### 2018　Advanced Topics in Microeconomics

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Graduate major in Industrial Engineering and Economics
Instructor(s)
Yamato Takehiko  Yamamura Hirohumi
Class Format
Lecture
Media-enhanced courses
Day/Period(Room No.)
Intensive (西9号館, 508号室)
Group
-
Course number
IEE.B431
Credits
2
2018
Offered quarter
4Q
Syllabus updated
2018/4/6
Lecture notes updated
-
Language used
Japanese
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### Course description and aims

This course provides lectures on classical models in microeconomic theory to students having basic knowledge on microeconomics. First, we explain the frameworks of models, notions and mathematical formulations, and how to use them in analyzing the models. Theorems derived from the models consist of assumptions and conclusions. We give a lecture on how a conclusion is derived from assumptions (that is, a proof). The models covered in this course include the general equilibrium model, the imperfect competition model, and the social choice model.
This course aims to enable students to understand and acquire meanings, theoretical structure, and implications of important theorems on classical microeconomics. By combining lectures and exercises, the course also teaches students logical operations in economics.

### Student learning outcomes

At the end of this course, students will be able to:
1) Analyze the Arrow–Debreu–McKenzie model of an economy.
2) Explain and prove the fundamental theorems of welfare economics in production economies.
3) Explain and prove theorems on the existence of competitive equilibrium in production economies.
4) Analyze the model of imperfect competition.
5) Analyze the model of social choice theory.

### Keywords

The Arrow–Debreu–McKenzie Model of an economy, the fundamental theorems of welfare economics and the existence theorems of competitive equilibrium in production economies, the theory of imperfect competition, and social choice theory

### Competencies that will be developed

 ✔ Specialist skills Intercultural skills Communication skills Critical thinking skills ✔ Practical and/or problem-solving skills

### Class flow

At the beginning of each class, solutions to exercise problems that were assigned during the previous class are reviewed. Towards the end of class, students are given exercise problems related to the lecture given that day to solve. To prepare for class, students should read the course schedule section and check what topics will be covered. Required learning should be completed outside of the classroom for preparation and review purposes.

### Course schedule/Required learning

Course schedule Required learning
Class 1 Mathematical preliminaries Explain mathematical preliminaries necessary for this course.
Class 2 The Arrow–Debreu–McKenzie model of an economy Analyze the Arrow–Debreu–McKenzie model of an economy.
Class 3 The fundamental theorems of welfare economics in production economies - The first theorem of welfare economics (1) Explain the first theorem of welfare economics.
Class 4 The fundamental theorems of welfare economics in production economies - The first theorem of welfare economics (2) Prove the first theorem of welfare economics.
Class 5 The fundamental theorems of welfare economics in production economies - The second theorem of welfare economics (1) Explain the second theorem of welfare economics.
Class 6 The fundamental theorems of welfare economics in production economies - The second theorem of welfare economics (2) Prove the second theorem of welfare economics.
Class 7 Theorems on the existence of competitive equilibrium in production economies - Conditions for the existence of equilibrium Explain the theorems on the existence of competitive equilibrium in production economies.
Class 8 Theorems on the existence of competitive equilibrium in production economies - Fixed point theorems Explain the mathematical theorems used to prove the theorems on the existence of competitive equilibrium.
Class 9 Theorems on the existence of competitive equilibrium in production economies - Proofs of the existence theorems (1) Explain the structure of the proofs of the theorems on the existence of competitive equilibrium in production economies.
Class 10 Theorems on the existence of competitive equilibrium in production economies - Proofs of the existence theorems (2) Prove the theorems on the existence of competitive equilibrium in production economies.
Class 11 The theory of imperfect competition - The theoretical model of imperfect competition Analyze the theoretical model of imperfect competition.
Class 12 The theory of imperfect competition - Oligopoly Explain and prove the theorems on oligopoly.
Class 13 The theory of imperfect competition - Monopolistic competition Explain and prove the theorems on monopolistic competition.
Class 14 Social choice theory - Arrow's impossibility theorem Explain and prove Arrow's impossibility theorem.
Class 15 Social choice theory - Gibbard–Satterthwaite theorem Explain and prove the Gibbard–Satterthwaite theorem.

### Textbook(s)

No textbook will be set. Course materials will be distributed.

### Reference books, course materials, etc.

Course materials will be distributed.
Arrow, K. J. (1951,1963), Social Choice and Individual Values, Yale University Press.
Mas-Collel, A., M.D. Whinston, and J.R. Green, Microeconomic Theory, Oxford University Press, 1995.
Nishimura, Kazuo, "Microeconmics," Tokyo Keizai Shinpou-sya, 1990. (Japanese)

### Assessment criteria and methods

Students' knowledge of the fundamental theorems of welfare economics and the existence theorems of competitive equilibrium in production economies, the theory of imperfect competition, and social choice theory, and their ability to apply them to problems will be assessed by exams and exercise problems.