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
- will have advanced knowledge of the main optimization techniques used in management and economics;
- will have advance 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;
- will be able to apply optimization techniques to formulate, analyse and solve problems met in economics and management;
- will be able to formulate those problems with the required degree of formalism;
- will be able to communicate this knowledge, both in written form and orally, with accuracy and intuition.