Dynamic Optimization

” I came to the position that mathematical analysis is not one of many ways of doing economic theory: It is the only way.                                              

 Economic theory is mathematical analysis. Everything else is just pictures and talk. ”                

  R.E.Lucas, Jr. (2001)

• This course is one of the core courses in the master program in Economics.

• The focus is on dynamic optimization methods, both in discrete and in continuous time.

PART I  – OPTIMIZATION

Recommended books to study

C - W :  A.Chiang and K. Wainwright, Fundamental Methods of Mathematical Economics, McGraw-Hill, 2005.

K :        M. Klein, Mathematical Methods for Economists, Addison-Wesley, 2001.

Lecture I : Introduction to Optimization

C – W, Chapter 9 : Optimization: A Special Variety of Equilibrium Analysis

C – W, Chapter 11 : The Case of More than One Choice Variable

K, Chapter 9 : Extreme Values of Univariate Functions

K, Chapter 10 : Extreme Values of Multivariate Functions

Lecture II : Constrained Optimization

C – W, Chapter 12 : Optimization with Equality Constraints

K, Chapter 11 : Constrained Optimization

Lecture III – The Kuhn-Tucker and Envelope Theorems 

C – W,  Chapter 13 : Further Topics in Optimization

PART II – DYNAMIC ANALYSIS

Recommended books to study

C -W :    A.Chiang and K. Wainwright, Fundamental Methods of Mathematical Economics, McGraw-Hill, 2005.

K:          M. Klein, Mathematical Methods for Economists, Addison-Wesley, 2001.

Lecture IV – Economic Dynamics and Integral Calculus

C-W, Chapter 14 : Economic Dynamics and Integral Calculus

K, Chapter 12 : Integral Calculus

Lecture V – Continuous Time 

C-W , Chapter 15 : First-Order Differential Equations, Chapter 16 : Higher-Order Differential Equations

K, Chapter 14:  Differential Equations

Lecture VI – Discrete Time

C -W , Chapter 17 :  First-Order Difference Equations, Chapter 18 : Higher-Order Difference Equations

K, Chapter 13 : Difference Equations

PART III – DYNAMIC OPTIMIZATION

Recommended books to study

D :           A.K. Dixit, Optimization in Economic Theory (2nd ed), Oxford University Press, 1990.

S - B  :    Carl P. Simon and Lawrence Blume, Mathematics for Economists, W.W. Norton, 1994.

C :           A. Chiang, Elements of Dynamic Optmization, Waveland Press, 1992.

Lecture VII – Introduction to Dynamic Optimization

C, Chapter 2 : The Calculus of Variations

Lecture VIII – The Kuhn-Tucker and Envelope Theorems

D, Chapters 2, 3, and 5

S-B, Chapters 18 and 19: Constranied Optimization

Lecture IX – The Maximum Principle

D, Chapter 10 : Maximum Principle

C, Chapter 3 : Optimal Control Theory

Lecture X – Dynamic Programming

D, Chapter 11 : Dynamic Programming