Mathematical Methods for Economics-II

Paper Code: 
ECO 212
Contact Hours: 

This course is the second part of a compulsory two-course sequence. This part is to be taught in Semester II following the first part in Semester I. The objective of this sequence is to transmit the body of basic mathematics that enables the study of economic theory at the undergraduate level, specifically the courses on microeconomic theory, macroeconomic theory, statistics and econometrics set out in this Syllabus. In this course, particular economic models are not the ends, but the means for illustrating the method of applying mathematical techniques to economic theory in general. The level of sophistication at which the material is to be taught is indicated by the contents of the prescribed textbook.

Unit I: 
Difference and Differential equations

First-Order Linear Difference equations: Solution, stability conditions, and applications-Compound interest and present discounted values, Cobweb model; First-Order Linear Differential equations with constant coefficient and constant term.

Unit II: 
Linear algebra

Vectors: algebraic and geometric properties, scalar products, norms, orthogonality; matrix and matrix operations; determinants: properties and applications; systems of linear equations and their solution; Leontief model.         

Unit III: 
Functions of several real variables

Geometric representations: graphs and level curves; Partial derivatives-first and second order derivatives: properties and applications; homogeneous and homothetic functions: characterizations and applications.

Unit IV: 
Multi-variable optimization-I

Convex sets; concave and convex functions; conditions for concavity and convexity; second-derivative tests for concavity/convexity; quasiconcave and quasiconvex functions.

Unit V: 
Multi-variable optimization-II

Unconstrained optimization: geometric characterizations, characterizations using calculus and applications; constrained optimization with equality constraints: geometric characterizations, lagrange characterization using calculus and applications; properties of value function: envelope theorem and applications.

Essential Readings: 

K. Sydsaeter and P. Hammond, Mathematics for Economic Analysis, Pearson Educational Asia: Delhi, 2002.

Academic Session: