AU kursuskatalog arkiv

2020: Macroeconomics, Mathematics and Statistics ( forår 2011 - 20 ECTS )

Rammer for udbud

• Uddannelsessprog: dansk
• Niveau: Compulsory course at the 2nd semester of the BSc Economics and Management programme.
• Semester/kvarter: Every spring semester
• Timer per uge: 8 lectures and 5 tutorials for 14 weeks. 4 lectures and 3 tutorials per week are devoted to macroeconomics while mathematics and statistics both have 2 lectures and 1 tutorial (on average) per week.
• Deltagerbegrænsning: None
• Undervisningssted: Århus
• Hovedområde: Det Samfundsvidenskabelige Fakultet
• Udbud ID: 26204

Formål

Macroeconomics:

The students should be able to:

• conduct the list below using formal verbal, graphical and in particular mathematical arguments
• analyze causes and consequences of business cycle fluctuations using explicitly mathematically formulated macroeconomic models
• explain and analyze macroeconomic models for open economies engaged in international trade in goods and capital, taking various exchange rate regimes into account
• explain and analyze the adjustment processes taking place from the short run to the long run
• explain and analyze the main macroeconomic policy areas, especially the effects of fiscal and monetary policy in closed and open economies 
• evaluate the importance of the assumptions made for the structure of the models and the results emanating from the models, in order to assess the strengths and weaknesses of the analyses.

Mathematics

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 Gaussian and Gauss-Jordan elimination to systems of linear equations
• analyse linear production models
• apply linear algebra to formulate and solve simultaneous linear equations systems
• identify and analyse quadratic forms
• 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 problem of optimizing the function
• apply the above mentioned mathematical tools on economic problems in order to find results, that can be applied and analyzed within an economic context

Statistics

In the statistical part of the course, the participants should learn to

• evaluate probability statements for two or more random variables
• derive properties of the binomial and negative binomial distributions relating to the Bernoulli process
• derive properties of the Poisson distribution relating to the Poisson process
• analyze families of continuous distributions
• describe the bivariate normal distribution
• apply generating functions

Indhold

The course consists of three parts: Macroeconomics, mathematics and statistics. The macroeconomic part extends the analyses introduced in the Principles of Economics course. The models from that course are extended both in terms of content and methodology, such that mathematical analysis will become an integral ingredient of the model analysis. Starting from analyses of short-run business cycle fluctuations for closed and open economies, the focus is turned to medium to long run issues where prices become flexible. The models are applied to descriptions of the problems encountered by politicians when creating the institutional settings for economic policy. An example hereof is how international monetary cooperation can take place (the EMU is a concrete example).  Throughout, the theoretical analyses are exemplified with studies of current economic-political problems. Finally, institutional aspects of macroeconomic importance are considered.

Many problems encountered in economics can 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 mathematical 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 without constraints. The course also introduces some important analytical tools from the economists mathematical toolbox, including comparative static analysis. Another main topic will be linear algebra, where prior knowledge is extended to handling and solving large systems of linear equations. Economic applications will be emphasized throughout the course, and the introduction of a mathematical software program will be an integral part of the teaching.

The statistical part extends the probability theory learned in the Introduction to Statistics & IT course. There is an introduction to stochastic processes and distributions relevant for Bernoulli and Poisson processes e.g. waiting times to events happen.

COURSE SUBJECT AREAS:

Macroeconomics

1. The IS-LM model for a closed economy
2. The IS-LM model for a small open economy
3. The supply side with and without nominal rigidities
4. The AD-AS and DAD-SAS models
5. Endogenous economic policy
6. Exchange rate cooperation and monetary policy institutions
7. Public deficits and public debt
8. Evaluating business cycles

Mathematics

1. Functions of several variables
2. Optimization of functions of one variable
3. Linear algebra
4. Multivariable optimization

Statistics

1. Multidimensional discrete and continuous distributions
2. Stochastic processes, inverse sampling and waiting times
3. Generating functions and properties of distributions

Faglige forudsætninger

REQUIRED COURSES:

The compulsory courses in the first semester of the BSc Economics and Management program

Underviser

Rune Vejlin, Gustav Bruze, Mark Strøm Kristoffersen, Kim Christensen.

Undervisnings- og arbejdsform

Lectures and tutorials.

Litteratur

Macroeconomics

Manfred Gärtner: Macroeconomics . Third Edition, FT Prentice Hall, 2009, ch. 3-8 and 11-14 (ch. 1-2 may be read as an introduction). 291 pages. 

Torben M. Andersen m.fl.: Beskrivende Dansk Økonomi. Third Edition, Bogforlaget Handelsvidenskab, 2008, kap. 1,2,4-7 (some parts will be cursory readings). 232 pages. 

Ministry of Finance: Økonomisk Redegørelse (latest edition). Only the summary is required reading (app. 35 pages). 

Lecture Notes and Exercises are required readings.  

Mathematics                                                    

• Carl P. Simon and Lawrence Blume: Mathematics for Economists. New York: W.W. Norton & Company, 1994. (approx. 350 pages)

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

Statistics

D.A. Berry and B.W. Lindgren, Statistics, Theory and Methods, 2008, chapters 1-7 (306 pages where about half is known from Introduction to Statistics and IT) 

Notes, approximately 30 pages. Notes, weekly exercises and assignments are part of the curriculum.

Studieordning og bedømmelse

Bacheloruddannelsen i økonomi

• Mundtlig, bedømt efter 7-skala med ekstern censur

FORM OF ASSESSMENT

Oral exam of 20 minutes duration without preparation.

For admission to the exam three compulsory assignments have to be answered and approved. Two of the compulsory assignments will be within the mathematical and statistical curriculum, while the third compulsory assignment will be within all three parts of the course.

Finally, in connection with the tutorials in macroeconomics at least 1
presentation at the blackboard of solutions to exercises should be approved for admission to the exam.

EXAMINATION AIDS ALLOWED: None