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Syllabus:

# Mathematical Economics I D7, 7.5 Credits

Swedish name: Matematik för ekonomer I D7

This syllabus is valid: 2022-01-03 and until further notice

Course code: 2NE007

Credit points: 7.5

Education level: Second cycle

Main Field of Study and progress level: Economics: Second cycle, has only first-cycle course/s as entry requirements

Responsible department: Department of Economics

Revised by: Rector of Umeå School of Business and Economics, 2021-10-28

## Contents

The course contains mathematical methods that are useful tools when applying economic theories and which facilitates understanding of economic literature. The course starts with a quick repetition of equilibrium analysis. Thereafter, matrix algebra, which facilitates the analysis of multi-equation models, is introduced. For example, matrices and vectors are defined and we go through the mathematical laws of matrices and how matrix algebra can be used to identify equilibriums.

The course then continues with a repetition of comparative statics and derivation rules in models with one explanatory variable, and we then go through the same things for the general functional models.

The third part of the course deals with optimization problems. This includes Maclaurin and Taylor series expansions, the second- and the Nth-derivative test. The exponential and logarithmic functions are reviewed and we go through optimization under equality and inequality constraints.

The last part of the course deals with integrals and includes rules of integration and some properties of definite integrals.

## Expected learning outcomes

After completing the course the student is expected tp:
- Be able to define and use the various ingredients in mathematical models such that different types of functions and sets.
- Be able to use the rules of exponents.
- Be able to differentiate and integrate function.
- Master equilibrium analysis and matrix algebra.
- Master comparative statics.
- Be able to set up and solve optimization problems without constraints, with equality constraints, and with inequality constraints.
- Understand and be able to use the Envelope Theorem.
- Understand the relationship between discounting in discrete time and discounting in continuous time.
- Be able to understand and properly use the accepted terms in the above fields, such as determinants, Taylor expansion, and homogeneous functions.
- Be able to present solutions to problems in the above mentioned areas in a logical and clear manner.

## Required Knowledge

90 credits of which 75 credits in economics whereof 15 credits bachelor courses (G2F). Proficiency in English equivalent to the Swedish upper secondary course English 6.

## Examination modes

The examination consists of a written examination in the end of the course.

A second exam opportunity is always offered within a short time span after the regular exam date for those students not achieving a Pass. The subsequent exam opportunity is either the re-take opportunity the week before the fall semester or the next regular exam date.

The following grading system will be used: Pass with Distinction (Väl Godkänd), Pass (Godkänd) or Fail (Underkänd).

When a student has failed an examination on two occasions, he or she has a right to have another grading teacher. A written request for an alternative examiner should be handed to the director of studies no later than two weeks before the next examination opportunity.

It is normally not possible to make additional examinations to reach a higher grade. Exceptions can be made for a student with the grade Fail on any of the examinations if the examiner (not the lecturer) finds this appropriate. The task must be a minor undertaking, closely related to the learning outcome not reached, and performed in close proximity to the original examination.

Credit transfer
Academic credit transfers are according to the University credit transfer regulations.

## Literature

### Valid from: 2022 week 1

Fundamental methods of mathematical economics
Chiang Alpha C., Wainwright Kevin
4. ed. : New York : McGraw-Hill : 2005 : 688 s. :
ISBN: 0-07-123823-9 (hft.)
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