ECON3202 Mathematical Economics - 2021

ECON3202
Undergraduate
Term 2
6 Units of Credit
On Campus and Online
Economics
The course outline is not available for current term. To view outlines from other year and/or terms visit the archives

1. Course Details

Summary of Course

Mathematical tools are an important part of theoretical economic analysis. The main purpose of this course is to introduce students to advanced mathematical techniques used in theoretical economic analysis. In addition, the course will provide a stepping stone to Honours programs in economics and related disciplines and to other advanced undergraduate courses.

This course gives students a working knowledge of basic analysis, topology, and static and dynamic optimisation techniques applied in economics. Topics include logic and set theory, topological principles in Euclidean spaces, properties of real-valued functions (continuity, concavity, quasi-concavity), differentiation in multi-dimensional Euclidean spaces, classical optimisation with and without constraints, comparative statics, and envelope theorems. All mathematical techniques are illustrated with mainstream theoretical applications such as consumer theory and game theory.

Teaching Times and Locations

Please note that teaching times and locations are subject to change. Students are strongly advised to refer to the Class Timetable website for the most up-to-date teaching times and locations.

View course timetable

Course Policies & Support

Course Aims and Relationship to Other Courses

This course is offered as part of the economics streams in the BCom and BEc degrees. A prerequisite for this course is ECON1202 Quantitative Economics.

This course is an introduction to advanced mathematics used in economic analysis. This course aims to:

  • introduce students to the mathematical concepts and methods used by professional economists;
  • provide a rich and rigorous foundation to complex problem solving;
  • equip students with the necessary knowledge to express economic ideas with formal mathematical concepts;
  • develop students’ ability to derive logical implications of formal economic models.

This course aims to develop the skills and knowledge that students will need if they advance to graduate studies in Economics. The course provides a strong foundation for Honours and further postgraduate study in economics.

2. Staff Contact Details

Position Title Name Email Location Phone Consultation Times
Lecturer-in-ChargeAProfJuan Carlos CarbajalRoom 407, UNSW Business School9385 3962Mondays 15:00 - 16:00 (online) and by appointment

Communication with staff

You should feel free to contact your lecturer about any academic matter. However, it is strongly encouraged, for efficiency reasons, that all enquiries about the subject material be made at lectures or during consultation time. Discussion of course subject material will not be entered into via lengthy emails.

Email correspondence on administrative matters will be responded to within 48 hours, but not over weekends. Please note that the lecturer has no advance notice of the date and time of the final exam.

Student Enrolment Requests

Students can vary their own enrolment (including switching lecture streams or tutorials) via myUNSW until the end of Week 1. In general, most other student enrolment requests should be directed to The Nucleus: Student Hub (formerly Student Central). These include enrolment in full courses or tutorials, course timetable clashes, waiving prerequisites for any course, transfer-of-credit (international exchange, transfer to UNSW, cross-institutional study, etc.), or any other request which requires a decision about equivalence of courses and late enrolment for any course. Where appropriate, the request will be passed to the School Office for approval before processing. Note that enrolment changes are rarely considered after Week 2 classes have taken place.

3. Learning and Teaching Activities

Approach to Learning and Teaching in the Course

​The philosophy underpinning this course and its teaching and learning strategies is based on “Guidelines on Learning" that Inform Teaching at UNSW".

Specifically, the lectures, tutorials and assessment have been designed to appropriately challenge students and support the achievement of the desired learning outcomes. A climate of inquiry and dialogue is encouraged between students and teachers and among students (in and out of class). The lecturers and tutors aim to provide meaningful and timely feedback to students to improve learning outcomes.

Learning Activities and Teaching Strategies

​The examinable content of the course is defined by the references given in the lecture and tutorial schedules, the content of lectures, and the content of the tutorial program.

Lectures

Lectures will be live via Zoom. The purpose of the lectures is to provide a logical structure for the topics that make up the course; to emphasise the important concepts and methods of each topic, and to provide relevant examples to which the concepts and methods are applied. Lecture attendance is essential. This course has been designed to highlight in-class discussions of complex material. In particular, the lecturer will make extensive use of a virtual white-board in Zoom to discuss, derive and explain mathematical concepts pertinent to theoretical economics. Thus, synchronous attendance to the lectures is encouraged.

