Course description
This course is devoted to the optimization theory, i.e., the art of finding the «best» element from some set of available alternatives given some objective function. The students will learn that (almost) any economic problem can be presented as an optimization problem, and any result can be explained as a solution to a correctly stated optimization problem. The students will master qualitative analysis of the solutions to maximization and minimization problems, with a particular attention to the economic interpretation of the necessary first-order conditions for such problems. The course covers a range of issues concerning one-dimensional optimization problems, multi-dimensional unconstrained and constrained optimization, the Lagrange multiplier method, convex analysis, multi-objective optimization and the Kuhn–Tucker theorem.
Topics
- Formulation and classification of mathematical programming problems
- Optimal resource allocation
- Linear programming
- Constrained optimization and the Lagrange multiplier method
- Convex analysis
- Economic efficiency and Pareto-optimality
- The Kuhn–Tucker theorem
Literature
- Carter M. Foundations of Mathematical Economics. Cambridge, Massachusetts: MIT Press, 2001.
- Klein M. Mathematical Methods for Economics. New York: Pearson Education Limited, 2014.
- Sydsæter K., Hammond P., Strom A. Essential Mathematics for Economic Analysis. London: Pearson Education Limited, 2012.
- Sydsæter K., Hammond P., Seierstad A., Strom A. Essential Mathematics for Economic Analysis. London: Pearson Education Limited, 2008.