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.


Recommended books to study

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

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

Lecture I : Introduction to Optimization

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

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

K, C.9 – Extreme Values of Univariate Functions

K, C.10 – Extreme Values of Multivariate Functions

Lecture II : Constrained Optimization

C – W, C.12 – Optimization with Equality Constraints

K, C.11 – Constrained Optimization

Lecture III – The Kuhn-Tucker and Envelope Theorems 

C – W,  C.13 – Further Topics in Optimization


Recommended books to study

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

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

Lecture IV – Economic Dynamics and Integral Calculus

C-W, C.14 – Economic Dynamics and Integral Calculus

K, C.12 – Integral Calculus

Lecture V – Continuous Time 

C-W , C.15 – First-Order Differential Equations, C.16 – Higher-Order Differential Equations

K, C.14 – Differential Equations

Lecture VI – Discrete Time

C -W , C.17 – First-Order Difference Equations, C.18 – Higher-Order Difference Equations

K, C.13  – Difference Equations


Recommended books to study

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

Carl P. Simon and Lawrence Blume, Mathematics for Economists, W.W. Norton, 1994.

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

Lecture VII – Introduction to Dynamic Optimization

C, P.2 – The Calculus of Variations

Lecture VIII – The Kuhn-Tucker and Envelope Theorems

D, C.2, 3, and 5

S-B, C. 18 – 19: Constranied Optimization

Lecture IX – The Maximum Principle

D, C.10 : Maximum Principle

C, P.3 – Optimal Control Theory

Lecture X – Dynamic Programming

D, C.11 – Dynamic Programming