ECO401 Optimisation and Microeconomic Theory
Autumn 2024

Topics
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 secondorder conditions of the problem, and a number of very useful byproducts 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 welldefined 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 nonnegativity constraints and inequality constraints: the KuhnTucker conditions. Shadow prices and maximum value functions. Linear approximations. The secondorder 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.

Learning outcome
Knowledge
Upon completion of the course, the student can…
 describe the main optimisation techniques used in management and economics
 explain and apply standard microeconomic price theory, in particular the notions of individual and aggregate market behavior, general equilibrium and efficiency properties of market allocations
Skills
Upon completion of the course, the student can…
 apply optimisation techniques to formulate, analyse and solve problems met in economics and management
 formulate those problems with the required degree of formalism
General competence
 communicate this knowledge, both in written form and orally, with accuracy and intuition.

Teaching
The course will be taught in the auditorium and lectures will in general not be recorded. This means that student attendance and active student participation during the lectures is strongly encouraged.
Lecture notes will be made available before each lecture.
Short videos explaining specific topics and technical details may be made available.

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.

Compulsory Activity
None.

Assessment
The assessment is based on two assignments during the term (one for each part of the course; 2x25%) and a three hour school exam at the end of the term (50%). The school exam will be written with pen and paper. The assignments should be handed in individually or in groups of max 2 students. The two assignments have to be taken in the same semester. The assignments and the exam should be written in English.
Expected release of the assignments will be at the end of the first part in September and at the end of the second part in October. The handingin deadline is 2 weeks after release.

Grading Scale
AF

Computer tools
Some use of Excel (Solver module).

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).

Permitted Support Material
 "Economist Mathematical Manual" (4.ed 2005) by K. Sydsæther, A. Strøm and P. Berck (chapters 1 24) distributed in the examination room.
 Calculator
 One bilingual dictionary (Category I)
All in accordance with Supplementary provisions to the Regulations for Fulltime Study Programmes at the Norwegian School of Economics Ch.4 Permitted support material
andhttps://www.nhh.no/en/forstudents/regulations/ https://www.nhh.no/en/forstudents/regulations/ https://www.nhh.no/en/forstudents/examinations/examinationsupportmaterials/ https://www.nhh.no/en/forstudents/examinations/examinationsupportmaterials/
Overview
 ECTS Credits
 7.5
 Teaching language
 English.
 Semester

Autumn. Offered autumn 2024.
Course responsible
Professor Fred Schroyen, Department of Economics, NHH (main course responsible).
Associate Professor Lukas Laffers, Department of Mathematics, University in Banska Bystrica.