This repository contains material for a one-week graduate course on mathematical methods for macroeconomics.
These lectures cover basic mathematical methods to study dynamical systems, in discrete time and in continuous time. Dynamical systems are systems that involve more than one time-period; they are prevalent in many areas of macroeconomics. The course covers three methods:
- Dynamic programming: to solve discrete-time optimization problems
- Optimal control: to solve continuous-time optimization problems
- Differential equations: to characterize continuous-time systems
All the material for the course is contained in the pdf
and tex
folders.
The pdf
folder contains all the material for the course in PDF format.
dynamicprogramming.pdf
: lecture notes covering dynamic programmingoptimalcontrol.pdf
: lecture notes covering optimal controldifferentialequations.pdf
: lecture notes covering differential equationsexercises.pdf
: 13 exercises covering all three topicsexercises_solutions.pdf
: solutions to the exercisesexam.pdf
: one-hour exam covering all three topicsexam_solutions.pdf
: solutions to the exam
The tex
folder contains the TEX files used to create the PDF files in the pdf
folder.
dynamicprogramming.tex
: source fordynamicprogramming.pdf
optimalcontrol.tex
: source foroptimalcontrol.pdf
differentialequations.tex
: source fordifferentialequations.pdf
exercises.tex
: source forexercises.pdf
exercises_solutions.tex
: source forexercises_solutions.pdf
exam.tex
: source forexam.pdf
exam_solutions.tex
: source forexam_solutions.pdf
paper.sty
,math.sty
,notes.sty
: style files used in the TEX filesphasediagrams.key
,phasediagrams.pdf
: figures imported into the TEX files
No textbook is required for this short course, but the following textbooks provide useful additional material:
- Chapters 6 & 7 of Introduction to Modern Economic Growth by Daron Acemoglu
- Differential Equations, Dynamical Systems, and an Introduction to Chaos by Morris Hirsch, Stephen Smale, and Robert Devaney
The course material was developed by Pascal Michaillat. It was initially developed for EC400 at the London School of Economics and then revised for ECON2080 at Brown University.