Mathematics II (S1, 2019)

OYAMA Daisuke
oyama@e.u-tokyo.ac.jp

TA: Takeshi Kawahara

Monday, Wednesday 10:25-12:10
First session April 3
Class room 8

Syllabus (PDF file)

The aim of this course is to provide students with basic tools in Analysis that are needed in advanced level micro and macro economics. The course covers the main part of the Mathematical Appendix in Mas-Colell, Whinston, and Green.

Exam

Final May 29 Examination Schedule

Textbook

A. Mas-Colell, M.D. Whinston, and J.R. Green, Microeconomic Theory, Oxford University Press, 1995. [Amazon]

References

G. Debreu, Theory of Value, Yale University Press, 1959. [Download]
D. M. Kreps, Microeconomic Foundations I: Choice and Competitive Markets, Princeton University Press, 2012. [Amazon] Student's Guide Errata
D. Oyama and T. Takenawa, On the (Non-)Differentiability of the Optimal Value Function When the Optimal Solution Is Unique, Journal of Mathematical Economics 76, 21-32 (2018).
M.L. Puterman, Markov Decision Processes: Discrete Stochastic Dynamic Programming, Wiley-Interscience, 2005. [Amazon]
N.L. Stokey and R.E. Lucas, Recursive Methods in Economic Dynamics, Harvard University Press, 1989. [Amazon]

Topics

  1. Real numbers
  2. Continuous functions and compact sets
  3. Correspondences
  4. Differentiation
  5. Convex sets and (quasi)concave functions
  6. Negative (semi)definite matrices
  7. Optimization
  8. Envelope theorem
  9. Separating hyperplane theorems
  10. Fixed point theorems
  11. Dynamic programming

Notes

Review on Nonnegative Matrices: Part I, Part II
On the Differentiability of the Value Function

Office hours

Friday 14:00-15:30
Economics Research Building 10th floor, 1012