Course title

Macroeconomic Analysis IIResponsible person
to enter grades
Numbering Code

Day・Period, etc. Mon2(対面)

開講区分単位数

1st semester

2.0

Timetable Slot
Code1J369

Lesson topic
This is an advanced course on general equilibrium theory. The course equips students with the methodologicalknowledge necessary to conduct independent research in this field. Students learn how to prove classical results on
efficiency, existence, and multiplicity of equilibrium, using methods from variational analysis, fixed point
theory, and differential topology as tools. A strong focus is placed on understanding markets with imperfections:
The course addresses how market incompleteness tampers not only with welfare but with the theoretical underpinningsof general equilibrium models. A discussion of recent results outlines the research frontier in the field ofincomplete markets.
Lesson target
Students will understand the structure of general equilibrium models, and the mathematical tools used inequilibrium analysis to a degree that enables independent research in this field.

Syllabus and plan
Tentative schedule and topics:
Week 1: Introduction, Mathematical Concepts
Week 2: Basics of Decision Theory, Variational Analysis I
Week 3: Allocations and Welfare, Differential Topology
Week 4: Variational Analysis II, Basics of Demand Theory
Week 5: Equilibrium and Welfare with Utility
Week 6: Basics of Fixed Point Theory, Existence of Equilibrium
Week 7: Uniqueness of Equilibrium
Week 8: <Midterm Exam>
Week 9: Equilibrium and Welfare without Utility, Financial Markets
Week 10: Radner Equilibrium, Special Case: Arrow-Debreu Equilibrium
Week 11: No-Arbitrage Valuation, Regular Economies
Week 12: Genericity Analysis and the Index Theorem
Week 13: Welfare Properties of Incomplete Markets
Week 14: Production in Incomplete Markets
Week 15: <Review Session>
Week 16: <Exam>
Evaluation method
Midterm Exam: 50%
Final Exam: 50%

Evaluation baseline
The exams will test students' understanding of the course content (theory and methods), and ability to write simple
mathematical proofs.

Notice (include info. on related class)
Even though this course relies heavily on mathematics, little prior knowledge is expected: Students are required tohave a good understanding of linear algebra, differential calculus, and constrained optimization. All othernecessary mathematical concepts are reviewed when first used. What is expected, though, is curiosity andwillingness to learn something new.

Review and preparation
Kobe University requires 45 hours of study from students to award one credit, including both in-class instructions
as well as study outside classes. However, depending on your background in mathematics and your research interests,
you may be inclined to invest more time to get the most out of this course. Students are strongly advised to solve
the weekly problem sets before the next lecture. Sample solutions will be provided in advance of the exams.

Office hour・Contact information
By appointment via email.

Message for student
This course is open to all students interested in mathematical economics. Taking "Macroeconomic Analysis I" prior
to this course is not necessary.

Improvemenets in Teaching

Text

Theory Of Incomplete Markets / Michael Magill and Martine Quinzii : The MIT Press ,2002 ,ISBN:9780262632546
Reference Material
Lecture slides will be provided on BEEF+.
Classroom Language
EnglishKeywords
General Equilibrium Theory

Incomplete Markets