2020 Advanced Microeconomics

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Academic unit or major
Graduate major in Industrial Engineering and Economics
Yamato Takehiko 
Class Format
Lecture    (ZOOM)
Media-enhanced courses
Day/Period(Room No.)
Tue7-8(W9-508)  Fri7-8(W9-508)  
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Academic year
Offered quarter
Syllabus updated
Lecture notes updated
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Course description and aims

This course will provide a comprehensive overview of theoretical microeconomic analysis using mathematical economic models at the graduate level. Topics covered in this course will include the following: axioms on consumer preferences, the existence of a utility function, the utility maximization problem, the expenditure minimization problem, the Slutsky equation, properties of demand functions, revealed preferences, consumer surplus, properties of cost (expenditure) functions, Shepard-McKenzie's lemma, duality in consumption and production, existence of competitive equilibria, the first and second theorems of welfare economics, the core convergence theorem, gross substitutability and uniqueness of equilibrium, and general equilibrium dynamics. The course will introduce basic economic concepts and then demonstrate how economically meaningful properties and results are derived and analyzed by using mathematical models. The course will conclude by discussing why market mechanisms are important and widely used.
Microeconomics is important for understanding economic phenomena, and it is essential for the studies of economics, industrial engineering, and other related fields. By combining lectures and exercises, the course aims to enable students to understand and acquire the fundamentals of analytical tools widely applicable to various economic and management situations. Mathematical approaches taught in this course are not only useful in analyzing market mechanisms, but are applicable to various other types of economic systems, and are highly effective in the field of economics and industrial engineering. Students will realize that the analytical tools acquired through this course are useful in other courses of economics and industrial engineering.

Student learning outcomes

At the end of this course, students will be able to:
1) Explain basic ideas behind microeconomics and mathematical models regarding consumer and producer behavior and market mechanisms.
2) Analyze utility maximization, profit maximization, and cost minimization behavior.
3) Calculate and derive demand functions, consumers' surplus, profit functions, and cost functions.
4) Explain the properties of competitive market equilibria in terms of Pareto efficiency and the core and prove the fundamental theorems of welfare economics.
5) Explain the conditions for existence, uniqueness, and stability of equilibrium and prove the theorems on existence, uniqueness, and stability.
6) Justify market mechanisms widely used in economic transactions.


Utility Maximization, Consumption Choice, Consumer's Surplus, Profit Maximization, Competitive Market Equilibrium, Pareto Efficiency, Core, Existence of Equilibrium, Uniqueness and Stability of Equilibrium

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 Introductory lecture on course objectives and microeconomics at the graduate level. Consumer Theory: 1. Utility Maximization - Axioms on consumer preferences and the existence of a utility function Explain axioms on consumer preferences and prove the existence of a utility function.
Class 2 Consumer Theory: 2. Consumption Choice - The utility maximization problem, the expenditure minimization problem, and the Slutsky equation Explain the utility maximization problem and the expenditure minimization problem. Derive the Slutsky equation.
Class 3 Consumer Theory: 3. Demand Function - Properties of demand functions and revealed preferences. Derive properties of demand functions and explain revealed preferences.
Class 4 Consumer Theory: 4. Consumer Surplus - Compensating variation, equivalent variation, and consumer surplus Compare compensating variation, equivalent variation, and consumer surplus.
Class 5 Producer Theory: 1. Production Technology, 2. Profit Maximization - Specification of production technology and properties of factor demand and supply functions Explain specification of production technology and derive properties of demand and supply functions.
Class 6 Producer Theory: 3. Profit Function - Properties of the profit function, Hotelling’s lemma, the envelope theorem, and properties of factor demand and output supply functions Derive properties of the profit function, Hotelling’s lemma, and the envelope theorem. Derive properties of factor demand and output supply functions.
Class 7 Producer Theory: 4. Cost Function, 5. Duality - Cost minimization, properties of the cost function, and duality in production Derive properties of the cost function and explain duality in production.
Class 8 Analysis of Competitive Markets, Exchange Economies - Properties of competitive equilibria and graphical analysis of exchange economies Analyze equilibria in competitive markets and their properties. Explain exchange economies. Conduct a graphical analysis of competitive equilibria in exchange economies.
Class 9 Existence of Competitive Equilibrium - Properties of the aggregate excess demand functions, fixed-point theorems, and existence of competitive equilibria Explain the conditions for existence of competitive equilibria and prove the existence theorem.
Class 10 The fundamental theorems of welfare economics - Weak and strong Pareto efficiency and the first theorem of welfare economics Explain the difference between weak and strong Pareto efficiency and prove their equivalence theorem. Prove the first theorem of welfare economics.
Class 11 The fundamental theorems of welfare economics - The second theorem of welfare economics Explain the second theorem of welfare economics and its proof.
Class 12 Core and competitive equilibrium allocations - The relation between the core and competitive equilibrium allocations, equal treatment in the core, and shrinking core Explain the relation between the core and competitive equilibrium allocations and prove the core convergence theorem.
Class 13 Uniqueness and stability of equilibrium - Gross substitutes implies unique equilibrium; WARP implies stability. Explain the conditions for uniqueness and stability of equilibrium and prove the theorems on uniqueness and stability.
Class 14 General Equilibrium Analysis in Production Economies - Properties of competitive equilibria in production Economies Derive properties of competitive equilibria in production economies.

Out-of-Class Study Time (Preparation and Review)

To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.


Varian, H.R., Microeconomic Analysis, 3rd edition, Norton, 1992.

Reference books, course materials, etc.

Download course materials from Tokyo Tech OCW-i.
Mas-Collel, A., M.D. Whinston, and J.R. Green, Microeconomic Theory, Oxford University Press, 1995.
Takekuma, Shinichi, "Microeconmics," Shinsei-sya, 1999. (Japanese)
Nishimura, Kazuo, "Microeconmics," Tokyo Keizai Shinpou-sya, 1990. (Japanese)

Assessment criteria and methods

Students' knowledge of consumer theory, producer theory, and market equilibrium, and their ability to apply them to problems will be assessed based on homework and reports.

Related courses

  • IEE.B402 : Advanced Macroeconomics
  • IEE.B403 : Advanced Noncooperative Game Theory
  • IEE.B404 : Advanced Cooperative Game Theory
  • IEE.B431 : Advanced Topics in Microeconomics
  • IEE.B433 : Advanced Topics in Mathematical Economics

Prerequisites (i.e., required knowledge, skills, courses, etc.)

Students must have successfully completed both Microeconomics I and Microeconomics II or have equivalent knowledge.

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