The main topic of the first part of the course 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.
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 function, minimal expenditure function). Comparative statics (Slutsky equation). Measurement of welfare and welfare changes. Aggregation of demand. Production theory, cost minimisation and profit maximisation. General equilibrium and decentralisation of resource allocation decisions.