EC251: Mathematical Methods in Economics - Course Materials ...
EC251: Mathematical Methods in Economics - Course Materials ...
EC251: Mathematical Methods in Economics - Course Materials ...
Create successful ePaper yourself
Turn your PDF publications into a flip-book with our unique Google optimized e-Paper software.
<strong>EC251</strong>: <strong>Mathematical</strong> <strong>Methods</strong> <strong>in</strong> <strong>Economics</strong><br />
Ludovic Renou<br />
Academic year 2012-2013
Welcome to <strong>EC251</strong>.<br />
The purpose of this module is to learn how to use mathematics to solve<br />
economic and social problems.<br />
Important: This is neither a course <strong>in</strong> mathematics nor a course <strong>in</strong><br />
economics.
<strong>EC251</strong><br />
Ludovic Renou<br />
Room: 5B 203, Telephone: 2767, e-mail: lrenou<br />
Office hours: Thursday: 16 to 17, and Friday: 10-11<br />
All students have to register for one of the classes associated to the<br />
course. Attendance <strong>in</strong> the classes is mandatory. Every week a problem<br />
set will be assigned and solved <strong>in</strong> the classes.<br />
There is a test for the course on Wednesday 15th of November. The<br />
syllabus for the test will be announced on the week start<strong>in</strong>g the 29th of<br />
October.<br />
Most, but not all, of the material used <strong>in</strong> the lectures will be available on<br />
the CMR. Most parts of the course material are similar to the one used<br />
dur<strong>in</strong>g 2011-2012 but others are new.
Textbooks<br />
◮ “Mathematics for <strong>Economics</strong>” by M. Hoy, J. Livernois, C. McKenna,<br />
R. Rees and T. Stengos, The MIT Press, Third Edition, 2011.<br />
◮ “Mathematics for Economists” by Malcolm Pemberton and Nicholas<br />
Rau, Manchester University Press, 2001.<br />
◮ “The Structure of <strong>Economics</strong>” by E. Silberberg and W. Suen,<br />
McGraw HIll, Third Edition, 2001.<br />
◮ Chiang, A. C. and Wa<strong>in</strong>wright, Kev<strong>in</strong>, Fundamental <strong>Methods</strong> of<br />
<strong>Mathematical</strong> <strong>Economics</strong>, McGraw-Hill Education, 2005.<br />
◮ Sydsaeter, K., and P. Hammond, Essential Mathematics for<br />
Economic Analysis, Second edition, Prentice Hall, 2006.<br />
◮ Simon, C., and L. Blume, Mathematics for Economists, W. W.<br />
Norton & Company, New York, 1994.<br />
◮ Along with a textbook, you may also f<strong>in</strong>d Mart<strong>in</strong> Osborne’s onl<strong>in</strong>e<br />
Mathematics tutorial useful. The tutorial is available at<br />
www.economics.utoronto.ca/osborne/MathTutorial/<strong>in</strong>dex.html
Provisional schedule for the course<br />
◮ Week 2 (three hours): Basic concepts (sets, sequences, limits).<br />
Chapters 2 and 3 <strong>in</strong> HLMRS. Systems of l<strong>in</strong>ear equations, Matrices:<br />
Def<strong>in</strong>itions and operations. Determ<strong>in</strong>ants. Chapters 7, 8, 9 <strong>in</strong><br />
HLMS. Chapters 11 <strong>in</strong> Pemberton and Rau.<br />
◮ Week 3: Determ<strong>in</strong>ant, Inversion, Cramers Rule, Economic<br />
Applications. Chapter 9 <strong>in</strong> HLMRS and Chapters 11, 12, 13 <strong>in</strong><br />
Pemberton and Rau.<br />
◮ Week 4: Vector Spaces, Eigenvectors, eigenvalues, quadratic forms,<br />
Chapter 10 <strong>in</strong> HLMRS and Chapters 13, 25 <strong>in</strong> Pemberton and Rau.<br />
◮ Week 5: Real analysis: cont<strong>in</strong>uity and differentiability of real-valued<br />
functions. Chapters 4, 5 <strong>in</strong> HLMRS.<br />
◮ Week 6: Advanced multivariate analysis: Cont<strong>in</strong>uity, Derivatives,<br />
Differentiability, Total derivative, Taylor Expansion, Implicit function<br />
Theorem, Convex and concave function. Chapter 11 <strong>in</strong> HLMRS and<br />
Chapters 14, 15 <strong>in</strong> Pemberton and Rau.
◮ Week 7: Unconstra<strong>in</strong>ed Optimization First and second order<br />
conditions, Restrictions on endogenous variables. Chapter 12 <strong>in</strong><br />
HLMRS and Chapters 8, 9, 10 <strong>in</strong> Pemberton and Rau.<br />
◮ Week 8: Constra<strong>in</strong>ed optimization: First and second order<br />
conditions, Existence, Uniqueness. Chapter 13 <strong>in</strong> HLMRS and<br />
Chapters 16, 17, 18 <strong>in</strong> Pemberton and Rau.<br />
◮ Week 9: Comparative static and economic applications.<br />
Comparative statics, Envelope theorem, Applications. Chapter 14 <strong>in</strong><br />
HLMRS and Chapter 18 <strong>in</strong> Pemberton and Rau.<br />
◮ Week 10: Integration. Chapters 19, 20 <strong>in</strong> Pemberton and Rau;<br />
Sections 16.1, 16.3, 16.4, 16.5 HLMRS.<br />
◮ Week 11: Review.
Other details<br />
◮ <strong>Course</strong> Material: The primary source for all course material will be<br />
the <strong>Course</strong> Material Repository located at<br />
http://courses.essex.ac.uk/ec/. This will conta<strong>in</strong>, among other<br />
th<strong>in</strong>gs, lecture slides, problem sets, answers to problem sets, sample<br />
exam questions, answers to tests and any other material that I th<strong>in</strong>k<br />
necessary. Please check the repository regularly.<br />
◮ Classes: All students are required to register for one of the classes<br />
that are an essential part of this course. Attendance <strong>in</strong> the classes is<br />
mandatory. The classes will provide for a closer <strong>in</strong>teraction with the<br />
teacher than is possible <strong>in</strong> the lectures. You are encouraged to<br />
carefully note th<strong>in</strong>gs that you do not understand <strong>in</strong> the lectures and<br />
raise them with the class teacher and myself.
◮ Problem Sets: A problem set will be put on the <strong>Course</strong> Material<br />
Repository towards the end of each week which will be solved <strong>in</strong><br />
class by the class teacher the follow<strong>in</strong>g week. You are strongly<br />
advised to try solv<strong>in</strong>g the problems before go<strong>in</strong>g to class. (It is<br />
recommended that you form groups to jo<strong>in</strong>tly solve the problems.)<br />
From time to time you will be asked to solve exercises <strong>in</strong> class and<br />
then to share your solutions with class members. This provides<br />
formative assessment and feedback about your progress.<br />
◮ Test: There will be a test dur<strong>in</strong>g the term on 15/11/2012,<br />
1700–1900 hrs. The test can potentially account for 50% of your<br />
total mark for this course and you are advised to take it seriously.<br />
Please note that attendance is compulsory. The syllabus and other<br />
details regard<strong>in</strong>g the test will be announced dur<strong>in</strong>g the course of the<br />
term.