Mathematical Economics
Mathematical modelling is particularly helpful in analysing a number of aspects of economic theory.
The course 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.
- 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.
If you complete the course successfully, you should be able to:
- Use and explain the underlying principles, terminology, methods, techniques and conventions used in the subject;
- Solve economic problems using the mathematical methods described in the subject.
- Dixit, Avinash K. Optimization in Economics Theory. Oxford University Press.
- Sydsæter, Knut, Peter Hammond, Atle Seierstad and Arne Strom. Further Mathematics for Economic Analysis. Pearson Prentice Hall.
