Introduction To Modern Economic Growth

156 5.4 The Representative Firm 158 5.5 Problem Formulation 160 5.6 Welfare Theorems 161 5.7 Proof of the Second Welfare Theorem (Theorem 5.7) * 168 5.8 Sequential Trading 171 5.9 Optimal Growth 174 5.10 Taking Stock 176 5.11 References and Literature 176 5.12 Exercises 178 Chapter 6: Infinite-Horizon Optimization and Dynamic Programming 182 6.1 Discrete-Time Infinite-Horizon Optimization 182 6.2 Stationary Dynamic Programming 185 6.3 Stationary Dynamic Programming Theorems 187 6.4 The Contraction Mapping Theorem and Applications * 190 6.5 Proofs of the Main Dynamic Programming Theorems * 194 6.6 Applications of Stationary Dynamic Programming 201 6.7 Nonstationary Infinite-Horizon Optimization 211 6.8 Optimal Growth in Discrete Time 215 6.9 Competitive Equilibrium Growth 219 6.10 Computation 221 6.11 Taking Stock 221 6.12 References and Literature 222 6.13 Exercises 223 Chapter 7: An Introduction to the Theory of Optimal Control 227 7.1 Variational Arguments 228 7.2 The Maximum Principle: A First Look 235 7.3 Infinite-Horizon Optimal Control 240 7.4 More on Transversality Conditions 250 7.5 Discounted Infinite-Horizon Optimal Control 253 7.6 Existence of Solutions, Concavity, and Differentiability * 259 7.7 A First Look at Optimal Growth in Continuous Time 268 7.8 The q-Theory of Investment and Saddle-Path Stability 269 7.9 Taking Stock 274 7.10 References and Literature 275 7.11 Exercises 278 Part III: Neoclassical Growth Chapter 8: The Neoclassical Growth Model 287 8.1 Preferences, Technology, and Demographics 287 8.2 Characterization of Equilibrium 293 8.3 Optimal Growth 298 8.4 Steady-State Equilibrium 300 8.5 Transitional Dynamics and Uniqueness of Equilibrium 302 8.6 Neoclassical Growth in Discrete Time 305 8.7 Technological Change and the Canonical Neoclassical Model 306 8.8 The Role of Policy 312 8.9 Comparative Dynamics 313 8.10 A Quantitative Evaluation 315 8.11 Extensions 317 8.12 Taking Stock 317 8.13 References and Literature 318 8.14 Exercises 319 Chapter 9: Growth with Overlapping Generations 327 9.1 Problems of Infinity 328 9.2 The Baseline Overlapping Generations Model 329 9.3 The Canonical Overlapping Generations Model 335 9.4 Overaccumulation and Pareto Optimality of Competitive Equilibrium in the Overlapping Generations Model 336 9.5 Role of Social Security in Capital Accumulation 339 9.6 Overlapping Generations with Impure Altruism 342 9.7 Overlapping Generations with Perpetual Youth 345 9.8 Overlapping Generations in Continuous Time 348 9.9 Taking Stock 353 9.10 References and Literature 354 9.11 Exercises 355 Chapter 10: Human Capital and Economic Growth 359 10.1 A Simple Separation Theorem 359 10.2 Schooling Investments and Returns to Education 361 10.3 The Ben-Porath Model 363 10.4 Neoclassical Growth with Physical and Human Capital 367 10.5 Capital-Skill Complementarity in an Overlapping Generations Model 371 10.6 Physical and Human Capital with Imperfect Labor Markets 374 10.7 Human Capital Externalities 379 10.8 The Nelson-Phelps Model of Human Capital 380 10.9 Taking Stock 382 10.10 References and Literature 384 10.11 Exercises 384 Chapter 11: First-Generation Models of Endogenous Growth 387 11.1 The AK Model Revisited 388 11.2 The AK Model with Physical and Human Capital 393 11.3 The Two-Sector AK Model 395 11.4 Growth with Externalities 398 11.5 Taking Stock 402 11.6 References and Literature 404 11.7 Exercises 404 Part IV: Endogenous Technological Change Chapter 12: Modeling Technological Change 411 12.1 Different Conceptions of