Dynamic Systems, Economic Growth, and the Environment (eBook)

Introduction 6
Contents 11
Contributors 16
Dynamic Systems in Growth Models 18
On Adequate Transversality Conditions for Infinite Horizon Optimal Control Problems-A Famous Example of Halkin 19
Introduction 19
Problem Formulation 20
Problem 20
Weighted Sobolev Spaces 21
Lebesgue and Improper Riemann Integrals 22
Problems with Lebesgue and Improper Riemann Integral 23
Optimality Criteria 24
Duality Theory 25
Examples 30
The Example of Halkin 30
A Resource Allocation Problem 34
Conclusions 37
References 37
Sequential Precision of Predictions in Models of Economic Growth 39
Introduction 40
Methodological Scheme of the Research 40
Model of Optimal Economic Growth 41
Dynamics of Capital and Labor 42
Dynamics of Useful Work per Worker 42
Optimal Control Design of the Model 43
Optimal Control Problem 43
Saddle Character of the Steady State 46
Nonlinear Stabilizers 47
Stabilizer of a Steady State 47
Stabilizers of the Hamiltonian System 48
Simulation of the Model 50
Econometric Analysis 50
Comparison with Real Data 51
Sequential Precision of Predictions Algorithm 53
The Case-Study 53
Model Verification 57
Sequential Precision of Predictions Algorithm 58
References 58
High Order Precision Estimates in Algorithms for Solving Problems of Economic Growth 60
Introduction 60
Outline of Optimal Control Problem for Economic Growth Model 61
Hamiltonians in the Pontryagin Maximum Principle 62
Concavity Properties of Hamiltonians 62
Hamiltonian Systems in the Pontryagin Maximum Principle 63
Numerical Algorithm 65
Precision Estimates of the Algorithm 65
Numerical Experiments 71
References 73
Growth and Environment 75
Growth and Climate Change: Threshold and Multiple Equilibria 76
Introduction 76
A Basic Growth Model with Non-optimal Abatement Spending 78
The Structure of the Model 78
The Dynamics of the Model 82
The Social Optimum 87
Conclusion 89
References 90
Optimal Economic Growth Under Stochastic Environmental Impact: Sensitivity Analysis 92
Introduction 92
Model 93
Economy 93
Natural Hazards 94
Utility 96
Optimal Production and Optimal Cleaning 97
Perturbed Period 97
Pre-perturbed Period 98
Global Calibration 103
Optimal GDP and Optimal GHG 104
Sensitivity Analysis 107
Discussion 109
Assumption (3) 111
Proof of Theorem 1 112
Proof of Lemma 1 115
Lemmas 3 and 4 116
References 119
Optimal Economic Growth with a Random Environmental Shock 121
Introduction 121
The Model 123
Solution of the Problem 132
Economic Interpretation 142
Conclusions 146
Appendix 147
References 149
Growth and Environmental Policy 150
Prices Versus Quantities in a Vintage Capital Model 151
Introduction 151
The Firm's Problem with an Emission Tax 152
The Emission Mapping 155
The Auction Price of Permits and Its Regularization 160
Numerical Analysis of the Market Price of Emission 166
References 168
International Emission Policy with Lobbying and Technological Change 170
Introduction 170
The Union 171
The Countries 173
Laissez-faire 174
Pareto Optimum 176
Lobbying over Nontraded Emission Quotas 177
The Local Planners 177
The Self-interested Central Planner 179
The Political Equilibrium 180
Lobbying over Traded Emission Quotas 182
The Local Planners 182
The Self-interested Central Planner 185
The Political Equilibrium 186
Conclusions 189
References 190
The Role of Product Differentiation in the Producer-targeted Promotion of Renewable Energy Technologies 191
Introduction 191
The Model 194
Competitive Dynamical System 195
The Degree of Product Differentiation and Stability of the Duopoly 196
Profits 198
A Numerical Example 200
The Minimal Sufficient Subsidy or Tax 201
Summary and Conclusions 202
References 202
Dynamic Oligopoly with Capital Accumulation and Environmental Externality 204
Introduction 204
The Set Up 205
Cournot Competition 207
The Social Optimum 211
Cournot Oligopoly vs. Social Planning 214
Extension: Pollution as a Function of Production 216
Concluding Remarks 220
References 220
On a Decentralized Boundedly Rational Emission Reduction Strategy 222
Introduction 222
Emission Reduction Process 224
Outcome of the Emission Reduction Process 228
Examples 233
Negotiation Pattern 237
References 242
Applications 244
Environmental Mortality and Long-Run Growth 245
Introduction 245
The Model 246
Optimal Consumption and Investment 248
Air Pollution Mortality in Europe 252
Generating the Missing Emission Data 253
Estimating the Country-Specific Parameters 254
Results 256
Conclusions 261
Local Stability of the Steady States 261
Countries and Variables 263
References 263
Development of Transportation Infrastructure in the Context of Economic Growth 265
Introduction 265
Optimal Control Approach to Infrastructure Investment & Economic Growth
Model 269
Specifying Functions 271
The Share of Road Infrastructure in Economic Output 274
Solution of Optimal Control Problem 275
Optimal Control Results: Country Case Studies 282
Infrastructure Quality & Steady State GDP
The Speed of Adjustment & Steady State GDP
The Share of Road Infrastructure in GDP & Steady State GDP
Summary and Conclusion 289
Appendix: Data & Calibration
Calibration Methods 290
Calibration Results 292
References 295