London School of Economics and Political Science (LSE)

Modules

Mathematical economics [120]

Note: this is a new unit expected to be examined for the first time in 2008.

Prerequisites (if taken as part of a BSc degree):
05a Mathematics 1 and 05b Mathematics 2 and 66 Microeconomics.

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.