Tutorials

Tutorials are an integral part of the subject. Tutorial presentations/discussions and questions/problems will build on the material discussed in class with the lecturer.  

Out-of-Class Study

While students may have preferred individual learning strategies, it is important to note that outside-of-class learning time is essential to reinforce the concepts developed in lectures and tutorials.

An “ideal” strategy (on which the provision of the course materials is based) might include:

  • Reading of the recommended material before the lecture. This will give you a general idea of the topic area.
  • Attending the lecture. Here the context of the topic in the course and the important elements of the topic are identified and explained. Examples are given, and formal results stated, discussed, and proven.
  • Attempting the weekly homework assignments.
  • Attending and participating in the tutorial sessions to reinforce learning.

The lectures will focus on aspects that are more difficult to understand or apply with the aim of providing greater comprehension and facility. The readings and the lectures give you an opportunity to learn the concepts and methods, see some simple applications, and begin the process of learning to use these models on your own.

You will be given homework assignments which are an essential part of the course. The homework assignments present the mathematical methods with statements and proofs of the main theorems and many examples and problems. The assignments will be marked, so you will be asked to submit your work. We will discuss the answers in the tutorial sessions and you will be expected to participate in the discussion. Since the problems on the exam will be similar in character to the assigned problems, your serious effort on the homework assignments is a necessary condition for good performance on the exam.

5. Course Resources

​The website for this course is on UNSW Moodle.

Since the emphasis in ECON3202 is on developing formal mathematics as applied to economic analysis, we shall use the mathematical appendix of the following textbook, which will be considered required reading:

  • Geoffrey Jehle and Philip Reny, Advanced Microeconomic Theory, Pearson Education, 3rd edition 2011. (JR)
A more advanced textbook that covers the same material in a more rigorous way, and that will be treated as a recommended textbook, is:
  • Rangarajan Sundaram, A First Course in Optimization Theory, Cambridge University Press, 1996.
Additional references for mathematics for economics include:
  • Alpha C. Chiang, Kevin Wainwright, Fundamental Methods of Mathematical Economics, McGraw-Hill Education, 4th ed. 2005, and
  • Simon, Carl P., Lawrence Blume, Mathematics for Economists, W. W. Norton, 1994.

6. Course Evaluation & Development

Feedback is regularly sought from students and continual improvements are made based on this feedback. At the end of this course, you will be asked to complete the myExperience survey, which provides a key source of student evaluative feedback. Your input into this quality enhancement process is extremely valuable in assisting us to meet the needs of our students and provide an effective and enriching learning experience. The results of all surveys are carefully considered and do lead to action towards enhancing educational quality.

​The School of Economics strives to be responsive to student feedback. If you would like more information on how the design of this course and changes made to it over time have taken students’ needs and preferences into account, please contact the Director of Education at the School of Economics.

Consent for De-Identified Data to be Used for Secondary Research into Improving Student Experience

To enhance your student experience, researchers at UNSW conduct academic research that involves the use of de-identified student data, such as assessment outcomes, course grades, course engagement and participation, etc. Students of this course are being invited to provide their consent for their de-identified data to be shared with UNSW researchers for research purposes after the course is completed.

Providing consent for your de-identified data to be used in academic research is voluntary and not doing so will not have an impact on your course grades.

Researchers who want to access your de-identified data for future research projects will need to submit individual UNSW Ethics Applications for approval before they can access your data.

A full description of the research activities aims, risks associated with these activities and how your privacy and confidentiality will be protected at all times can be found here.

If you consent to have your de-identified data used for academic research into improving student experience, you do not need to do anything. Your consent will be implied, and your data may be used for research in a format that will not individually identify you after the course is completed.

If you do not consent  for this to happen, please email the opt-out form  to seer@unsw.edu.au  to opt-out from having your de-identified data used in this manner. If you complete the opt-out form, the information about you that was collected during this course will not be used in academic research.

