**PRINCIPLES AND METHODS OF LAW AND ECONOMICS**

This is an introductory book that targets the reader who aspires to apply economic analysis but seeks a technical introduction to its mathematical techniques or a structured elaboration of its philosophical principles. It juxtaposes economic analysis with moral philosophy, political theory, egalitarianism, and other methodological principles. It then presents the details of methods, such as model building, derivatives, differential equations, statistical tests, and the use of computer programs.

Nicholas Georgakopoulos is Professor of Law at Indiana University School of Law. He received his master’s degree and doctorate from Harvard Law School, where he specialized in finance and the regulation of financial markets. His publications are cited prominently, including citations by the U.S. Supreme Court and the Securities Exchange Commission.

# Principles and Methods of

Law and Economics

## Basic Tools for Normative Reasoning

Nicholas L. Georgakopoulos

Indiana University

CAMBRIDGE UNIVERSITY PRESS

Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo

Cambridge University Press

40 West 20th Street, New York, NY 10011-4211, USA

www.cambridge.org

Information on this title: www.cambridge.org/9780521826815

© Nicholas L. Georgakopoulos 2005

This publication is in copyright. Subject to statutory exception

and to the provisions of relevant collective licensing agreements,

no reproduction of any part may take place without

the written permission of Cambridge University Press.

First published 2005

Printed in the United States of America

*A catalog record for this publication is available from the British Library.*

*Library of Congress Cataloging in Publication Data*

Georgakopoulos, Nicholas Leonidas.

Principles and methods of law and economics : basic tools

for normative reasoning / Nicholas L. Georgakopoulos.

p. cm.

Includes bibliographical references and index.

ISBN 0-521-82681-0 (hardcover) – ISBN 0-521-53411-9 (pbk.)

1. Law and economics. 2. Law–Methodology.

3. Economics–Mathematical models. I. Title.

K487.E3G46 2005

340 .11–dc22 2004029141

ISBN-13 978-0-521-82681-5 hardback

ISBN-10 0-521-82681-0 hardback

ISBN-13 978-0-521-53411-6 paperback

ISBN-10 0-521-53411-9 paperback

Cambridge University Press has no responsibility for

the persistence or accuracy of URLs for external or

third-party Internet Web sites referred to in this publication

and does not guarantee that any content on such

Web sites is, or will remain, accurate or appropriate.

