Introduction to dynamic optimization with economic applications (2017/2018)

Course partially running (all years except the first)

Course code
Name of lecturers
Claudio Zoli, Giam Pietro Cipriani
Claudio Zoli
Number of ECTS credits allocated
Academic sector
NN - -
Language of instruction
not yet allocated

Learning outcomes

This is a 2 credits optional module taught in English by Dr. Martin Forster (University of York, UK)
The aim of the module is to introduce students to dynamic optimisation, with applications in Economics.
By the end of the course students should be able to:
1. explain why taking a dynamic perspective to solving economic problems can be important
2. solve analytically/analyse qualitatively some simple difference and differential equations
in one and two dependent variables
3. explain the methodology underlying dynamic programming and solve a simple economic
model using dynamic programming
4. explain the methodology underlying the maximum principle and solve simple economic
models using the maximum principle


The module is divided into three parts:
1. Part I. Preliminaries: Difference and differential equations in one and two dependent variables
2. Part II. Deterministic dynamic optimisation: Dynamic programming
3. Part III. Deterministic dynamic optimisation: The Maximum Principle

The timetable will consider 4 lectures of 3 hours each covering:
Lecture 1 and Workshop: Difference and Differential Equations in One Dependent
Lecture 2 and Workshop: Systems of Differential Equations.
Lecture 3 and Workshop: Dynamic Programming.
Lecture 4: The Maximum Principle and Applications in Economics.

Workshops following lectures will give students the chance to apply the material that has been covered.

Reading is referred to at the end of the lectures. The best texts are:
Mathematics for Economists. C. Simon and L. Blume. (Part I)
Optimal Control Theory and Static Optimization in Economics. D. Leonard and N. van
Long. (Parts II and III)
Foundations of Dynamic Economic Analysis. M. Caputo. (Parts II and III)
Advanced Macroeconomics. D. Romer. (Part III)

Reference books
Author Title Publisher Year ISBN Note
D. ROMER Advanced Macroeconomics McGraw-Hill 2011
M. Caputo Foundations of Dynamic Economic Analysis Cambridge University Press 2005
C.P. SIMON, L.E. BLUME Mathematics for Economists New York, London: Norton & Company Press, Cambridge 1994 0-393-95733-0
D. Leonard and N. van Long Optimal Control Theory and Static Optimization in Economics. Cambridge University Press 1992

Assessment methods and criteria

Exercises: In addition to the material covered in the workshops following lectures additional exercises are provided as practice for homework.

The evaluation of the students is based on classwork and on an average across two pieces of assessed work:
Assessed work 1: an exercise on phase diagrams.
Assessed work 2: an exercise on the maximum principle.