Shanghai Jiaotong University Postgraduate Syllabus

Postgraduate Syllabus
Shanghai University of Finance and Economics
Ⅰ、Course Basic Information
Course No.:210012
Course Name:Mathematical Economics
Credits/teaching Hours:3/45
Experiment Hours: 0
Discussion Hours:0
Course Season: Autumn
Course Level:Master course
Department:School of Economics
Teacher:Sun Ning
Office Room:510
Office hour:Wednesday 1:30 —5:00 PM
TA:Yao Yao
Office Room:323
Pre-reading Courses:Calculus; Mathematical Analysis
Object Student:
Ⅱ、Course Introduction
This course is intended as a preparation for the courses of Advanced
Microeconomics I, II, Advanced Macroeconomics. In this course, you will
learn the central mathematical tools utilized in the mathematical approach
to economic analysis, and how these mathematical methods are applied in the
economic theory. This course will assist you in understanding the modern
Ⅲ、Course Arrangement and Requirements
1. Optimization with equality constraints
2. Optimization problem with inequality constraints
The Kuhn-Tucker Theory (calculus-based approach)
3. Convexity and separation theorems
4. The Farkas Lemma
5. The proof of the Kuhn-Tucker Theorem (and the mid-term exam)
6. Convex optimization problems
7. More general convex optimization problems
8. Infinite horizon convex optimization problems and
the transversality condition
9. Basic topology of R n
10. Continuous functions and the Berge Theorem
11. Comparative statics of optimal solutions
12. Fixed point theorem
13. Introduction of dynamic programming
14. The existence of Nash equilibrium and competitive equilibrium
15. The final exam.
Ⅳ、Course Examination Requirements
In-class participation and attendance rate: 15%
Homework: 15%
Mid-term exam: 20%
Final exam: 50%
Ⅴ、Reference books
Lin Zhou, Lecture Notes of Mathematical Economics.
Cark P. Simon and Lawrence Blume, Mathematical Economics, Norton, 1994
Morton I. Kamien and Nancy L. Schwartz, Dynamic Optimization, North-Holland,
Akira Takayama, Mathematical Economics, the Dryden Press, 1974