*In memory of my mother.
May justice and welfare end random violence.*

## Contents

Preface |
xiii | ||

INTRODUCTION: INNOVATION IN LEGAL THINKING |
1 | ||

A. Proposals, Consequences, and Ideals ● 1 | |||

B. Toward Scientific Analysis of Law ● 3 | |||

C. Bibliographical Note ● 7 | |||

PART 1: PRINCIPLES |
|||

1. |
FROM FORMAL LOGIC TO NORMATIVE REASONING |
11 | |

A. Formal Deontic Logic ● 12 | |||

B. Formal Logic’s Failure in Normative Reasoning ● 13 | |||

C. The Informal Normative Syllogism ● 15 | |||

Proposals, Consequences, and Ideals in Normative Reasoning ● 16 |
|||

D. Concluding Exercises ● 17 | |||

E. Bibliographical Note ● 19 | |||

2. |
SOCIAL WELFARE VERSUS MORAL PHILOSOPHY |
20 | |

A. Ideals behind Law and Economics: Welfarism and Pragmatism ● 23 | |||

B. Juxtaposition with Other External Derivations of Ideals ● 25 | |||

i. Deriving Ideals from Existing Rules (Including Formalism) ● 25 |
|||

ii. Rawls’ Contractarianism ● 26 |
|||

iii. The Potential Equivalence of Derived Ideals and Preferences ● 27 |
|||

C. Distinguishing Features of Economic Analysis ● 29 | |||

i. Avoidance of Moral Relativity ● 30 |
|||

ii. Preference for Applications over Refinement of Principles ● 30 |
|||

iii. Ubiquitous Importance of Incentives ● 30 |
|||

iv. Treatment of Preferences as Objective ● 31 |
|||

v. Lack Bias for Rule Proliferation ● 34 |
|||

vi. Orientation Toward the Future ● 34 |
|||

D. Concluding Exercises ● 35 | |||

E. Bibliographical Note ● 36 | |||

3. |
FROM POLITICAL PHILOSOPHY TO GAME THEORY |
37 | |

A. Political Theory ● 38 | |||

i. Inefficiencies of Majority Rule ● 39 |
|||

ii. Legal Process: Explaining the Administrative State ● 40 |
|||

iii. Civic Republicanism ● 42 |
|||

iv. Perfectionism ● 43 |
|||

B. Voting System Design ● 44 | |||

C. Game Theory ● 50 | |||

i. Cooperation Games: Prisoner’s Dilemma ● 51 |
|||

ii. Coordination Games: Driving Side ● 54 |
|||

iii. Game Theory in Legal Scholarship ● 55 |
|||

D. Social Norms ● 57 | |||

E. Bounded Rationality ● 59 | |||

F. Concluding Exercises ● 66 | |||

G. Bibliographical Note ● 70 | |||

4. |
THE IMPORTANCE OF DISTRIBUTION OF WEALTH |
72 | |

A. Redistribute! ● 75 | |||

B. Do Not Redistribute! ● 79 | |||

C. Delegating Redistribution to Tax Policy ● 84 | |||

D. Concluding Exercises ● 89 | |||

E. Bibliographical Note ● 94 | |||

5. |
COASE AND LAW’S IRRELEVANCE |
95 | |

A. Coasean Irrelevance ● 96 | |||

B. Normative Use ● 98 | |||

i. Revealing Imperfections ● 98 |
|||

ii. An Example ● 99 |
|||

C. Transaction Costs: The Usual Suspect ● 99 | |||

i. Vantage Point Makes Transaction Costs ● 103 |
|||

ii. Innovations Transform Transaction Costs ● 104 |
|||

iii. Litigation Costs: Transaction Cost or Not? ● 105 |
|||

iv. Example: Increasing Social Gain from Private Litigation ● 105 |
|||

v. Normative Implications for Litigation of the Analysis of Transaction Costs ● 107 |
|||

D. Concluding Exercises ● 109 | |||

E. Bibliographical Note ● 111 | |||

6. |
MORE FAILURES OF COASEAN IRRELEVANCE |
112 | |

A. Negotiation Holdouts ● 112 | |||

B. Systematic Errors ● 115 | |||

C. Risk Aversion ● 115 | |||

i. Imposing a Transaction Cost ● 118 |
|||

ii. Substantive Solutions of Risk Aversion ● 118 |
|||

D. Distribution ● 120 | |||

E. Concluding Exercises ● 121 | |||

F. Bibliographical Note ● 126 | |||

PART 2: METHODS |
|||

7. |
MATHEMATICAL MODELING |
129 | |

A. Symbols, Functions, and Idioms ● 131 | |||

B. Simplification and the Model as a Premise ● 140 | |||

C. Modeling Applications ● 142 | |||

i. Modeling Negligence Law: Optimization ● 143 |
|||

ii. Modeling the End of Affirmative Action: Differential Equations ● 146 |
|||

D. Concluding Exercises ● 148 | |||

E. Bibliographical Note ● 152 | |||

8. |
CONFRONTING UNCERTAINTY: BASIC PROBABILITY THEORY |
154 | |

A. Describing Randomness: Probability and Expectation ● 155 | |||

B. Mathematical Models of Expectation ● 159 | |||

C. Uncertain Uncertainty: Conditional Probability ● 161 | |||

D. Concluding Exercises ● 166 | |||

E. Bibliographical Note ● 174 | |||

9. |
ADVANCED PROBABILITY: DISTRIBUTIONS AS THE SHAPE OF RANDOMNESS |
175 | |

A. The Shape of Randomness: Distribution Functions ● 176 | |||

i. Visual Comparison of Discrete and Continuous Distributions ● 177 |
|||

ii. CDF and PDF: Features and Relations ● 178 |
|||

iii. Truncated and Censored Distributions ● 181 |
|||

B. The Normal Distribution ● 186 | |||

C. Concluding Exercise: Imperfect Enforcement ● 188 | |||

D. Bibliographical Note ● 196 | |||

10. |
HOW TO PRICE UNCERTAINTY: FINANCE |
197 | |

A. Valuation in Perfect Markets ● 199 | |||

i. Known Rates: Discounting ● 199 |
|||

ii. Risky Assets ● 203 |
|||

B. Normative Implications of the CAPM ● 211 | |||

i. Financial Information ● 211 |
|||

ii. Forecasts ● 212 |
|||

C. Financial Market Microstructure: The Game-Theoretical Foundation of the CAPM ● 213 | |||

D. Normative Application of Microstructure: Insider Trading ● 214 | |||

E. Concluding Exercises ● 220 | |||

F. Bibliographical Note ● 224 | |||

11. |
FINANCE AND PROBABILITY: OPTIONS AND DERIVATIVES |
225 | |

A. Option Pricing ● 227 | |||

B. Normative Implications of Option Pricing ● 234 | |||

i. Recipients of Fiduciary Obligation ● 235 |
|||

ii. Automated Reorganizations via Options ● 236 |
|||

iii. The Options Understanding of the New Value Exception ● 240 |
|||

C. Concluding Exercises ● 244 | |||

D. Bibliographical Note ● 248 | |||

12. |
USING SPREADSHEETS |
249 | |

A. The Basics ● 249 | |||

i. Obtaining Built-in Help about Functions ● 251 |
|||

ii. Using the Function Wizard ● 253 |
|||

iii. Categories of Built-in Functions ● 255 |
|||

iv. Relative and Absolute References in Copying ● 258 |
|||

B. Graphics ● 261 | |||

i. Chart Types ● 262 |
|||

ii. Completing the Chart Wizard ● 265 |
|||

iii. Manipulating Charts ● 267 |
|||

C. Solving Equations ● 269 | |||

i. The Solver ● 269 |
|||

ii. Goal Seek ● 270 |
|||

D. Macros and User-Defined Functions ● 271 | |||

i. Recording a Macro ● 271 |
|||

ii. Editing a Macro ● 273 |
|||

iii. Assigning a Macro to a Graphic ● 274 |
|||

iv. Entering a Function ● 274 |
|||

E. Downloading and Combining Data ● 274 | |||

i. Data Files Separating Columns with Commas or Tabs ● 275 |
|||

ii. Specifying the Type of Data ● 277 |
|||

iii. Fixed-Width Data ● 278 |
|||

iv. Combining Data ● 279 |
|||

F. Concluding Exercises ● 280 | |||

G. Bibliographical Note ● 281 | |||

13. |
STATISTICS |
283 | |

A. The Use of Statistics in Legal Thinking ● 284 | |||

B. Fundamentals: Descriptive Statistics and Distributions ● 287 | |||

C. Empirical Research ● 288 | |||

i. Basics: Comparing Data That Take Values and Data That Fall into Categories ● 289 |
|||

