Graduate School of Economics; Kagawa University; Academic Year 1997
Advanced Economic Theory A (Foundations of Normative Economics: An
Axiomatic Approach)
4 credits; First and Second Semesters, 1997
Room and Schedule: Not offered due to insufficient demand (the corresponding
undergraduate course is offered)
Instructor: H. Reiju Mihara
Office phone: 0878-36-1878
1. Course Description
Normative Economics is concerned with value judgments ("what is good?" or "what should be done?"). In particular, it deals with various rules in society. For each such rule (or mechanism), normative economics asks questions such as "Does it treat individuals equally?" or "Is it likely to be followed by many people? (Doesn't it ignore individuals' incentives to exploit it?)"
Normative economics belongs to the intersection of several disciplines---including ethics, political science and economics. This course, however, will emphasize its theoretical foundations, focusing on a contemporary approach ("axiomatic approach") that uses abstract mathematics (though not far beyond elementary set theory as far as this course is concerned). Why do we use abstract mathematics in normative science? In conventional human and social sciences, criteria of value judgments were usually expressed in a natural language (such as English). But this caused confusion since the same word was used in different meanings by different writers and in different contexts. A simple solution to the confusion is to remove meanings from the language. Translating words into meaningless symbols, we can get a conclusion free of interpretation, through a manipulation of the symbols. We can then give an interpretation back to the conclusion, which is actually just a sequence of symbols. Abstract mathematics is particularly useful for this translation.
Using about thirty axioms, the textbook provides a unified study of welfarism, cooperative games, public decision making, and voting and social choice theory. Each axiom expresses a certain criterion of value judgments, such as "equality of individuals." If time is available, we will also deal with related topics such as mechanism design and mathematical theory of individual rights. Although we will emphasize the developments during the past decade in that case, our aim will not be deciphering original papers on the research frontier, but putting them in context.
The course will be useful to students of economic theory and theoretically inclined students of any social sciences. It will also be valuable to any students who want to train themselves in mathematics as a language.
2. Organization
(Only the contents of the textbook are included here; other topics may be covered.)
Part I. Welfarism
Chapter 1. Egalitarianism versus utilitarianism
Chapter 2. Social welfare orderings
Chapter 3. Axiomatic bargaining
Part II. Cooperative games
Chapter 4. Cost-sharing games and the core
Chapter 5. Values of cooperative games
Part III. Public decision mechanisms
Chapter 6. Equal versus proportional sharing
Chapter 7. Regulated monopoly
Chapter 8. Strategyproof mechanisms
Part IV. Voting and social choice
Chapter 9. Majority voting and scoring methods
Chapter 10. Strategyproofness and core stability
Chapter 11. Aggregation of preferences
3. Format of the Class
The instructor or a student will present each chapter of the textbook. The participants are encouraged (or required) to ask questions or make comments. The discussion will be in Japanese or in English. Each chapter (19-36 pages long) will typically be covered in two class meetings. The emphasis will be on understanding definitions, axioms, and theorems. Proofs of results may also be covered, depending on the quality and the interest of the students.
4. Required Textbook
-Moulin, H., Axioms of Cooperative Decision Making, Cambridge University Press, 1988. ISBN 0-521-42458-5 paperback.
5. References and Supplementary Readings
For references in English, see page 7 of the textbook. More recent developments
in economic theory in general are included in the following textbook (which
is the most reputable introduction to microeconomic theory at the graduate
level; using more than 400 figures, its presentation is intuitive as well
as mathematically rigorous):
-Mas-Colell, A., M.D. Whinston, and J.R. Green, Microeconomic Theory,
Oxford University Press, 1995.
In particular, Part V on welfare economics and incentives is closely related
to many of our topics.
In Japanese, several textbooks in Public Economics present related topics; however, most of them are not as advanced as the textbook. A book [佐伯胖『「決め方」の論理：社会的決定理論への招待』東京大学出版会，1980] by the cognitive scientist Sayeki is a highly readable and amusing introduction to several topics covered in the course.
6. Related Courses
Students are expected to have a background in elementary calculus. Taking graduate or undergraduate courses in formal (mathematical) subjects, such as microeconomics, welfare economics, set theory, probability theory, cooperative game theory, and noncooperative game theory, will be helpful. Courses in public economics and mathematical economics are also related. Although knowledge of ethics and political science may be helpful for understanding the significance of normative economics at an informal level, it is probably not so helpful for understanding the formal approach adopted in the course.
7. Grading
Evaluation of each student will be based on the combination of several of the following: oral examinations, written examinations, problem assignments, class participation (presentations, questions and comments, preparation of teaching materials), and other factors. (This means, in short, the grading policy is undecided.) Emphasis will be on understanding mathematical expressions as a language. If an examination is given, then it will probably include true-or-false problems and translation problems between mathematical expressions and natural language (English or Japanese) expressions, in addition to conventional problem-solving questions. Those students showing a precise understanding of proofs at least in a few chapters will be highly evaluated.