Mathematical Methods for Macroeconomics

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

Course Webpage

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

Overview

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:

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

Folder Organization

The material is organized in 3 folders:

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

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

Software

The material was produced on a Mac (macOS Monterey 12.2.1) with the MacTeX-2021 distribution. The LaTeX files should be compiled with pdfTeX. The graphics were produced with Keynote (version 11.2).

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

Author

The course material was developed by Pascal Michaillat for EC400 at the London School of Economics & Political Science.

License

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