7. Course Schedule

Note: for more information on the UNSW academic calendar and key dates including study period, exam, supplementary exam and result release, please visit: https://student.unsw.edu.au/new-calendar-dates
Week Activity Topic Assessment/Other
Week 1: 31 MayLecture
  • Logic and methods of proof
  • Set theory
  • Convex sets

JR Mathematical Appendix sections A1.1 and A1.2

Tutorial

No tutorial session

Week 2: 7 JuneLecture
  • Euclidean spaces
  • Basic topology
  • Operations with open and closed sets

Homework Assignment 01 due Wednesday

JR Mathematical Appendix section A1.3

Tutorial

Review of Homework Assignment 01

 

 

 

Week 3: 15 JuneLecture
  • Sequences in one-dimensional spaces
  • Limits of sequences
  • Limits of functions

Homework Assignment 02 due Wednesday

JR Mathematical Appendix section A1.3

Tutorial

Review of Homework Assignment 02

 

 

Week 4: 21 JuneLecture
  • Continuity of functions
  • Operations preserving continuity
  • Sequences in multidimensional Euclidean spaces

Homework Assignment 03 due Wednesday

JR Mathematical Appendix section A1.4

Tutorial

Review of Homework Assignment 03

Week 5: 28 JuneLecture
  • Continuity in multidimensional spaces
  • Existence theorems
  • Linear functions

Homework Assignment 04 due Wednesday

JR Mathematical Appendix sections A1.4 and A2.1

Tutorial

Review of Homework Assignment 04

Week 6: 5 JulyLecture

No lecture

Tutorial

No tutorial session

 

 

Week 7: 12 JulyLecture
  • Differentiability in one-dimensional Euclidean spaces
  • Concavity and convexity via differentiability
  • Quasi-concave functions

Homework Assignment 05 due Wednesday

JR Mathematical Appendix section A2.2

Tutorial

Review of Homework Assignment 05

 

 

Week 8: 19 JulyLecture
  • Differentiation in multidimensional Euclidean spaces
  • Concavity and convexity in multidimensional Euclidean spaces
  • Directional derivatives

Homework Assignment 06 due Wednesday

JR Mathematical Appendix section A2.3

Tutorial

Review of Homework Assignment 06

 

 

Week 9: 26 JulyLecture
  • Unconstrained optimisation in single-dimensional spaces
  • Constrained optimisation in single-dimensional spaces

Homework Assignment 07 due Wednesday

JR Mathematical Appendix section A2.4

Tutorial

Review of Homework Assignment 07

 

 

Week 10: 2 AugustLecture
  • Unconstrained optimisation in multidimensional spaces
  • Constrained optimisation in multidimensional spaces
  • Envelope theorems (optional)
  • Theorem of the maximum (optional)

Homework Assignment 08 due Wednesday

 

 

 

Tutorial

Review of Homework Assignment 08

8. Policies and Support

Information about UNSW Business School program learning outcomes, academic integrity, student responsibilities and student support services. For information regarding special consideration and viewing final exam scripts, please go to the key policies and support page.

Program Learning Outcomes

The Business School places knowledge and capabilities at the core of its curriculum via seven Program Learning Outcomes (PLOs). These PLOs are systematically embedded and developed across the duration of all coursework programs in the Business School.

PLOs embody the knowledge, skills and capabilities that are taught, practised and assessed within each Business School program. They articulate what you should know and be able to do upon successful completion of your degree.

Upon graduation, you should have a high level of specialised business knowledge and capacity for responsible business thinking, underpinned by ethical professional practice. You should be able to harness, manage and communicate business information effectively and work collaboratively with others. You should be an experienced problem-solver and critical thinker, with a global perspective, cultural competence and the potential for innovative leadership.

All UNSW programs and courses are designed to assess the attainment of program and/or course level learning outcomes, as required by the UNSW Assessment Design Procedure. It is important that you become familiar with the Business School PLOs, as they constitute the framework which informs and shapes the components and assessments of the courses within your program of study.

PLO 1: Business knowledge

Students will make informed and effective selection and application of knowledge in a discipline or profession, in the contexts of local and global business.

