Mathematical Methods for Macroeconomics

This repository contains material for a one-week graduate course on mathematical methods for macroeconomics.

Instructor

The course 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.

• lectures folder - 3 sets of lecture notes
• homework folder - 13 exercises and their solutions
• exam folder - a one-hour 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.

Lectures

The lectures folder contains the following material:

• dynamicprogramming.pdf - lecture notes covering dynamic programming
• dynamicprogramming.tex - LaTeX file producing dynamicprogramming.pdf
• optimalcontrol.pdf - lecture notes covering optimal control
• optimalcontrol.tex - LaTeX file producing optimalcontrol.pdf
• differentialequations.pdf - lecture notes covering differential equations
• differentialequations.tex - LaTeX file producing differentialequations.pdf
• phasediagrams.key - Keynote file containing phase diagrams included in the lecture notes
• phasediagrams.pdf - PDF version of phasediagrams.key
• paper.sty - LaTeX style file for scientific papers
• notes.sty - LaTeX style file for lecture notes
• math.sty - LaTeX style file containing mathematical formatting and shortcuts

Homework

The homework folder contains the following material:

• exercises.pdf - 13 exercises covering all three topics
• exercises.tex - LaTeX file producing exercises.pdf
• exercises_solutions.pdf - solutions to the exercises
• exercises_solutions.tex - LaTeX file producing exercises_solutions.pdf
• paper.sty - LaTeX style file for scientific papers
• notes.sty - LaTeX style file for lecture notes
• math.sty - LaTeX style file containing mathematical formatting and shortcuts

Exam

The exam folder contains the following material:

• exam.pdf - one-hour exam covering all three topics
• exam.tex - LaTeX file producing exam.pdf
• exam_solutions.pdf - solutions to the exam
• exam_solutions.tex - LaTeX file producing exam_solutions.pdf
• paper.sty - LaTeX style file for scientific papers
• notes.sty - LaTeX style file for lecture notes
• math.sty - LaTeX style file containing mathematical formatting and shortcuts

Useful resources

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

License

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