Mathematical Methods for Economics

Semester and Year Offered: 4th Semester and 2nd year

Course Coordinator and Team: Parma Chakravartti

Email of course coordinator: parma[at]aud[dot]ac[dot]in

Pre-requisites: Students must have taken mathematics at the 10+2 level

Aim: This is a compulsory course for Economics Students. This course aims to introduce mathematical methods required to analyse economic problems. It introduces various mathematical concepts along with its applications in economics. Topics include functions, set theory, matrix algebra, limits, differentiation, logarithmic and exponential functions and both constrained and unconstrained optimization. This course integrates with other courses of Economics; microeconomics and macroeconomics.

Course Outcomes:

On successful completion of this course, students will be able to:

1. Use mathematical techniques to analyse economic problems
2. Model economic questions in mathematical framework
3. Evaluate range of problems using mathematical techniques
4. Acquire mathematical skills used in economic analysis

Brief description of modules/ Main modules:

The course is divided into six modules: Review of relations and functions, Functions of single variable, Linear Algebra, Function of several variables, Single-variable optimization and Multi-variable optimization. Brief outline of the modules are as follows:

1. Review of relations and functions

• Logic and proof techniques
• Sets and set operations
• Relations, functions and their properties, number systems

2. Functions of single variable

• Graphs, types of functions
• Exponential and logarithmic functions- properties and applications
• Single variable differentiation
• Limits, continuous functions, application of continuity and differentiability.

3. Linear Algebra

• Matrices and matrix operations
• Systems of linear equations; determinants, inverse of a matrix

4. Function of several variables

• Differentiable functions- characterizations, properties and applications
• Second order derivatives- properties and applications
• Homogeneous and homothetic functions

5. Single-variable optimization

• Concave and convex functions of single variable, their properties and applications; local and global extremum; optimization problem using calculus and applications.

6. Multi-variable optimization

• Concave and convex functions of two variables, their properties and applications
• Constrained optimization with equality constraints- the Lagrange multiplier method.

Assessment Details with weights:

• Two class tests of 30% weightage and one end semester exam of 40% weightage.
• Test 1 (30%), Test 2 (30%) and End semester exam (40%).

Reading List:

• Sydsaeter, Knut., and Peter Hammond (2002) , Mathematics for Economic Analysis, Pearson Education India, 1st edition, 2002.
• Alpha C. Chiang and Kevin Wainwright (2005), Fundamental Methods of Mathematical Economics, 4th Edition, McGraw-Hill, 2005.

ADDITIONAL REFERENCE: