2 Marginal Analysis of Bequests......Page 266
5.1.3 Altruism and the Neutrality of Economic Policy......Page 268
5.1.4 When are Bequests Positive?......Page 272
5.2 HUMAN CAPITAL AND EDUCATION......Page 276
5.2.1 Modeling Education......Page 277
5.2.2 Parental Funding: Private vs Public Education......Page 279
5.2.3 Market Funding......Page 289
5.2.4 The Tradeoff between Studying and Working......Page 294
5.3 INTER-GENERATIONAL EXTERNALITIES......Page 300
5.3.1 Inter-generational Taste Externalities in the Competitive Economy......Page 301
5.3.2 The Optimal Allocation......Page 306
5.3.3 Extensions......Page 309
5.3.4 Conclusion......Page 310
5.4 MACRO-ECONOMICS AND GENERAL EQUILIBRIUM......Page 311
5.4.1 Modeling Arrow–Debreu Market Equilibria......Page 312
5.4.2 Arrow–Debreu Market Equilibria from…......Page 314
5.4.3 Sequence Equilibrium from…......Page 315
5.4.4 Arrow –Debreu Equilibria from…......Page 317
5.4.5 Example......Page 320
5.4.6 Conclusion......Page 324
A.1.1 Homogeneity......Page 325
A.1.2 Limits off f(k) and f(k)......Page 327
A.1.3 The Marginal Productivity of Labor......Page 328
A.1.4 The Limit of omega (k)/k......Page 329
A.1.5 The Cobb–Douglas Function as a Limit Case......Page 330
A.2.2 The Implicit Function Theorem......Page 331
A.2.3 Limits, lim sup, and lim inf......Page 332
A.3.1 Monotonic Dynamics......Page 334
A.3.2 Local Stability (Dimension One)......Page 335
A.3.3 Linear Dynamics in the Plane......Page 336
A.3.4 Local Stability of Non-linear Dynamics (Dimension 2)......Page 340
A.3.5 Bifurcations of Monotonic Dynamics......Page 342
A.4.1 The Value Function......Page 346
A.4.2 Necessary and Sufficient Conditions for Optimality......Page 355
A.5.1 The Cobb–Douglas Model......Page 358
A.5.2 The Model with a CES Production Function......Page 360
A.5.3 Introduction of Policies in the Model with CES Production......Page 361
A.5.4 Numerical Solution to Non-linear Forward-looking Models......Page 363
A.6.1 Dynamics of Distributions......Page 364
A.6.2 Normal and Log-normal Distributions......Page 365
List of Definitions......Page 367
List of Propositions......Page 369
List of Assumptions......Page 373
Bibliography......Page 375
Author Index......Page 389
Subject Index......Page 393