ECO401 Optimisation and Microeconomic Theory
Part 1: Linear algebra, vectors and matrices. Lagrange´s multiplier method. Extension of Lagrange´s technique to non-negativity constraints and inequality constraints: the Kuhn-Tucker conditions. Shadow prices and maximum value functions. Linear approximations. The second-order conditions to an optimisation problem.
Part 2: Introduction to microeconomic theory. Preferences and consumer demand. Derived concepts (indirect utility, expenditure). Comparative statics (Slutsky). Measurement of welfare and welfare changes. Aggregation of demand. Production theory, cost minimisation and profit maximisation. General equilibrium and decentralisation of resource allocation decisions.
The main topic of the first part is the theory and practice of constrained optimisation. After rehearsing the necessary mathematical tools, we focus on Lagrange's technique to solve a maximisation (or minimisation) problem when side constraints need to be respected. We pay attention to the so called first- and second-order conditions of the problem, and a number of very useful by-products of Lagrange's technique, such as maximal value functions, shadow prices and comparative statics.
The second part gives a solid introduction to the standard microeconomic theory. Equipped with Lagrange's technique, we first study the behaviour of individual agents (consumers, business firms, investors) in the economy, and later their interaction through markets. This will give us an understanding of the main results in microeconomics, and a feeling for the methodology used in economic theory.
Almost every scientific article or paper in economics makes use of the technique of constrained optimisation and uses a microeconomic model to describe individual and market behaviour. This course will therefore enable students to read and understand the recent economic literature, as well as to engage in economic model building. But it will also teach how to formulate a well-defined problem and how to solve it. In that sense it is of interest to the applied economist whether he or she will work as an analyst in a firm, as a consultant, or as a researcher.
At the end of the course, the student shall
- have knowledge of the main optimization techniques used in management and economics;
- have knowledge of the standard microeconomic price theory, in particular the notions of individual and aggregate market behavior, general equilibrium and efficiency properties of market allocations;
- be able to apply optimization techniques to formulate, analyse and solve problems met in economics and management;
- be able to formulate those problems with the required degree of formalism;
- be able to communicate this knowledge, both in written form and orally, with accuracy and intuition.
Regular lectures and assignment classes.
Students should be familiar with the material covered in the undergraduate mathematics course MET020/MET1.
Evaluation is based on two compulsory exercise sets during the term (one for each part of the course) and a three hour written school exam consisting of problems related to both parts of the course. The compulsory exercise sets can be handed in individually or by groups of max two students.
The final evaluation will for 70% be based on the school exam and for 15% on each of two compulsory exercise sets. The two exercise sets have to be taken in the same semester. Both the exam and the compulsory assignments should be written in English.
Exercise set 1 (15%) -- grading scale A-F.
Exercise set 2 (15%) -- grading scale A-F.
Written school exam (70%) -- grading scale A-F.
Overall course grade A-F.
Some use of Excel
Part 1: Avinish Dixit (1990) Optimization in economic theory - 2nd ed (Oxford: Oxford University Press).
Part 2: Frank Cowell (2005) Microeconomics: Principles and Analysis (Oxford: Oxford University Press).
- ECTS Credits
- Teaching language
Course responsible: Professor Fred Schroyen, Department of Economics.
Lecturers: Fred Schroyen and Assistant professor Thomas de Haan, Department of Economics.