PLO 2: Problem solving

Students will define and address business problems, and propose effective evidence-based solutions, through the application of rigorous analysis and critical thinking.

PLO 3: Business communication

Students will harness, manage and communicate business information effectively using multiple forms of communication across different channels.

PLO 4: Teamwork

Students will interact and collaborate effectively with others to achieve a common business purpose or fulfil a common business project, and reflect critically on the process and the outcomes.

PLO 5: Responsible business practice

Students will develop and be committed to responsible business thinking and approaches, which are underpinned by ethical professional practice and sustainability considerations.

PLO 6: Global and cultural competence

Students will be aware of business systems in the wider world and actively committed to recognise and respect the cultural norms, beliefs and values of others, and will apply this knowledge to interact, communicate and work effectively in diverse environments.

PLO 7: Leadership development

Students will develop the capacity to take initiative, encourage forward thinking and bring about innovation, while effectively influencing others to achieve desired results.

These PLOs relate to undergraduate and postgraduate coursework programs.  Separate PLOs for honours and postgraduate research programs are included under 'Related Documents'.

Business School course outlines provide detailed information for students on how the course learning outcomes, learning activities, and assessment/s contribute to the development of Program Learning Outcomes.

RELATED DOCUMENTS

 

UNSW Graduate Capabilities

The Business School PLOs also incorporate UNSW graduate capabilities, a set of generic abilities and skills that all students are expected to achieve by graduation. These capabilities articulate the University’s institutional values, as well as future employer expectations.

UNSW Graduate CapabilitiesBusiness School PLOs
Scholars capable of independent and collaborative enquiry, rigorous in their analysis, critique and reflection, and able to innovate by applying their knowledge and skills to the solution of novel as well as routine problems.
  • PLO 1: Business knowledge
  • PLO 2: Problem solving
  • PLO 3: Business communication
  • PLO 4: Teamwork
  • PLO 7: Leadership development

Entrepreneurial leaders capable of initiating and embracing innovation and change, as well as engaging and enabling others to contribute to change
  • PLO 1: Business knowledge
  • PLO 2: Problem solving
  • PLO 3: Business communication
  • PLO 4: Teamwork
  • PLO 6: Global and cultural competence
  • PLO 7: Leadership development

Professionals capable of ethical, self-directed practice and independent lifelong learning
  • PLO 1: Business knowledge
  • PLO 2: Problem solving
  • PLO 3: Business communication
  • PLO 5: Responsible business practice

Global citizens who are culturally adept and capable of respecting diversity and acting in a socially just and responsible way.
  • PLO 1: Business knowledge
  • PLO 2: Problem solving
  • PLO 3: Business communication
  • PLO 4: Teamwork
  • PLO 5: Responsible business practice
  • PLO 6: Global and cultural competence

While our programs are designed to provide coverage of all PLOs and graduate capabilities, they also provide you with a great deal of choice and flexibility.  The Business School strongly advises you to choose a range of courses that assist your development against the seven PLOs and four graduate capabilities, and to keep a record of your achievements as part of your portfolio. You can use a portfolio as evidence in employment applications as well as a reference for work or further study. For support with selecting your courses contact the UNSW Business School Student Services team.





Academic Integrity and Plagiarism

Academic Integrity is honest and responsible scholarship. This form of ethical scholarship is highly valued at UNSW. Terms like Academic Integrity, misconduct, referencing, conventions, plagiarism, academic practices, citations and evidence based learning are all considered basic concepts that successful university students understand. Learning how to communicate original ideas, refer sources, work independently, and report results accurately and honestly are skills that you will be able to carry beyond your studies.

The definition of academic misconduct is broad. It covers practices such as cheating, copying and using another person’s work without appropriate acknowledgement. Incidents of academic misconduct may have serious consequences for students.

Plagiarism

UNSW regards plagiarism as a form of academic misconduct. UNSW has very strict rules regarding plagiarism. Plagiarism at UNSW is using the words or ideas of others and passing them off as your own. All Schools in the Business School have a Student Ethics Officer who will investigate incidents of plagiarism and may result in a student’s name being placed on the Plagiarism and Student Misconduct Registers.

Below are examples of plagiarism including self-plagiarism:

Copying: Using the same or very similar words to the original text or idea without acknowledging the source or using quotation marks. This includes copying materials, ideas or concepts from a book, article, report or other written document, presentation, composition, artwork, design, drawing, circuitry, computer program or software, website, internet, other electronic resource, or another person's assignment, without appropriate acknowledgement of authorship.

Inappropriate Paraphrasing: Changing a few words and phrases while mostly retaining the original structure and/or progression of ideas of the original, and information without acknowledgement. This also applies in presentations where someone paraphrases another’s ideas or words without credit and to piecing together quotes and paraphrases into a new whole, without appropriate referencing.

Collusion: Presenting work as independent work when it has been produced in whole or part in collusion with other people. Collusion includes:

  • Students providing their work to another student before the due date, or for the purpose of them plagiarising at any time
  • Paying another person to perform an academic task and passing it off as your own
  • Stealing or acquiring another person’s academic work and copying it
  • Offering to complete another person’s work or seeking payment for completing academic work

Collusion should not be confused with academic collaboration (i.e., shared contribution towards a group task).

Inappropriate Citation: Citing sources which have not been read, without acknowledging the 'secondary' source from which knowledge of them has been obtained.

Self-Plagiarism: ‘Self-plagiarism’ occurs where an author republishes their own previously written work and presents it as new findings without referencing the earlier work, either in its entirety or partially. Self-plagiarism is also referred to as 'recycling', 'duplication', or 'multiple submissions of research findings' without disclosure. In the student context, self-plagiarism includes re-using parts of, or all of, a body of work that has already been submitted for assessment without proper citation.

To see if you understand plagiarism, do this short quiz: https://student.unsw.edu.au/plagiarism-quiz

Cheating

The University also regards cheating as a form of academic misconduct. Cheating is knowingly submitting the work of others as their own and includes contract cheating (work produced by an external agent or third party that is submitted under the pretences of being a student’s original piece of work). Cheating is not acceptable at UNSW.

If you need to revise or clarify any terms associated with academic integrity you should explore the 'Working with Academic Integrity' self-paced lessons available at: https://student.unsw.edu.au/aim.

For UNSW policies, penalties, and information to help you avoid plagiarism see: https://student.unsw.edu.au/plagiarism as well as the guidelines in the online ELISE tutorials for all new UNSW students: http://subjectguides.library.unsw.edu.au/elise. For information on student conduct see: https://student.unsw.edu.au/conduct.

For information on how to acknowledge your sources and reference correctly, see: https://student.unsw.edu.au/referencing. If you are unsure what referencing style to use in this course, you should ask the lecturer in charge.



Student Responsibilities and Conduct

​Students are expected to be familiar with and adhere to university policies in relation to class attendance and general conduct and behaviour, including maintaining a safe, respectful environment; and to understand their obligations in relation to workload, assessment and keeping informed.

Information and policies on these topics can be found on the 'Managing your Program' website.

Workload

It is expected that you will spend at least ten to twelve hours per week studying for a course except for Summer Term courses which have a minimum weekly workload of twenty to twenty four hours. This time should be made up of reading, research, working on exercises and problems, online activities and attending classes. In periods where you need to complete assignments or prepare for examinations, the workload may be greater. Over-commitment has been a cause of failure for many students. You should take the required workload into account when planning how to balance study with employment and other activities.

We strongly encourage you to connect with your Moodle course websites in the first week of semester. Local and international research indicates that students who engage early and often with their course website are more likely to pass their course.

View more information on expected workload

Attendance

Your regular and punctual attendance at lectures and seminars or in online learning activities is expected in this course. The Business School reserves the right to refuse final assessment to those students who attend less than 80% of scheduled classes where attendance and participation is required as part of the learning process (e.g., tutorials, flipped classroom sessions, seminars, labs, etc.).

View more information on attendance

General Conduct and Behaviour

You are expected to conduct yourself with consideration and respect for the needs of your fellow students and teaching staff. Conduct which unduly disrupts or interferes with a class, such as ringing or talking on mobile phones, is not acceptable and students may be asked to leave the class.

View more information on student conduct

Health and Safety

UNSW Policy requires each person to work safely and responsibly, in order to avoid personal injury and to protect the safety of others.

View more information on Health and Safety

Keeping Informed

You should take note of all announcements made in lectures, tutorials or on the course web site. From time to time, the University will send important announcements to your university e-mail address without providing you with a paper copy. You will be deemed to have received this information. It is also your responsibility to keep the University informed of all changes to your contact details.




Student Support and Resources

The University and the Business School provide a wide range of support services and resources for students, including:

Business School Learning Support Tools
Business School provides support a wide range of free resources and services to help students in-class and out-of-class, as well as online. These include:

  • Academic Communication Essentials – A range of academic communication workshops, modules and resources to assist you in developing your academic communication skills.
  • Learning consultations – Meet learning consultants who have expertise in business studies, literacy, numeracy and statistics, writing, referencing, and researching at university level.
  • PASS classes – Study sessions facilitated by students who have previously and successfully completed the course.
  • Textbook access scheme – To support the inclusion and success of students from equity groups enrolled at UNSW Sydney in first year undergraduate Business programs.

The Nucleus - Business School Student Services team
The Nucleus Student Services team provides advice and direction on all aspects of enrolment and graduation. Level 2, Main Library, Kensington 02 8936 7005 / https://nucleus.unsw.edu.au/en/contact-us

Business School Equity, Diversity and Inclusion
The Business School Equity, Diversity and Inclusion Committee strives to ensure that every student is empowered to have equal access to education. The Business School provides a vibrant, safe, and equitable environment for education, research, and engagement that embraces diversity and treats all people with dignity and respect. BUSEDI@unsw.edu.au

UNSW Learning & Careers Hub
The UNSW Learning & Careers Hub provides academic skills and careers support services—including workshops, individual consultations and a range of online resources—for all UNSW students. See their website for details.
Lower Ground Floor, North Wing Chancellery Building.
learningcentre@unsw.edu.au
02 9385 2060

Student Support Advisors
Student Support Advisors work with all students to promote the development of skills needed to succeed at university, whilst also providing personal support throughout the process.
John Goodsell Building, Ground Floor.
advisors@unsw.edu.au
02 9385 4734

International Student Support
The International Student Experience Unit (ISEU) is the first point of contact for international students. ISEU staff are always here to help with personalised advice and information about all aspects of university life and life in Australia.
Advisors can support you with your student visa, health and wellbeing, making friends, accommodation and academic performance.
International.student@unsw.edu.au
02 9385 4734

Equitable Learning Services
Equitable Learning Services (formerly Disability Support Services) is a free and confidential service that provides practical support to ensure that your health condition doesn't adversely affect your studies. Register with the service to receive educational adjustments.
Ground Floor, John Goodsell Building.
els@unsw.edu.au
02 9385 4734

UNSW Counselling and Psychological Services
Provides support and services if you need help with your personal life, getting your academic life back on track or just want to know how to stay safe, including free, confidential counselling.
Level 2, East Wing, Quadrangle Building.
counselling@unsw.edu.au
02 9385 5418

Library services and facilities for students
The UNSW Library offers a range of collections, services and facilities both on-campus and online.
Main Library, F21.
02 9065 9444

Moodle eLearning Support
Moodle is the University’s learning management system. You should ensure that you log into Moodle regularly.
externalteltsupport@unsw.edu.au
02 9385 3331

UNSW IT
UNSW IT provides support and services for students such as password access, email services, wireless services and technical support.
UNSW Library Annexe (Ground floor).
02 9385 1333



Support for Studying Online

The Business School and UNSW provide a wide range of tools, support and advice to help students achieve their online learning goals. 

The UNSW Guide to Online Study page provides guidance for students on how to make the most of online study.

We recognise that completing quizzes and exams online can be challenging for a number of reasons, including the possibility of technical glitches or lack of reliable internet. We recommend you review the Online Exam Preparation Checklist of things to prepare when sitting an online exam.

ECON3202