EC251: Mathematical Methods in Economics - Course Materials ...

EC251: Mathematical Methods in Economics
Ludovic Renou
Academic year 2012-2013

Welcome to EC251.
The purpose of this module is to learn how to use mathematics to solve
economic and social problems.
Important: This is neither a course in mathematics nor a course in
economics.

EC251
Ludovic Renou
Room: 5B 203, Telephone: 2767, e-mail: lrenou
Office hours: Thursday: 16 to 17, and Friday: 10-11
All students have to register for one of the classes associated to the
course. Attendance in the classes is mandatory. Every week a problem
set will be assigned and solved in the classes.
There is a test for the course on Wednesday 15th of November. The
syllabus for the test will be announced on the week starting the 29th of
October.
Most, but not all, of the material used in the lectures will be available on
the CMR. Most parts of the course material are similar to the one used
during 2011-2012 but others are new.

Textbooks
◮ “Mathematics for Economics” by M. Hoy, J. Livernois, C. McKenna,
R. Rees and T. Stengos, The MIT Press, Third Edition, 2011.
◮ “Mathematics for Economists” by Malcolm Pemberton and Nicholas
Rau, Manchester University Press, 2001.
◮ “The Structure of Economics” by E. Silberberg and W. Suen,
McGraw HIll, Third Edition, 2001.
◮ Chiang, A. C. and Wainwright, Kevin, Fundamental Methods of
Mathematical Economics, McGraw-Hill Education, 2005.
◮ Sydsaeter, K., and P. Hammond, Essential Mathematics for
Economic Analysis, Second edition, Prentice Hall, 2006.
◮ Simon, C., and L. Blume, Mathematics for Economists, W. W.
Norton & Company, New York, 1994.
◮ Along with a textbook, you may also find Martin Osborne’s online
Mathematics tutorial useful. The tutorial is available at
www.economics.utoronto.ca/osborne/MathTutorial/index.html

Provisional schedule for the course
◮ Week 2 (three hours): Basic concepts (sets, sequences, limits).
Chapters 2 and 3 in HLMRS. Systems of linear equations, Matrices:
Definitions and operations. Determinants. Chapters 7, 8, 9 in
HLMS. Chapters 11 in Pemberton and Rau.
◮ Week 3: Determinant, Inversion, Cramers Rule, Economic
Applications. Chapter 9 in HLMRS and Chapters 11, 12, 13 in
Pemberton and Rau.
◮ Week 4: Vector Spaces, Eigenvectors, eigenvalues, quadratic forms,
Chapter 10 in HLMRS and Chapters 13, 25 in Pemberton and Rau.
◮ Week 5: Real analysis: continuity and differentiability of real-valued
functions. Chapters 4, 5 in HLMRS.
◮ Week 6: Advanced multivariate analysis: Continuity, Derivatives,
Differentiability, Total derivative, Taylor Expansion, Implicit function
Theorem, Convex and concave function. Chapter 11 in HLMRS and
Chapters 14, 15 in Pemberton and Rau.

◮ Week 7: Unconstrained Optimization First and second order
conditions, Restrictions on endogenous variables. Chapter 12 in
HLMRS and Chapters 8, 9, 10 in Pemberton and Rau.
◮ Week 8: Constrained optimization: First and second order
conditions, Existence, Uniqueness. Chapter 13 in HLMRS and
Chapters 16, 17, 18 in Pemberton and Rau.
◮ Week 9: Comparative static and economic applications.
Comparative statics, Envelope theorem, Applications. Chapter 14 in
HLMRS and Chapter 18 in Pemberton and Rau.
◮ Week 10: Integration. Chapters 19, 20 in Pemberton and Rau;
Sections 16.1, 16.3, 16.4, 16.5 HLMRS.
◮ Week 11: Review.

Other details
◮ Course Material: The primary source for all course material will be
the Course Material Repository located at
http://courses.essex.ac.uk/ec/. This will contain, among other
things, lecture slides, problem sets, answers to problem sets, sample
exam questions, answers to tests and any other material that I think
necessary. Please check the repository regularly.
◮ Classes: All students are required to register for one of the classes
that are an essential part of this course. Attendance in the classes is
mandatory. The classes will provide for a closer interaction with the
teacher than is possible in the lectures. You are encouraged to
carefully note things that you do not understand in the lectures and
raise them with the class teacher and myself.

◮ Problem Sets: A problem set will be put on the Course Material
Repository towards the end of each week which will be solved in
class by the class teacher the following week. You are strongly
advised to try solving the problems before going to class. (It is
recommended that you form groups to jointly solve the problems.)
From time to time you will be asked to solve exercises in class and
then to share your solutions with class members. This provides
formative assessment and feedback about your progress.
◮ Test: There will be a test during the term on 15/11/2012,
1700–1900 hrs. The test can potentially account for 50% of your
total mark for this course and you are advised to take it seriously.
Please note that attendance is compulsory. The syllabus and other
details regarding the test will be announced during the course of the
term.