AU kursuskatalog arkiv

Mathematics for Economists ( forår 2011 - 10 ECTS )

Rammer for udbud

• Uddannelsessprog: dansk
• Niveau: COURSE LEVEL: Elective course in the BSc program
• Semester/kvarter: SEMESTER FOR WHICH THE COURSE DESCRIPTION APPLIES: Spring 2010
• Timer per uge: NUMBER OF HOURS PER WEEK: 2 lectures and 1 tutorial (on average) for 14 weeks in both the spring and the fall semesters.
• Deltagerbegrænsning: RESTRICTIONS ON ADMISSION: None
• Undervisningssted: Århus
• Hovedområde: Det Samfundsvidenskabelige Fakultet
• Udbud ID: 26213

Formål

LEARNING OBJECTIVES:

The objectives are that the student after having participated in the mathematics part of this course should be able to

• formulate and interpret economic and mathematical statements precisely by help of mathematical terminology and symbols
• apply functions of several variables and derive and interpret different types of derivatives and total differentials of these functions
• apply the method of integration to find indefinite integrals and evaluate definite integrals of general as well as specific functions
• analyse linear production models
• explain and apply Taylor approximation
• solve optimization problems with functions of one or several variables
• analyse the characteristics of functions of one or several variables in order to determine whether one or several solutions exist to the optimization of the function
• solve optimization problems with functions of one or several variables under one or several linear or non-linear constraints
• analyse the characteristics of the functions of several variables in order to determine whether one or several solutions exist to optimization problems with several linear or non-linear constraints
• identify and analyse quadratic forms
• explain and analyse implicit functions
• explain and apply the envelope theorem
• apply linear algebra to formulate and solve simultaneous linear equations systems
• explain and apply eigen values and eigen vectors
• identify and analyse homogenous and homethetic functions
• apply the above mentioned mathematical tools on economic problems in order to find results, that can be applied and analyzed within an economic context

Indhold

COURSE DESCRIPTION:

Many problems encountered in economics can often be formulated and solved by using mathematical methods, and therefore, mathematics is an important tool in the analysis of fundamental problems in economics. Economic decisions are in most situations mutually dependent through their influence on demand and supply, and therefore, the purpose of the course is to develop mathematical skills to be able to analyse such dependencies and their importance for the allocation of economic resources. The first part of this course builds on the students' knowledge about mathematical analysis of functions of one variable and the optimization of this type of functions. This knowledge is extended by an introduction to the analysis of functions of several variables and by studying economic optimization problems with and without constraints, linear as well as non-linear. In addition, the course introduces some important tools from the economists' mathematical toolbox, including comparative static analysis. Furthermore, the students' knowledge of basic linear algebra will be extended to cover vectors, matrices, determinants, inverse matrix, linearly dependence, the rank of a matrix and eigen­values and -vectors. Finally, integral calculus will be covered. Economic applications will be emphasized throughout the course, and the introduction of a mathematical software program will be an integral part of the teaching.

COURSE SUBJECT AREAS:

• 1. Functions of one or several variables
• 2. Optimization of functions of one variable
• 3. Multivariable optimization
• 4. Constrained optimization
• 5. Non-linear programming
• 6. Functions of several variables: The Economist toolbox
• 7. Implicit functions
• 8. Linear algebra: The basic elements
• 9. Determinants and inverse matrices
• 10. Linear dependence, rank, eigenvalues and -vectors
• 11. Integral calculus

Faglige forudsætninger

REQUIRED COURSES (progression): The courses at the 1. semester of the BSc.oecon program

Underviser

LECTURER: Michael H.J. Stæhr

Undervisnings- og arbejdsform

TEACHING METHOD: Lectures and tutorials.

TEACHING LANGUAGE: Danish

Litteratur

LITERATURE:

Carl P. Simon and Lawrence Blume: Mathematics for Economists. New York: W.W. Norton & Company, 1994. Chapter 1-4, 6-23, 26, 28 & 30, and appendix A1 & A4 (630 pages, some of which are well known stuff from high-school).

Notes, weekly exercises and assignments are part of the curriculum.

Studieordning og bedømmelse

Bacheloruddannelsen i økonomi

• Mundtlig, bedømt efter Bestået/ikke bestået med intern censur

FORM OF ASSESSMENT: Oral exam of 30 minutes duration without preparation.

In connection with the tutorials in mathematics at least 4 assignments, 2 in the spring semester part of the course and 2 in the fall semester part of the course, should be handed in and approved for admission to the exam.

The assessment is made on a pass/non-pass basis. This course may not appear in a diploma with neither of the courses "Microeconomics, Mathematics and Statistics" and "Microeconomics, Mathematics and Statistics".

EXAMINATION AIDS ALLOWED: None