Differential Equations, Optimal Control Theory and Macroeconomics.
1. Multivariable Calculus
(Preliminaries, Convex sets, Convex and concave functions, Quasi-convex and quasi-concave functions)
2. Nonlinear Programming
(Extreme points, Equality constraints, Inequality constraints, Non-negativity constraints,
3. Sensitivity Analysis
(Comparative statics, Envelope theorem, Elements of microeconomic theory, Elasticity of factor substitution)
4. Some Applications to Microeconomic Theory
(Inferior inputs, Marginal and average costs, Marginal cost pricing,
Factor prices, Supply of labour, Peak-load problem)
5. Differential Equations and Elements of Nonlinear Systems
(First- and second-order differential equations, Higher-order equations, Systems of equations)
6. Some Applications to Macroeconomic Theory
(Macroequilibrium, Money and growth)
7. Optimal Control Theory and Applications
(Elements of control theory, Infinite horizon control problem and applications, Some extensions of
optimal control themes)
1) Takayama, A.: Analytical Methods in Economics, Harvester-Wheatsheaf, 1994.
2) Sydsaeter, K.; Hammond, P.; Seierstad, A.; Strom, A.:
Further Mathematics for Economic Analysis, Financial Times/Prentice Hall, 2005.
3) Takayama, A.: Mathematical Economics, Cambridge University Press, 2nd edition, 1985.
4) Werner, F.; Sotskov, Y.N.:
Mathematics of Economics and Business, Routledge, Abingdon, New York, 2006.
Some presented slides from the lecture: