1 | T H E A U S T R A L I A N N A T I O N A L U N I V E R S I T Y

EMET 7001 Introduction to the Analysis of Economic Models and Data

The course teaches the mathematical foundations of models in economics, business and finance and its applications. Mathematical topics covered include set theory, functions, series, limits, univariate and multivariate calculus, unconstrained and constrained optimisation, matrix algebra. Applications include effective interest rates, present value, annuities, production functions, average and marginal cost functions, profit maximisation. Mode of Delivery On campus Co-requisite None Incompatible Courses EMET 1001 Course Convener: Dr Damien Eldridge Phone: 6125 1178 Email: Damien.Eldridge@anu.edu.au Office hours for student consultation:

TBA

Research Interests Microeconomics, Mathematical Economics, Industrial Economics, Public Economics.

Relevant administrator Karissa Carkeet Phone: 6125 0384 Email: Enquiries.rse@anu.edu

http://programsandcourses.anu.edu.au/course/EMET7001

SEMESTER ONE 2016

2 | T H E A U S T R A L I A N N A T I O N A L U N I V E R S I T Y

COURSE OVERVIEW Course Description The course teaches the mathematical foundations of models in economics, business and finance and its applications. Mathematical topics covered include set theory, functions, series, limits, univariate and multivariate calculus, unconstrained and constrained optimisation, matrix algebra. Applications include effective interest rates, present value, annuities, production functions, average and marginal cost functions, profit maximisation. Learning Outcomes By the end of the course students will:

1. have a sound understanding of mathematical techniques discussed; 2. formulate economic problems in mathematical terms and apply the tools provided in

the module for analysing them; 3. demonstrate an understanding of many of the common functional forms used in

economics their derivatives; 4. apply the basic principles of maximisation and minimisation to optimisation

problems; 5. apply matrix algebra to simple economic problems and models; and 6. make use of some basic principles of financial arithmetic in economic and financial

problems. Assessment Summary

Assessment Task Value Due Date Date for Return of Assessment

Linked Learning Outcomes (optional)

1. Final exam for the supplementary part of this unit.

15 % To be scheduled by the ANU Administration. It will be sometime during the official final exam period.

Exam scripts can be viewed upon request at some point following the release of results for Semester One in 2016.

All learning outcomes.

2. Complete all required assessment tasks for EMET 1001.

85 % Various. See EMET 1001 course outline.

All learning outcomes.

Feedback Staff Feedback Students will have the opportunity to obtain verbal feedback during classes and consultation times.

3 | T H E A U S T R A L I A N N A T I O N A L U N I V E R S I T Y

Student Feedback ANU is committed to the demonstration of educational excellence and regularly seeks feedback from students. One of the key formal ways students have to provide feedback is through Student Experience of Learning Support (SELS) surveys. The feedback given in these surveys is anonymous and provides the Colleges, University Education Committee and Academic Board with opportunities to recognise excellent teaching, and opportunities for improvement. For more information on student surveys at ANU and reports on the feedback provided on ANU courses, go to

http://unistats.anu.edu.au/surveys/selt/students/ and http://unistats.anu.edu.au/surveys/selt/results/learning/

Policies ANU has educational policies, procedures and guidelines, which are designed to ensure that staff and students are aware of the University’s academic standards, and implement them. You can find the University’s education policies and an explanatory glossary at: http://policies.anu.edu.au/ Students are expected to have read the Student Academic Integrity Policy before the commencement of their course.

Other key policies include: • Student Assessment (Coursework) • Student Surveys and Evaluations

Recommended Resources

There is no required textbook for this unit. A reading guide is provided at the end of this course outline. The readings in that guide will, wherever possible, be made available online through links from the Wattle site for this course or in hardcopy through short-loan at the Chifley Library at ANU.

COURSE SCHEDULE Weeks Tentative Summary of Activities

2-5 Vectors, matrices, and linear equation systems.

The concept of vectors and matrices. Matrix arithmetic. Special types of matrices. Linear equation systems. Representation of a linear equation system as an augmented row matrix. Representation of a linear equation system as a matrix equation. Elementary row operations and Gauss-Jordan elimination. Cofactors, determinants and matrix inversion. Cramer’s rule. Parametric solutions, unique solutions and no solutions for a linear equation system. An introduction to linear combinations and linear

4 | T H E A U S T R A L I A N N A T I O N A L U N I V E R S I T Y

independence. Linear and quadratic forms. The characteristic equation and Eigen-values. Applications to linear Marshallian demand functions, linear inverse Marshallian demand functions, linear supply functions, linear inverse supply functions, single market linear Marshallian cross models, multi-market linear Marshallian cross models, linear Keynesian cross models, linear IS-LM models, input-output models and the classical linear regression model.

6-9 Sequences, series, induction, and financial mathematics. The concept of a sequence. Arithmetic progressions and geometric progressions as special types of sequences. Summation notation. Finite series as the partial sum of a sequence. Infinite series as the total sum of a sequence. The partial sum of an arithmetic progression. The partial sum of a geometric progression. Proof by induction. Applications to financial economics, including simple interest, compound interest, frequency of compounding, continuous compounding, present values and future values of payment streams, annuities, annuities due, perpetuities, perpetuities due, amortisation, net present values, internal rates of return, and benefit-cost ratios.

10-13 Unconstrained optimisation and equality-constrained optimisation. Unconstrained optimisation: Maximisation and minimisation, the objective function, first-order conditions, critical points, second-order conditions, optimal values of the independent variables, optimal value of the objective function. Equality-constrained optimisation: Maximisation versus minimisation, the objective function, the constraints, conversion to an unconstrained optimisation problem by using the constraints to eliminate some variables, recovery of the optimal values of the eliminated variables, the Lagrangian function, first-order conditions, critical values, second-order conditions, optimal values of the independent variables, optimal

5 | T H E A U S T R A L I A N N A T I O N A L U N I V E R S I T Y

value of the objective function, and the interpretation of the optimal value of the Lagrange multiplier. Applications to utility maximisation problems, expenditure minimisation problems, cost minimisation problems, profit maximisation problems, Pareto efficiency problems, and the derivation of the ordinary least squares estimators of the coefficient parameters in the classical linear regression model.

ASSESSMENT REQUIREMENTS

Assessment Tasks Assessment Task 1: Final exam for the supplementary part of this unit. Details of task: This will be a closed book final exam that will be held at a time

and location chosen by the ANU Administration. It will be sometime during the official final exam period.

Assessment Task 2: The assessment tasks for EMET 7001. Details of task: See the EMET 7001 course outline for details. SUPPORT FOR STUDENTS The University offers a number of support services for students. Information on these is available online from http://students.anu.edu.au/studentlife/

READING GUIDE

Topic 1: Vectors, Matrices, and Linear Equation Systems

• Haeussler, EF Jr, and RS Paul (1987), Introductory mathematical analysis for business, economics, and the life and social sciences (fifth edition), Prentice-Hall International Edition, Prentice-Hall, USA: Chapters 1, 2, 4 and 8 (pp. 34-74, 101-141 and 238-309).

• Shannon, J (1995), Mathematics for business, economics and finance, John Wiley and Sons,

Brisbane: Chapters 2-5 (pp. 28-230).

• Sydsaeter, K, and P Hammond (2006), Essential mathematics for economic analysis (second edition), Prentice Hall Financial Times (Pearson Education), Gosport: Chapters 2, 15 and 16 (pp. 37-54 and 549-628).

6 | T H E A U S T R A L I A N N A T I O N A L U N I V E R S I T Y

Topic 2: Sequences, Series, Induction, and Financial Mathematics

• Haeussler, EF Jr, and RS Paul (1987), Introductory mathematical analysis for business, economics, and the life and social sciences (fifth edition), Prentice-Hall International Edition, Prentice-Hall, USA: Chapter 6 (pp. 164-193).

• Shannon, J (1995), Mathematics for business, economics and finance, John Wiley and Sons,

Brisbane: Chapter 7 (pp. 285-355).

• Sydsaeter, K, and P Hammond (2006), Essential mathematics for economic analysis (second edition), Prentice Hall Financial Times (Pearson Education), Gosport: Chapters 3 and 10 (pp. 55-82 and 349-376).

Topic 3: Unconstrained Optimisation and Equality-Constrained Optimisation

• Haeussler, EF Jr, and RS Paul (1987), Introductory mathematical analysis for business, economics, and the life and social sciences (fifth edition), Prentice-Hall International Edition, Prentice-Hall, USA: Chapters 12, 13 and 17 (pp. 473-532 and 668-731).

• Shannon, J (1995), Mathematics for business, economics and finance, John Wiley and Sons,

Brisbane: Chapters 8 and 10 (pp. 356-407 and 450-509).

• Sydsaeter, K, and P Hammond (2006), Essential mathematics for economic analysis (second edition), Prentice Hall Financial Times (Pearson Education), Gosport: Chapters 8, 13 and 14 (pp. 269-304 and 463-548).