Yeshiva University M.Q.E.

Mathematics for Economists

ECON 5201

Fall 2015

Syllabus

Course Objectives

This course covers some basic mathematical techniques for economists. It focuses on the theory and

applications of optimization in both static and dynamic settings. It also introduces fixed point theorems that

are fundamental for general equilibrium analysis and game theory models with multiple decision-makers.

Detailed topics

Part 1. Static Optimization Theory

1.1 Review of optimization problems with equality constraints, and introduction of optimization

problems with inequality constraints

1.2 Convexity, separation theorems and the Farkas Lemma

1.3 Kuhn-Tucker theory for optimization problems with inequality constraints

1.4 Convex optimization problems

Part 2. Comparative Statics of Static Optimization Theory

and Dynamic Optimization Theory

2.1 Elementary set topology, continuity properties of correspondences

2.2 Correspondences

2.3 Comparative statics of optimal solutions

2.4 Basics of dynamic programming

2.5 Calculus of Variation, Optimal Control, and Pontryagin’s principle

Part 3. Fixed Point Theorems

3.1 Fixed point theorems

Course materials and textbooks

Handouts are distributed in class. The following textbooks are only recommended, and referenced in class:

S. Sundaram, A First Course in Optimization Theory, 1996– edition 1– ISBN 0521497701

The Master of Science in Quantitative Economics

L. Simon and L. Blume, Mathematics for Economists, 1994 – edition 1– ISBN 0393957330

N. Stokey and R. Lucas, Recursive Methods in Economic Dynamics, 1989 – edition 1– ISBN 0674750969

Prerequisites

Multivariate calculus.

Grading

Homework assignments 30%

Midterm Exam 30%

Final exam 40%

Administrative details

Dr. Ran Shao

Classroom: 215 Lexington Ave., Room 506

Class time: TR 9:00 – 10:15 am

Phone: 917-326-4815

E-mail: rshao@yu.edu

Office: 215 Lex. RM 717C

Office hour: Mon. 10:30am – 11:30am, or by appointment

Schedule (Tentative)

Class 1&2: Introduction & Optimization Problem with Equality Constraints

Class 3&4: The Kuhn-Tucker Theory& Convexity, separation theorems

Class 5&6: The Proof of the Kuhn-Tucker Theorem& Convex Optimization Problems

Class 7&8: Convex Optimization Problems& Quiz 1

Class 9&10: Basic Topology of Real Line and Euclidean Space

Class 11&12: Basic Topology, Continuous Functions and the Weierstrass Theorem

Class 13&14: Correspondence, Comparative Statics of Optimal Solutions

Class 15&16: Basics of Dynamic Programming & Quiz 2

Class 17&18: Calculus of Variation, Optimal Control

Class 19&20: Optimal Control, and Pontryagin’s principle

Class 21&22: Fixed Point Theorems

Class 23&24: Fixed Point Theorems

Class 25&26: Review & Final Exam