ECO401 Optimisation and Microeconomic Theory

• Topics

  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.

• Learning outcome

  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

  Knowledge

  - 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;

  Skills

  - 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;

  General competence

  - be able to communicate this knowledge, both in written form and orally, with accuracy and intuition.

• Teaching

  Regular lectures and assignment classes.

• Required prerequisites

  Students should be familiar with the material covered in the undergraduate mathematics course MET1 or in a similar course in their bachelor studies.  This includes:

  • Functions in  a single variable: derivation, sketching of the function in space, elasticities, integration.
  • Functions in several variables: partial derivatives, differentiating, optimisation without and with a side constraint.
  • Linear algebra: system of linear equations, matrix notation, inverse of a matrix, determinant of a matrix.

• Requirements for course approval

  None.

• Assessment

  Evaluation is based on two compulsory asignments 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 assignments can be handed in individually or by groups of max two students. 

  The final evaluation will be based for 70% on the school exam and for 15% on each of two compulsory assignments. The two assignments have to be taken in the same semester. Both the exam and the compulsory assignments should be written in English.

  Expected release of the compulsory assignments will be in September and October. The handing-in deadline is 2 weeks after release. 

• Grading Scale

  Assignment 1 (15%) -- grading scale A-F.

  Assignment 2 (15%) -- grading scale A-F.

  Written school exam (70%) -- grading scale A-F.

  Overall course grade A-F.

• Computer tools

  Some use of Excel.

• Literature

  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).