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Principles and Methods of Law & Economics: Basic Tools for Normative Reasoning NICHOLAS L. GEORGAKOPOULOS PREFACE XI INTRODUCTION: INNOVATION IN LEGAL THINKING 1 A. Proposals, Consequences, and Ideals 2 B. Toward Scientific Analysis of Law 3 C. Bibliographical Note 8 PART 1: PRINCIPLES 11 1. FROM FORMAL LOGIC TO NORMATIVE REASONING 13 A. Formal Deontic Logic 15 B. Formal Logic's Failure in Normative Reasoning 16 C. The Informal Normative Syllogism 17 i. Proposals, Consequences, and Ideals in Normative Reasoning 19 D. Concluding Exercises 21 E. Bibliographical Note 22 2. SOCIAL WELFARE VERSUS MORAL PHILOSOPHY 25 A. Ideals behind Law & Economics: Welfarism and Pragmatism 29 B. Juxtaposition with other External Derivations of Ideals 31 i. Deriving Ideals from Existing Rules (including Formalism) 31 ii. Rawls' Contractarianism 32 iii. The Potential Equivalence of Derived Ideals and Preferences 34 C. Distinguishing Features of Economic Analysis 36 i. Avoidance of Moral Relativity 36 ii. Preference for Applications over Refinement of Principles 37 iii. Ubiquitous Importance of Incentives 37 iv. Treatment of Preferences as Objective 38 v. Lack Bias for Rule Proliferation 41 vi. Orientation Toward the Future 42 D. Concluding Exercises 42 E. Bibliographical Note 43 3. FROM POLITICAL PHILOSOPHY TO GAME THEORY 45 A. Political Theory 46 i. Inefficiencies of Majority Rule 47 ii. Legal Process: Explaining the Administrative State 49 iii. Civic Republicanism 50 iv. Perfectionism 52 B. Voting System Design 53 C. Game Theory 60 i. Cooperation Games: Prisoner's Dilemma 61 ii. Coordination Games: Driving Side 64 iii. Game Theory in Legal Scholarship 66 D. Social Norms 67 E. Bounded Rationality 70 F. Concluding Exercises 78 G. Bibliographical Note 82 4. THE IMPORTANCE OF DISTRIBUTION OF WEALTH 85 A. Redistribute! 88 B. Do not Redistribute! 93 C. Delegating Redistribution to Tax Policy 99 D. Concluding Exercises 106 E. Bibliographical Note 110 5. COASE AND LAW'S IRRELEVANCE 113 A. Coasean Irrelevance 115 B. Coasean Irrelevance 116 i. Revealing Imperfections 117 ii. An Example of Deploying Coasean Irrelevance 117 C. Transaction Costs: The Usual Suspect 118 i. Vantage Point Makes Transaction Costs 123 ii. Innovations Transform Transaction Costs 124 iii. Litigation Costs: Transaction Cost or Not? 124 iv. Increasing Social Gain from Private Litigation 125 v. Normative Implications for Litigation of the Analysis of Transaction Costs 127 D. Concluding Exercises 129 E. Bibliographical Note 132 6. MORE FAILURES OF COASEAN IRRELEVANCE 133 A. Negotiation Holdouts 133 B. Systematic errors 136 C. Risk-Aversion 137 i. Imposing a Transaction Cost 140 ii. Substantive Solutions of Risk Aversion 140 D. Distribution 142 E. Concluding Exercises 144 F. Bibliographical Note 149 PART 2: METHODS 151 7. MATHEMATICAL MODELLING 153 A. Symbols, Functions, and Idioms 155 B. Simplification and the Model as a Premise 166 C. Modelling Applications 170 i. Modelling Negligence Law: Optimisation 170 ii. Modelling the End of Affirmative Action: Differential Equations 174 D. Concluding Exercises 176 E. Bibliographical Note 180 8. CONFRONTING UNCERTAINTY: BASIC PROBABILITY THEORY 183 A. Describing Randomness: Probability and Expectation 185 B. Mathematical Models of Expectation 188 C. Uncertain Uncertainty: Conditional Probability 191 D. Concluding Exercises 196 E. Bibliographical Notes 206 9. ADVANCED PROBABILITY: DISTRIBUTIONS AS THE SHAPE OF RANDOMNESS 207 A. The Shape