Foreword .................................................... ix
Introduction ................................................. 1
Some History ................................................. 2
Current Tax Systems .......................................... 5
Overview of the Book ......................................... 8
References .................................................. 11
I The Effects of Taxation ..................................... 13
1 Distortions and Welfare Losses .............................. 15
1.1 The Effects of Taxation ................................ 17
1.1.1 Labor Supply .................................... 18
1.1.2 The Effects of Taxation on Savings .............. 25
1.1.3 Taxation and Risk-Taking ........................ 30
1.2 Welfare Losses ......................................... 33
2 Tax Incidence ............................................... 41
2.1 Partial Equilibrium .................................... 43
2.1.1 The Effect of Payroll Taxes ..................... 43
2.1.2 The General Analysis of Partial Equilibrium ..... 45
2.2 General Equilibrium .................................... 49
2.2.1 The No-Taxation Economy ......................... 50
2.2.2 Introducing Taxes ............................... 51
2.2.3 General Remarks ................................. 53
2.2.4 Infinitesimal Analysis .......................... 54
2.2.5 Final Remarks ................................... 60
II Optimal Taxation ........................................... 63
3 Indirect Taxation ........................................... 67
3.1 Ramsey's Formula ....................................... 67
3.1.1 An Informal Approach ............................ 67
3.1.2 The General Model ............................... 68
3.1.3 Some Special Cases .............................. 73
3.2 Productive Efficiency .................................. 77
4 Direct Taxation ............................................. 83
4.1 The Emergence of the Model ............................. 83
4.2 Mirrlees's Model ....................................... 87
4.2.1 The Two-Type Case ............................... 88
4.2.2 The Rawlsian Case ............................... 94
4.2.3 The General Approach ............................ 97
4.2.4 The Quasi-linear Case .......................... 101
4.3 Generalizations ....................................... 107
4.3.1 Heterogeneous Preferences and the Extensive
Margin ......................................... 108
4.3.2 Endogenous Wage Rates .......................... 111
4.3.3 The Income Tax as an Insurance Device .......... 114
4.4 Simulations ........................................... 115
5 Mixed Taxation ............................................. 123
5.1 The Negative Income Tax ............................... 124
5.2 Is Indirect Taxation Useful? .......................... 125
5.3 Criticisms ............................................ 129
6 Risk and Time .............................................. 133
6.1 Taxing Savings in a Riskless Economy .................. 135
6.2 A Stochastic Economy .................................. 137
6.3 The Inverse Euler Condition ........................... 139
6.4 Discouraging Savings .................................. 142
6.5 Optimal Taxes ......................................... 144
6.5.1 Zero Aggregate Wealth Taxes .................... 146
6.5.2 Introducing Productive Capital ................. 147
6.5.3 Illustrations .................................. 149
7 Corrective Taxes ........................................... 153
7.1 Pigovian Taxation in Partial Equilibrium .............. 154
7.2 optimal Green Taxes ................................... 156
7.2.1 The First-Best ................................. 157
7.2.2 The Second-Best ................................ 159
7.3 Is There a Double Dividend? ........................... 161
8 Criticisms of Optimal Taxation ............................. 165
8.1 Representing Social Preferences ....................... 165
8.1.1 Tax Reforms .................................... 166
8.1.2 Horizontal Equity .............................. 169
8.2 Putting Tax Theory to Work ............................ 172
8.2.1 Taxing Households .............................. 174
8.2.2 Behavioral Economics and Taxation .............. 176
III Some Current Debates ...................................... 179
9 Low-Income Support ......................................... 181
9.1 Measuring Poverty ..................................... 182
9.2 The Main Benefits ..................................... 183
9.2.1 Guaranteed Minimum Income ...................... 185
9.2.2 The Negative Income Tax ........................ 185
9.2.3 Low-Wage Subsidies ............................. 186
9.2.4 The Minimum Wage ............................... 187
9.3 The Lessons from Theory ............................... 188
9.3.1 The Negative Income Tax ........................ 188
9.3.2 Low-wage Subsidies ............................. 194
9.3.3 The Guaranteed Minimum Income .................. 194
9.3.4 The Minimum Wage ............................... 195
9.4 Empirical Evaluations ................................. 197
9.5 Recent Reforms ........................................ 199
10 Taxation and Global Warming ................................ 203
10.1 The Optimal Price of Carbon ........................... 205
10.1.1 The Social Discount Rate ....................... 205
10.1.2 Catastrophic Change ............................ 210
10.1.3 Discounting Environmental Changes .............. 211
10.2 International Issues .................................. 213
10.3 The Dynamics of Carbon Taxation ....................... 215
IV Appendixes ................................................. 219
A Some Basic Microeconomics .................................. 221
A.l Consumer Theory ....................................... 221
A.1.1 Hicksian and Marshallian Demands ............... 221
A.1.2 The Slustky Equations .......................... 223
A.1.3 Interpretation ................................. 224
A.2 Producer Theory ....................................... 224
A.2.1 The Producer's Problem ......................... 225
A.2.2 Factor Demands ................................. 225
A.2.3 The Special Case of Constant Returns ........... 227
В Optimal Control ............................................ 229
Index ......................................................... 233
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