Mathematical Methods of Economics

Semester and Year Offered:

Course Coordinator and Team: Jyotirmoy Bhattacharya

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

Pre-requisites:

Knowledge of calculus and linear algebra at the level of undergraduate texts in mathematicaly methods of economics.

Aim: The course covers selected mathematical methods of economics for students who would like to pursue advanced work in economic theory. This is not a survey course. Instead it aims to discuss a few topics at a high level in order improve the mathematical maturity of students.

Course Outcomes:

At the successful completion of this course students would be able to

1. Successfully read and construct mathematical proofs at the level of advanced undergraduate/beginning graduate courses in mathematics.
2. Have an in-depth understanding of selected topics in mathematics beyond what is taught in undergraduate courses in economics and the core MA courses.
3. Appreciate better how abstract mathematical reasoning can be put to use in economic analysis.

Brief description of modules/ Main modules:

1. These topics are indicative and not all may necessarily be covered in each instance. Instructors may select from them and introduce additional topics based on their and the students’ interests.
2. Linear algebra. Idea of abstract vector space, linear transforms; eigenvalues, eigenvectors and the Jordan normal form; inner-product spaces and the spectral theorem.
3. Basic point-set topology on Euclidean spaces and metric spaces. Open, compact and connected sets. Sequences. Limits. Continuity. Sequences of functions. Uniform continuity.
4. Convex functions and convex sets.
5. Set-valued functions (correspondences). Upper and lower hemicontinuity. The theorem of the maximum.
6. Fixed point theorems: contraction mapping theorem, Brouwer's Fixed-Point Theorem, Kakutani's Fixed-Point Theorem.

Assessment Details with weights:

Reading List:

1. Axler, S. (2014). Linear Algebra Done Right, Springer.
2. Berge, C. (2003). Topological Spaces, Dover.
3. Binmore, K.G. Mathematical Analysis, Cambridge University Press
4. Border, K.C. (1989) Fixed-Point Theorems with Applications to Economics and Game Theory, Cambridge University Press
5. Halmos, P.R. (1987). Finite-Dimensional Vector Spaces, Springer.
6. Ok, E.A. (2007). Real Analysis with Economic Applications. Princeton University Press.
7. Pugh, C.C. (2017). Real Mathematical Analysis, 2nd ed., Springer.
8. Sundaram, R. (1996). A First Course in Optimization Theory, Cambridge University Press