of Randomness: Distribution Functions 208 i. Visual Comparison of Discrete and Continuous Distributions 209 ii. CDF and PDF: Features and Relations 211 iii. Truncated and Censored Distributions 214 B. The Normal Distribution 219 C. Concluding Exercise: Imperfect Enforcement 221 D. Bibliographical Note 229 10. HOW TO PRICE UNCERTAINTY: FINANCE 231 A. Valuation in Perfect Markets 233 i. Known Rates: Discounting 234 ii. Risky Assets 237 B. Normative Implications of the CAPM 247 i. Financial Information 247 ii. Forecasts 249 C. Financial Market Microstructure: The Game-Theoretical Foundation of the CAPM 249 D. Normative Application of Microstructure: Insider Trading 251 E. Concluding Exercises 256 F. Bibliographical Note 261 11. FINANCE AND PROBABILITY: OPTIONS AND DERIVATIVES 263 A. Option Pricing 266 B. Normative Implications of Option Pricing 274 i. Recipients of Fiduciary Obligation 274 ii. Automated Reorganizations via Options 276 iii. The Options Understanding of the New Value Exception 280 C. Concluding Exercises 284 D. Bibliographical Note 289 12. USING SPREADSHEETS 291 A. The Basics 292 i. Obtaining Built-In Help about Functions 293 ii. Using the Function Wizard 295 iii. Categories of Built-In Functions 297 iv. Relative and Absolute References in Copying 301 B. Graphics 305 i. Chart Types 308 ii. Completing the Chart Wizard 310 iii. Manipulating Charts 312 C. Solving Equations 314 i. The Solver 315 ii. Goal Seek 316 D. Macros and User-Defined Functions 316 i. Recording a Macro 317 ii. Editing a Macro 318 iii. Assigning a Macro to a Graphic 319 iv. Entering a Function 320 E. Downloading and Combining Data 320 i. Data Files Separating Columns with Commas or Tabs 321 ii. Specifying the Type of Data 323 iii. Fixed-Width Data 324 iv. Combining Data 325 F. Concluding Exercises 327 G. Bibliographical Note 327 13. STATISTICS 329 A. The Use of Statistics in Legal Thinking 330 B. Fundamentals: Descriptive Statistics and Distributions 334 C. Empirical Research 335 i. Basics: Comparing Data that Take Values and Data that Fall into Categories 336 ii. Determining Influences: Multiple Outcomes 346 iii. Determining Influences: Yes/No Outcomes 358 iv. Observations that are filtered by a Threshold 360 D. Concluding exercises 361 E. Bibliographical Note 364 14. CONCLUSION: IMPORTING METHODOLOGICAL INNOVATIONS 367 A. Cellular Automata 368 B. Fractals 369 C. Evolutionary Theory 372 D. To End 373 E. Bibliographical Note 373 APPENDIX A: MEINHARD V. SALMON 375 APPENDIX B: GLOSSARY 383 APPENDIX C: MATHEMATICA NOTEBOOKS 389 A. Differential Equations in Law: The Effect of Terminating Affirmative Action 392 i. Determining the Participation in the Workforce 393 ii. Add the Initial Condition 393 iii. Manipulating the Exponent to See it Disappear 394 iv. The Long-Run Participation 394 v. The composition of the candidates 394 vi. Graphics 395 B. Derivation of the Normal Distribution 396 i. Derive the normal distribution as Gauss did 396 ii. The Standard Normal Distribution 398 iii. Restating with Standard Deviation 398 iv. Restating with Average Deviation 399 v. The Triangular Distribution 400 C. Application of triangular distribution: the uncertain apprehension of speed limit violations 403 D. a comparison of insider trading regimes 407 i. Foundation 408 ii. Problem 408 iii. Solution: Statement 408 iv. Solution: Proof 409 v. Illustration of Price Path 411

Library of Congress Subject Headings for this publication:

Law and economics.

Law -- Methodology.

Economics -- Mathematical models.