Introduction to Modern Economic Growth 6.9 Taking Stock 6.10 References and Literature 6.11 Exercises 305 306 307 Chapter Review of the Theory of Optimal Control 7.1 Variational Arguments 7.2 The Maximum Principle: A First Look 7.3 Infinite-Horizon Optimal Control 7.4 More on Transversality Conditions 7.5 Discounted Infinite-Horizon Optimal Control 7.6 A First Look at Optimal Growth in Continuous Time 7.7 The q-Theory of Investment 7.8 Taking Stock 7.9 References and Literature 7.10 Exercises 313 314 324 330 342 345 351 352 359 361 363 Part 371 Neoclassical Growth Chapter The Neoclassical Growth Model 8.1 Preferences, Technology and Demographics 8.2 Characterization of Equilibrium 8.3 Optimal Growth 8.4 Steady-State Equilibrium 8.5 Transitional Dynamics 8.6 Technological Change and the Canonical Neoclassical Model 8.7 Comparative Dynamics 8.8 The Role of Policy 8.9 A Quantitative Evaluation 8.10 Extensions 8.11 Taking Stock 8.12 References and Literature 8.13 Exercises 373 373 378 383 384 387 390 398 400 402 405 406 407 408 Chapter Growth with Overlapping Generations 417 9.1 Problems of Infinity 418 9.2 The Baseline Overlapping Generations Model 421 9.3 The Canonical Overlapping Generations Model 427 9.4 Overaccumulation and Pareto Optimality of Competitive Equilibrium in the Overlapping Generations Model 429 9.5 Role of Social Security in Capital Accumulation 433 9.6 Overlapping Generations with Impure Altruism 436 9.7 Overlapping Generations with Perpetual Youth 441 9.8 Overlapping Generations in Continuous Time 445 v