Technology 411 12.2 Science and Profits 414 12.3 The Value of Innovation in Partial Equilibrium 416 12.4 The Dixit-Stiglitz Model and Aggregate Demand Externalities 422 12.5 Individual R&D Uncertainty and the Stock Market 428 12.6 Taking Stock 429 12.7 References and Literature 430 12.8 Exercises 431 Chapter 13: Expanding VarietyModels 433 13.1 The Lab-Equipment Model of Growth with Input Varieties 433 13.2 Growth with Knowledge Spillovers 444 13.3 Growth without Scale Effects 446 13.4 Growth with Expanding Product Varieties 448 13.5 Taking Stock 452 13.6 References and Literature 453 13.7 Exercises 453 Chapter 14: Models of Schumpeterian Growth 458 14.1 A Baseline Model of Schumpeterian Growth 459 14.2 A One-Sector Schumpeterian Growth Model 468 14.3 Innovation by Incumbents and Entrants 472 14.4 Step-by-Step Innovations * 479 14.5 Taking Stock 489 14.6 References and Literature 490 14.7 Exercises 491 Chapter 15: Directed Technological Change 497 15.1 Importance of Biased Technological Change 498 15.2 Basics and Definitions 500 15.3 Baseline Model of Directed Technological Change 503 15.4 Directed Technological Change with Knowledge Spillovers 514 15.5 Directed Technological Change without Scale Effects 518 15.6 Endogenous Labor-Augmenting Technological Change 519 15.7 Generalizations and Other Applications 522 15.8 An Alternative Approach to Labor-Augmenting Technological Change* 523 15.9 Taking Stock 526 15.10 References and Literature 527 15.11 Exercises 529 Part V: Stochastic Growth Chapter 16: Stochastic Dynamic Programming 537 16.1 Dynamic Programming with Expectations 537 16.2 Proofs of the Stochastic Dynamic Programming Theorems * 544 16.3 Stochastic Euler Equations 549 16.4 Generalization to Markov Processes * 552 16.5 Applications of Stochastic Dynamic Programming 554 16.6 Taking Stock 561 16.7 References and Literature 561 16.8 Exercises 562 Chapter 17: Stochastic Growth Models 566 17.1 The Brock-Mirman Model 567 17.2 Equilibrium Growth under Uncertainty 571 17.3 Application: Real Business Cycle Models 579 17.4 Growth with Incomplete Markets: The Bewley Model 583 17.5 The Overlapping Generations Model with Uncertainty 586 17.6 Risk, Diversification, and Growth 588 17.7 Taking Stock 603 17.8 References and Literature 604 17.9 Exercises 605 Part VI: Technology Diffusion, Trade, and Interdependences Chapter 18: Diffusion of Technology 611 18.1 Productivity Differences and Technology 611 18.2 A Benchmark Model of Technology Diffusion 613 18.3 Technology Diffusion and Endogenous Growth 619 18.4 Appropriate and Inappropriate Technologies and Productivity Differences 623 18.5 Contracting Institutions and Technology Adoption 630 18.6 Taking Stock 642 18.7 References and Literature 643 18.8 Exercises 644 Chapter 19: Trade and Growth 648 19.1 Growth and Financial Capital Flows 648 19.2 Why Does Capital Not Flow from Rich to Poor Countries? 653 19.3 Economic Growth in a Heckscher-Ohlin World 655 19.4 Trade, Specialization, and the World Income Distribution 663 19.5 Trade, Technology Diffusion, and the Product Cycle 674 19.6 Trade and Endogenous Technological Change 678 19.7 Learning-by-Doing, Trade, and Growth 680 19.8 Taking Stock 684 19.9 References and Literature 685 19.10 Exercises 687 Part VII: Economic Development and Economic Growth Chapter 20: Structural Change and Economic Growth 697 20.1 Nonbalanced Growth: The Demand Side 697 20.2 Nonbalanced Growth: The Supply Side 703 20.3 Agricultural Productivity and Industrialization 715 20.4 Taking Stock 719 20.5 References and Literature 720 20.6 Exercises 721 Chapter 21: Structural Transformations and Market Failures in Development 725 21.1 Financial Development 726 21.2 Fertility, Mortality, and the Demographic Transition 729 21.3 Migration, Urbanization, and the Dual Economy 736 21.4 Distance to the Frontier and Changes in the Organization of Production 744 21.5 Multiple Equilibria from Aggregate Demand Externalities and the Big Push 752 21.6 Inequality, Credit Market Imperfections, and Human Capital 758 21.7 Toward a Unified Theory of Development and Growth? 