AU kursuskatalog arkiv

2030: Microeconomics, Mathematics and Statistics ( efterår 2011 - 20 ECTS )

Rammer for udbud

• Uddannelsessprog: dansk
• Niveau:   COURSE LEVEL: Compulsory course in the 3rd semester of the BSc program  
• Semester/kvarter: Autumn 2011
• Timer per uge: 8 lectures and 5 tutorials for 14 weeks. 4 lectures and 3 tutorials per week are devoted to microeconomics, while mathematics and statistics each have 2 lectures and 1 tutorial (on average) per week. Timetables can be found at: http://econ.au.dk/studies/teaching-and-examination/teaching/timetables/
• Deltagerbegrænsning:   RESTRICTIONS ON ADMISSION: None  
• Undervisningssted: Århus
• Hovedområde: Det Samfundsvidenskabelige Fakultet
• Udbud ID: 28714

Formål

LEARNING OBJECTIVES:

Microeconomics

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

• describe, interpret and formulate the models from the curriculum
• relate the methods of the curriculum to real world economic problems
• apply the tools from consumer behavior, firm behavior, etc. to analyze economic problems and analyze in a comparative static way variations of known problems
• relate known results to variations of known problems within the subject areas of the course

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
• solve optimization problems under several linear or non-linear constraints
• analyse the characteristics of the functions of several variables in order to determine whether one or several solutions exists to optimization problems with several linear or non-linear constraints
• explain and analyse implicit functions
• explain and apply the envelope theorem
• explain and apply eigenvalues and eigenvectors
• explain and apply Taylor approximations
• apply the above mentioned mathematical tools on economic problems in order to find results, that can be applied and analyzed within an economic context
• identify and analyse homgenous and homothetic functions

Statistics

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

• Derive the properties of moment, least squares, and maximum likelihood estimators of the parameters in the distributions introduced in the second semester Statistics course.
• Formulate models for simple problems in economics, derive estimates of the parameters, and derive test statistics for hypotheses about the parameters.
• Evaluate possible errors related to hypothesis testing.
• Derive confidence intervals for population parameters.
• Apply simple analysis of variance (ANOVA) models, and derive estimates for their parameters.
• Derive goodness of fit tests, and apply simple contingency tables for categorical data.

Indhold

COURSE DESCRIPTION:

The microeconomics part of the course is a course in basic microeconomic theory including consumer and firm behavior. It takes the topics of the Principles of Economics course as the point of departure. These topics are now considered in much more detail and a range of new topics that extend and build on the topics of the Principles of Economics course are introduced. Especially, this part of the course (complemented by the math and statistics parts of the course) should enable students to work with microeconomic problems at a higher theoretical and technical level.

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 purpose of the mathematical part of this course is to extend the students' knowledge of optimization of functions of several variables to more complicated situations with linear as well as non-linear constraints. In addition, the course builds further on the students' knowledge about linear algebra. 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 of the course provides the students with the ability to make estimates of important parameters in economic models, and to formulate hypothesis tests for these parameters. These methods form the basis for further statistical analysis of economic variables. An introduction is given to Analysis of Variance (ANOVA) models, regression models with dummy variables, and models for categorical data.

COURSE SUBJECT AREAS:

Microeconomics

• Consumer behavior (preferences, utility and demand)
• Decisions under uncertainty
• Firm behavior (production, costs and profit maximazation)
• Partial equilibrium
• General equilibrium
• Market power (monopoly and imperfect competition)
• Input markets (labor markets and capital markets)

Mathematics

• Constrained optimization
• Implicit functions
• Non-linear programming
• Further topics in linear algebra
• Taylor approximations

Statistics

• Samples and data analysis.
• Statistics and the central limit theorem.
• Estimators: Maximum likelihood, method of moments, least squares.
• Asymptotic theory, properties of estimators (unbiasedness, consistency, efficiency).
• Chi-squared distribution, t-distribution, F-distribution.
• Confidence intervals.
• Hypothesis tests, power function.
• Likelihood ratio- , Wald-, and Lagrange multiplier tests.
• Tests on means, proportions, and variances in 2 samples.
• Non-parametric tests.
• Goodness of fit, contingency tables.
• Analysis of Variance (ANOVA), regression with dummy variables.

Faglige forudsætninger

REQUIRED COURSES:

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

Underviser

LECTURER: Michael Stæhr, Leonidas Enrique de la Rosa, Tom Engsted and Gustaf Bruze

Undervisnings- og arbejdsform

TEACHING METHOD: Lectures and tutorials.

TEACHING LANGUAGE: Danish

Litteratur

LITERATURE:

Microeconomics
Snyder, S. and W. Nicholson. 2008. Microeconomic Theory - Basic Principles and Extensions. 10th edition. (Chapters 1-7, 9-17, approximately 570 pages)

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

Mathematics

Carl P. Simon and Lawrence Blume: Mathematics for Economists. New York: W. W. Norton & Company, 1994 (approx. 300 pages).

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

Statistics

D.A. Berry and B.W. Lindgren, Statistics, Theory and Methods . 1996, chapt. 7-15.

Approx. 330 pages plus lecture notes

Bedømmelse

FORM OF ASSESSMENT: 4 hours written exam. 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.
Furthermore, in connection with the tutorials in microeconomics at least 4 assignments must be handed in and approved for admission to the exam.

EXAMINATION AIDS ALLOWED: All, except any electronic communication equipment, including calculators, mobile phones and PCs. A calculator will be handed out at the examination.