ii. Determining Influences: Multiple Outcomes ● 298 |
|||

iii. Determining Influences: Yes/No Outcomes ● 308 |
|||

iv. Observations That Are Filtered by a Threshold ● 310 |
|||

D. Concluding Exercises ● 311 | |||

E. Bibliographical Note ● 313 | |||

14. |
CONCLUSION: IMPORTING METHODOLOGICAL INNOVATIONS |
315 | |

A. Cellular Automata ● 315 | |||

B. Fractals ● 317 | |||

C. Evolutionary Theory ● 320 | |||

D. To End ● 320 | |||

E. Bibliographical Note ● 321 | |||

APPENDIX A: MEINHARD V. SALMON 249 N.Y. 458 (1928) |
323 | ||

APPENDIX B: GLOSSARY |
332 | ||

APPENDIX C: MATHEMATICA NOTEBOOKS |
339 | ||

A. Differential Equations in Law: The Effect of Terminating Affirmative Action ● 342 | |||

i. Determine the Participation in the Workforce ● 342 |
|||

ii. Add the Initial Condition ● 343 |
|||

iii. Manipulate the Exponent to See It Disappear ● 343 |
|||

iv. The Long-Run Participation ● 344 |
|||

v. The Composition of the Candidates ● 344 |
|||

vi. Graphics ● 345 |
|||

B. Derivation of the Normal Distribution ● 347 | |||

i. Derive the Normal Distribution as Gauss Did ● 347 |
|||

ii. The Standard Normal Distribution ● 349 |
|||

iii. Restating with Standard Deviation ● 349 |
|||

iv. Restating with Average Deviation ● 350 |
|||

iv. The Triangular Distribution ● 351 |
|||

C. Application of Triangular Distribution: The Uncertain Apprehension of Speed Limit Violations ● 355 | |||

D. A Comparison of Insider Trading Regimes ● 360 | |||

i. Foundation ● 360 |
|||

ii. Problem ● 361 |
|||

iii. Solution: Statement ● 361 |
|||

iv. Solution: Proof ● 362 |
|||

v. Illustration of Price Path ● 365 |
|||

Index |
369 |

## Preface

This book breaks with several traditions of legal scholarship. Rather than focus on one topic, it seeks to show how broad the application of economic analysis of law can be. Rather than explain existing knowledge, it seeks to show how new methodologies develop. Rather than convey the safety of stability, it seeks comfort in the reality of change. My hope is that it will serve as an adequate introduction for ambitious readers who are eager to follow the bright tradition of innovative legal scholarship.

I hope that this book, which is to a significant extent the result of this approach, helps to orient new jurists in an increasingly complex field. Several voices within the legal academy readily use new methods, expressing with deed their belief that the law of diminishing returns must apply to methodological efforts as well. This book owes much to those pioneers, too numerous to count. The breadth of this book cannot help but force a brevity that is unfair to every one of its topics.

The overall shape of this book, however, is due to the extraordinary editor of Cambridge University Press, Finola O’Sullivan. She provided significant guidance toward an exciting target. Also very significant was the help of her colleagues at Cambridge University Press, John Berger and Scott Parris. Unusually deep is my gratitude to my dear colleague Daniel Cole at Indiana University Law School–Indianapolis. Also voluminous was the help of Andrew Klein and Stephen Utz. I have received great benefit from comments of John Armour, Judge Guido Calebresi, John Donohue, Peg Brinig, Judge Richard Posner, Mark Ramseyer, Eric Rasmusen, Steve Shavell, Peter Siegelman, Jay Weiser, and George Wright.

I stress my gratitude to my numerous teachers, in temporal order: my parents and schoolteachers, my professors at the Athens University Law School, Greece; my professors at Harvard Law School, and particularly my doctorfather, Reinier Kraakman; my professors at Harvard Business School; my colleagues at the University of Connecticut and Indiana University, both in Indianapolis and in Bloomington; my co-authors of the second edition of Blumberg on Corporate Groups (Aspen, 2004); and, finally, the numerous presenters at the seminars that I have had the luck to attend in several schools, the law and economics seminar of Harvard Law School, the finance seminar of Harvard Business School, the faculty seminar of the University of Connecticut School of Law, the law and economics seminar at Yale Law School, which received me with unmatched hospitality; and the law and economics seminar at the Law School of the University of Chicago, as well as the presenters at the annual meetings of the American, Canadian, and European associations of law and economics. To all my professors and almost all the presenters I subjected to questioning and for the occasions that it may have crossed any boundaries, I apologize.

Deep thanks to Liz and Vicki. No bounds have my thanks to my children, Lee and Dimitri. They taught me more than they think. They lost more of my time than I would have liked. Their forbearance is admirable. Their support is precious. They make magic daily and every day magical.