Mathematical Methods for Macroeconomics

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

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

Material

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 programming
• optimalcontrol.pdf: lecture notes covering optimal control
• differentialequations.pdf: lecture notes covering differential equations
• exercises.pdf: 13 exercises covering all three topics
• exercises_solutions.pdf: solutions to the exercises
• exam.pdf: one-hour exam covering all three topics
• exam_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 for dynamicprogramming.pdf
• optimalcontrol.tex: source for optimalcontrol.pdf
• differentialequations.tex: source for differentialequations.pdf
• exercises.tex: source for exercises.pdf
• exercises_solutions.tex: source for exercises_solutions.pdf
• exam.tex: source for exam.pdf
• exam_solutions.tex: source for exam_solutions.pdf
• paper.sty, math.sty, notes.sty: style files used in the TEX files
• phasediagrams.key, phasediagrams.pdf: figures imported into the TEX files

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. It was initially developed for EC400 at the London School of Economics and then revised for ECON2080 at Brown University.