Department of Economics
ECON 270 Introduction to Mathematical Economics
Course outline
Teaching period Semester Two 2009
Points 18 (Equates to 12 hrs/week)
Pre-requisites BSNS 104 and ECON 112 and ((QUAN 102 or FINQ 102 or
MATH 160 or (MATH 102 and MATH 103))
Lectures Tuesdays Noon to 12:50 pm
Thursdays 4:00 pm to 4:50 pm
Fridays 11:00 am to 11:50 am
Help session Mondays 11:00am to 11:50 am (starting in the second week
of the course)
Lecturing staff All lectures and tutorials will be taken by Robert Alexander.
Co-ordinator Robert Alexander
Room 7.16
Phone 479-8647
Email robert.alexander@otago.ac.nz
Office hours Currently planned for Wednesdays 1:00 pm to 2:50 pm,
or please email for an appointment time to suit.
Textbook Mathematical Economics (second edition, 2005), by Baldani,
Bradfield and Turner, South-Western, Mason, Ohio, USA.
This course will cover the first half of the textbook and
ECON377 will cover the second half.
Notes Copies of lecture outlines will be available on Blackboard.
Please check on Blackboard regularly for updates.
You should come to class prepared to think, try out problems
and ask questions, not just to take notes, although you should
take notes, especially on what you personally find difficult.
Assessment
Assessment will consist of weekly problem sets, three in-class tests and a final
examination, as detailed in the table below. Plussage will be allowed on the tests.
However, you should be aware that, aside from providing feedback on how you are
coping with the paper and some insurance against a poor performance on the final
exam, your internal assessment grade is also an important factor in determining
eligibility for Terms Carried Over (should you fail the paper) and the form of Special
Consideration that might be offered (should you be ill or otherwise impaired during
the final exam).
Problem sets Fridays by 2 pm 10% (best 10 of 11)
Test1 Friday 14 August 10% or 0%
Test 2 Friday 25 September 10% or 0%
Test 3 Friday 9 October 10% or 0%
Final exam 60% to 90%
Terms requirements Completion of at least 9 of 11 weekly problem sets in weeks 2
to 12 of the course and all tests, unless excused for good reason.
Course objective The principal aim of the course is to introduce students to how
mathematics can be used to sharpen and clarify economic analysis. By the end of the
course, successful students will be comfortable with the basic mathematical methods
which are indispensable for a proper understanding of economics and will have some
facility at tackling economic problems using a mathematical framework. The course
will focus on presenting common micro and macro topics in a more rigorous
mathematical way than standard core economics courses, and on those techniques
which will be of use to students continuing in economics. ECON270 is the pre-
requisite for ECON377 Mathematical Economics.
How to succeed in this course
Exercises will be set and their completion is essential to a full understanding of the
course. All problems will be economic ones; there will be no maths for the sake of
maths. One of the most important skills that you need to develop is in translation of an
economic problem into mathematical form, as well as the interpretation of the
solution. Please make use of the help session and office hours. They are provided for
you to ask questions. Doing the exercises is much more important than attending
lectures and hoping for an infusion of knowledge! Every attempt will be made in
class to motivate you and to explain things carefully, but there is no substitute for
doing problems yourself.
Please note that the choice of level and consistency of effort is entirely your own. No-
one else will push you to work. If you want to do well then you should:
(a) Attend classes; participate by attempting problems set in class and ask about any
difficulties you have.
(b) Attempt as many of the set exercises as you can and ask for help when you need it.
(c) Revise thoroughly for each test. For most people it is easier to score well in a test
on a few weeks of work than on the final exam which covers the whole course.
(d) At the end of the course, if you have conscientiously tried all of the exercises, your
revision can focus on examination-type questions.
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Brief course outline
This table sets out the plan of what we will cover but may be subject to change.
Week Topic Chapter in text
beginning
Monday
13 July Introduction to economic models 1
20 July Introduction to economic models 2
27 July Matrices and linear economic models 3
3 August Matrices and linear economic models 4
10 August Review and test
17 August Applications of multivariate calculus 5
24 August Applications of multivariate calculus 6
31 August Mid-semester break
7 September Optimization 7
14 September Optimization 8
21 September Review and test
28 September Constrained optimization 9
5 October Constrained optimization; test 10
12 October Review
Test your readiness
A small amount of time will be spent in the first couple of classes reviewing
necessary mathematical background. This is to remind you of material that you
should already be familiar with. If you find this material largely familiar then you are
a strong position to take this course. If not, you probably have some catching up to
do.
Below you will find a brief self-test to allow you to check on your mastery of this
material. Answers for this test will be available on Blackboard at the end of the first
week of the course.
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Mathematics self-test
Spend no more than about 30 minutes on this test. You should be aiming for 80% or
more. Answers will be posted on Blackboard at the end of the first week of the
course.
dy
1. Find dx if y =
(a) 2x5 – 15x3 + 11x (2 marks)
(b) e5x + lnx (3 marks)
2. At what values of x are the local maximum/minimum values of the function
f(x) = x3 + 6x2 + 7
Classify each as max or min, but do not bother to calculate the function
values at these points. (6 marks)
3. Find the following integrals
(a) ⌠ t dt
⌡ (2 marks)
⌠10 1
(b) ⎮ x dx (3 marks)
⌡
1
4. If U(x,y) = x0.4y0.6
∂U
find (a) ∂x (1 mark)
∂U
(b) ∂y (1 mark)
∂2 U
(c) ∂x∂y (1 mark)
∂2 U
(d) (1 mark)
∂y2
⎛ 3 2⎞
⎛2 2⎞
5. If A = ⎜ 0 –2 ⎟ and C = ⎝ 6 8 ⎠ , if possible, find:
⎜ ⎟
⎝ 0 10 ⎠
(a) AT (1 mark)
(b) AC (2 marks)
(c) |C| (1 mark)
(d) C-1 (2 marks)
6. Find ∫ ln xdx (4 marks)
(Use integration by parts with f ′ = 1 and g = ln x)
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