Mathematical Methods for Macroeconomics

This repository contains teaching material for a week-long graduate course on mathematical methods for macroeconomics. The material was developed by Pascal Michaillat for EC400 at the London School of Economics & Political Science.

Course webpage

The course is hosted at https://www.pascalmichaillat.org/t3.html.

Course overview

The course covers 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:

1. Dynamic programming - to solve discrete-time optimization problems
2. Optimal control - to solve continuous-time optimization problems
3. Differential equations - to characterize continuous-time systems

Course material

The repository contains all the material for the course. It is organized in 3 folders:

• lectures folder - 3 sets of lecture notes
• homework folder - 3 problem sets and their solutions
• exam folder - a one-hour cumulative exam and its solutions

The material is available both as LaTeX files and as PDF files. The PDF files are produced by compiling the LaTeX files using pdfTeX and the MacTeX-2021 distribution.

LaTeX style files

The 3 folders contain the following LaTeX style files:

• paper.sty - style file for scientific papers
• notes.sty - style file modifying paper.sty for lecture notes
• math.sty - style file containing mathematical formatting and shortcuts

Lectures

The lectures folder contains the following material:

• dynamicprogramming.pdf - lecture notes on dynamic programming
• dynamicprogramming.tex - LaTeX file producing dynamicprogramming.pdf
• optimalcontrol.pdf - lecture notes on optimal control
• optimalcontrol.tex - LaTeX file producing optimalcontrol.pdf
• differentialequations.pdf - lecture notes on differential equations
• differentialequations.tex - LaTeX file producing differentialequations.pdf
• phasediagrams.pdf - phase diagrams included in differentialequations.tex
• phasediagrams.key - Keynote file producing phasediagrams.pdf

Homework

The homework folder contains the following material:

• ps1.pdf - problem set on dynamic programming
• ps1.tex - LaTeX file producing ps1.pdf
• ps1solutions.pdf - solutions to the problem set on dynamic programming
• ps1solutions.tex - LaTeX file producing ps1solutions.pdf
• ps2.pdf - problem set on optimal control
• ps2.tex - LaTeX file producing ps2.pdf
• ps2solutions.pdf - solutions to the problem set on optimal control
• ps2solutions.tex - LaTeX file producing ps2solutions.pdf
• ps3.pdf - problem set on differential equations
• ps3.tex - LaTeX file producing ps3.pdf
• ps3solutions.pdf - solutions to the problem set on differential equations
• ps3solutions.tex - LaTeX file producing ps3solutions.pdf

Exam

The exam folder contains the following material:

• exam.pdf - one-hour exam covering all three topics
• exam.tex - LaTeX file producing exam.pdf
• examsolutions.pdf - solutions to the exam
• examsolutions.tex - LaTeX file producing exam_solutions.pdf

Useful resources

No textbook is required for this 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

License

The content of this repository is licensed under the terms of the Creative Commons Attribution 4.0 International License (CC BY 4.0).