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Aiming Pareto Optimality
Mathematical Methods for Economics II
DEMO LECTURE
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Book  Sydsaeter, K., Hammond
MME 2 Syllabus DU
Unit 1 Functions of several real variables
Geometric representations: graphs and level curves; differentiable functions: characterisations, properties with respect to various operations and applications; second order derivatives: properties and applications; the implicit function theorem, and application to comparative statics problems; homogeneous and homothetic functions: characterisations and applications
Unit 2 Multivariate optimization
Convex sets; geometric properties of functions: convex functions, their characterisations, properties and applications; further geometric properties of functions: quasiconvex functions, their characterisations, properties and applications; unconstrained optimisation: geometric characterisations, characterisations using calculus and applications; constrained optimisation with equality constraints: geometric characterisations, Lagrange characterisation using calculus and applications; properties of value function: envelope theorem and applications
Unit 3  Linear programming
Introduction, graphical solution, matrix formulation, duality, economic interpretation
Unit 4 Integration, differential equations, and difference equations Definite integrals, indefinite integrals and economic applications; first order difference equations, equilibrium and its stability; first order differential equations, phase diagrams and stability
References Books
1. Sydsaeter, K., Hammond, P. (2002). Mathematics for economic analysis. Pearson Educational.
Keywords
Functions of several real variables, multivariate optimisation, linear programming, integration, differential equations, and difference equations
Amendment as per the last meeting on 15th January, 2020
1. Leave out Theorem 17.17 (the bordered Hessian test).
2. Do only the statement and interpretation of Lagrange's theorem (Theorem 18.1 in Section 18.3), not the proof.
3. Leave out Sections 18.8, 18.9, and 18.10.
4. All of Chapter 10 (Integration) is to be done.
5. Do only Section 20.1 on difference equations.
6. In differential equations, do only Sections 21.1, 21.5, 21.6, and 21.7.
*As per the notice on DSE Website
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