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London School of
Economics and Political Science (LSE)
Modules120
Mathematical economics
Prerequisite
If taken as part of a BSc degree, 02 Introduction to Economics, 05a
Mathematics 1,
05b Mathematics 2, and 66 Microeconomics.
Aims and objectives
Mathematical modelling is particularly helpful in analysing a number of
aspects of
economic theory. The unit content includes a study of several
mathematical models
used in economics. Considerable emphasis is placed on the economic
motivation
and interpretation of the models discussed.
The unit is designed to:
? Demonstrate to the student the importance of the use of mathematical
techniques in theoretical economics
? Enable the student to develop skills in mathematical modelling
Learning outcomes
Having followed this unit, students should
? be able to solve economic problems posed in a mathematical form
? be able to formulate economic problems in mathematical terms
Syllabus
Techniques of constrained optimisation. This is a rigorous treatment of
the
mathematical techniques used for solving constrained optimisation
problems,
which are basic tools of economic modelling. Topics include: Definitions
of a
feasible set and of a solution, sufficient conditions for the existence
of a solution,
maximum value function, shadow prices, Lagrangian and Kuhn Tucker
necessity
and sufficiency theorems with applications in economics, for example
General
Equilibrium theory, Arrow-Debreu securities and arbitrage.
Intertemporal optimisation. Bellman approach. Euler equations.
Stationary
infinite horizon problems. Continuous time dynamic optimisation (optimal
control). Applications, such as habit formation, Ramsey-Kass-Coopmans
model,
Tobin’s q, capital taxation in an open economy, are considered.
Tools for optimal control: ordinary differential equations. These are
studied in
detail and include linear 2nd order equations, phase portraits, solving
linear
systems, steady states and their stability.
Essential reading
Dixit, Avinash K. Optimization in Economic Theory. (Oxford: Oxford
University
Press, 1990) second edition [ISBN 0198772106].
Sydsaeter, Knut, Peter Hammond, Atle
Seierstad and Arne Strom, Further
Mathematics for Economic Analysis, (Pearson Prentice-Hall 2005) [ISBN
0273655760].
Assessment
This unit is assessed by a three hour unseen written examination. |