764 21.8 Taking Stock 768 21.9 References and Literature 769 21.10 Exercises 771 Part VIII: The Political Economy of Growth Chapter 22: Institutions, Political Economy, and Growth 781 22.1 The Impact of Institutions on Long-Run Development 781 22.2 Distributional Conflict and Economic Growth in a Simple Society 784 22.3 The Canonical Cobb-Douglas Model of Distributional Conflict 792 22.4 Distributional Conflict and Competition 793 22.5 Subgame Perfect versus Markov Perfect Equilibria 799 22.6 Inefficient Economic Institutions: A First Pass 802 22.7 Heterogeneous Preferences, Social Choice, and the Median Voter * 805 22.8 Distributional Conflict and Economic Growth: Heterogeneity and the Median Voter 814 22.9 The Provision of Public Goods: Weak versus Strong States 817 22.10 Taking Stock 822 22.11 References and Literature 823 22.12 Exercises 825 Chapter 23: Political Institutions and Economic Growth 831 23.1 Political Regimes and Economic Growth 832 23.2 Political Institutions and Growth-Enhancing Policies 834 23.3 Dynamic Trade-offs 837 23.4 Understanding Endogenous Political Change 850 23.5 Taking Stock 856 23.6 References and Literature 857 23.7 Exercises 858 Epilogue: Mechanics and Causes of Economic Growth 861 What Have We Learned? 861 A Possible Perspective on Growth and Stagnation over the Past 200 Years 864 Many Remaining Questions 872 Part IX: Mathematical Appendixes Appendix A: Odds and Ends in Real Analysis and Applications to Optimization 877 A.1 Distances and Metric Spaces 878 A.2 Mappings, Functions, Sequences, Nets, and Continuity 880 A.3 A Minimal Amount of Topology: Continuity and Compactness * 885 A.4 The Product Topology * 889 A.5 Absolute Continuity and Equicontinuity * 891 A.6 Correspondences and Berge's Maximum Theorem 894 A.7 Convexity, Concavity, Quasi-Concavity, and Fixed Points 898 A.8 Differentiation, Taylor Series, and the Mean Value Theorem 900 A.9 Functions of Several Variables and the Inverse and Implicit Function Theorems 904 A.10 Separation Theorems * 907 A.11 Constrained Optimization 910 A.12 Exercises 915 Appendix B: Review of Ordinary Differential Equations 917 B.1 Eigenvalues and Eigenvectors 917 B.2 Some Basic Results on Integrals 918 B.3 Linear Differential Equations 920 B.4 Solutions to Linear First-Order Differential Equations 921 B.5 Systems of Linear Differential Equations 924 B.6 Local Analysis and Stability of Nonlinear Differential Equations 926 B.7 Separable and Exact Differential Equations 927 B.8 Existence and Uniqueness of Solutions 929 B.9 Continuity and Differentiability of Solutions 930 B.10 Difference Equations 930 B.11 Exercises 932 Appendix C: Brief Review of Dynamic Games 934 C.1 Basic Definitions 934 C.2 Some Basic Results 937 C.3 Application: Repeated Games with Perfect Observability 941 C.4 Exercises 942 Appendix D: List of Theorems 944 Chapter 2 944 Chapter 5 944 Chapter 6 944 Chapter 7 945 Chapter 10 945 Chapter 16 945 Chapter 22 946 Appendix A 946 Appendix B 947 Appendix C 947 References 949 Name Index 971 Subject Index 977