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