EC3120 Mathematical economics
Prerequisites (applies to degree students only)MT105B Mathematics 2 and EC2066 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.