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巴罗-经济增长.pdf
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Contents
Preface xv
About theAuthors xvii
Introduction1
I.1 TheImportance of Growth 1
I.2 TheWorld Income Distribution 6
I.3Empirical Regularities about Economic Growth 12
I.4 A BriefHistory of Modern Growth Theory 16
I.5 SomeHighlights of the Second Edition 21
1Growth Models with Exogenous Saving Rates
(theSolow–Swan Model) 23
1.1 TheBasic Structure 23
1.2 TheNeoclassical Model of Solow and Swan 26
1.2.1 TheNeoclassical Production Function 26
1.2.2 TheFundamental Equation of the Solow–Swan Model 30
1.2.3Markets 31
1.2.4 TheSteady State 33
1.2.5 TheGolden Rule of Capital Accumulation
and DynamicInefficiency 34
1.2.6Transitional Dynamics 37
1.2.7Behavior of Input Prices During the Transition 40
1.2.8 PolicyExperiments 41
1.2.9 AnExample: Cobb–Douglas Technology 43
1.2.10Absolute and Conditional Convergence 44
1.2.11Convergence and the Dispersion of Per Capita Income 50
1.2.12Technological Progress 51
1.2.13 AQuantitative Measure of the Speed of Convergence 56
1.3 Modelsof Endogenous Growth 61
1.3.1Theoretical Dissatisfaction with Neoclassical Theory 61
1.3.2 The AK Model 63
1.3.3Endogenous Growth with Transitional Dynamics 66
1.3.4Constant-Elasticity-of-Substitution Production Functions 68
1.4 OtherProduction Functions . . . OtherGrowth Theories 71
1.4.1 TheLeontief Production Function and
the Harrod–DomarControversy 71
1.4.2 GrowthModels with Poverty Traps 74
vi Contents
1.5Appendix: Proofs of Various Propositions 77
1.5.1 ProofThat Each Input Is Essential for Production
with aNeoclassical Production Function 77
1.5.2Properties of the Convergence Coefficient
in the Solow–SwanModel 78
1.5.3 ProofThat Technological Progress Must
Be LaborAugmenting 78
1.5.4Properties of the CES Production Function 80
1.6 Problems81
2Growth Models with Consumer Optimization
(theRamsey Model) 85
2.1Households 86
2.1.1 Setupof the Model 86
2.1.2First-Order Conditions 89
2.2 Firms 94
2.3Equilibrium 97
2.4Alternative Environments 98
2.5 TheSteady State 99
2.6Transitional Dynamics 102
2.6.1 ThePhase Diagram 102
2.6.2 TheImportance of the Transversality Condition 104
2.6.3 TheShape of the Stable Arm 105
2.6.4Behavior of the Saving Rate 106
2.6.5 ThePaths of the Capital Stock and Output 110
2.6.6 Speedsof Convergence 111
2.6.7Household Heterogeneity 118
2.7Nonconstant Time-Preference Rates 121
2.7.1Results under Commitment 123
2.7.2Results without Commitment under Log Utility 124
2.7.3Population Growth and Technological Progress 129
2.7.4Results under Isoelastic Utility 130
2.7.5 TheDegree of Commitment 132
2.8 Appendix2A: Log-Linearization of the Ramsey Model 132
2.9 Appendix2B: Irreversible Investment 134
Contents vii
2.10Appendix 2C: Behavior of the Saving Rate 135
2.11Appendix 2D: Proof That γˆκ Declines Monotonically
If theEconomy Starts from ˆk(0) < ˆk ∗ 137
2.12Problems 139
3Extensions of the Ramsey Growth Model 143
3.1Government 143
3.1.1Modifications of the Ramsey Framework 143
3.1.2Effects of Tax Rates 146
3.1.3Effects of Government Purchases 147
3.2Adjustment Costs for Investment 152
3.2.1 TheBehavior of Firms 152
3.2.2Equilibrium with a Given Interest Rate 155
3.2.3Equilibrium for a Closed Economy with a Fixed
Saving Rate159
3.3 AnOpen-Economy Ramsey Model 161
3.3.1 Setupof the Model 161
3.3.2Behavior of a Small Economy’s Capital Stock and Output 162
3.3.3Behavior of a Small Economy’s Consumption and Assets 163
3.3.4 TheWorld Equilibrium 164
3.4 TheWorld Economy with a Constraint on International Credit 165
3.4.1 Setupof a Model with Physical and Human Capital 166
3.4.2 TheClosed Economy 167
3.4.3 TheOpen Economy 168
3.5Variations in Preference Parameters 177
3.6 EconomicGrowth in a Model with Finite Horizons 179
3.6.1Choices in a Model with Finite Horizons 179
3.6.2 TheFinite-Horizon Model of a Closed Economy 183
3.6.3 TheFinite-Horizon Model of an Open Economy 186
3.7 SomeConclusions 189
3.8Appendix: Overlapping-Generations Models 190
3.8.1Households 190
3.8.2 Firms192
3.8.3Equilibrium 193
3.9 Problems200
viiiContents
4One-Sector Models of Endogenous Growth 205
4.1 The AK Model 205
4.1.1Behavior of Households 205
4.1.2Behavior of Firms 206
4.1.3Equilibrium 207
4.1.4Transitional Dynamics 208
4.1.5 ThePhase Diagram 209
4.1.6Determinants of the Growth Rate 210
4.2 AOne-Sector Model with Physical and Human Capital 211
4.3 Modelswith Learning by Doing and Knowledge Spillovers 212
4.3.1Technology 212
4.3.2Equilibrium 216
4.3.3 ParetoNonoptimality and Policy Implications 216
4.3.4 A Cobb–DouglasExample 217
4.3.5 ScaleEffects 218
4.4 PublicServices and Endogenous Growth 220
4.4.1 APublic-Goods Model 220
4.4.2 ACongestion Model 223
4.5Transitional Dynamics, Endogenous Growth 226
4.5.1 A Cobb–DouglasExample 226
4.5.2 A CESExample 230
4.6Concluding Observations 232
4.7Appendix: Endogenous Growth in the One-Sector Model 232
4.8 Problems235
5Two-Sector Models of Endogenous Growth (with Special
Attentionto the Role of Human Capital) 239
5.1 AOne-Sector Model with Physical and Human Capital 240
5.1.1 TheBasic Setup 240
5.1.2 TheConstraint of Nonnegative Gross Investment 242
5.2Different Technologies for Production and Education 247
5.2.1 TheModel with Two Sectors of Production 247
5.2.2 TheUzawa–Lucas Model 251
5.2.3 TheGeneralized Uzawa–Lucas Model 266
5.2.4 TheModel with Reversed Factor Intensities 267
5.3Conditions for Endogenous Growth 268
Contents ix
5.4 SummaryObservations 271
5.5 Appendix5A: Transitional Dynamics with Inequality Restrictions
on GrossInvestment in the One-Sector Model 271
5.6 Appendix5B: Solution of the Uzawa–Lucas Model 274
5.7 Appendix5C: The Model with Reversed Factor Intensities 280
5.8 Problems282
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