Mathematical Methods for Economists I

Catalog description

The course begins with a quick review of basic methods of optimization theory, including necessary and sufficient conditions for optimality, the method of Lagrange multipliers and the Kuhn-Tucker conditions. These methods are required in the microeconomics and macroeconomics courses in the program. The course then develops the tools of real analysis and studies convergent sequences, compact sets, continuous and differentiable functions, the Heine-Borel Theorem and the Weierstrass Theorem. Several applications are presented, including one-dimensional discrete dynamic systems and price adjustment models, and existence of optimal solutions in economic problems, The course then goes on to study convex and concave functions, derive the basic results for unconstrained optimization, and provide some applications to risk theory. Finally, the course investigates the basic properties of convex sets and cones, proves Caratheodory’s Theorem (on convex closures), and deduces some important results (such as Radon’s Lemma and Helly’s Intersection Theorem).