Mathematics II (S1, 2021)

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

Wednesday, Friday	10:25-12:10
First session	April 7

Syllabus/Introduction

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

May 28

10:10-12:10

Examination Timetable

While the time slot has 2 hours, consider the time for answering to be 90 minutes and allow 30 minutes to submit your script. For whatever the reason, submission past the deadline will not be accepted.

Either handwrite your answers on papers, take photos of them (or scan them by a scanner), and submit them to ITC-LMS,
or type/handwrite your answers on a computer (or tablet or smart phone) and submit the file (only PDF is accepted) to ITC-LMS.

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).

Topics

Real numbers
Continuous functions and compact sets
Correspondences
Convex sets and (quasi-)concave functions
Differentiation
Negative (semi-)definite matrices
Separating hyperplane theorems
Optimization
Envelope theorem
Fixed point theorems
Dynamic programming

Notes

On the Differentiability of the Value Function