### Mathematical Economics (Paper 3) M.A. Part-I **MA./M.Sc. ****Economics Part-II**

The aim of this course is to equip students with the basic mathematical tools that are useful as an approach to economic analysis. Participants of this course would approach the fundamental theories of micro and macroeconomics using mathematical models. In particular, students would learn the static and/or equilibrium analysis, comparative-static analysis, and static optimization problems. The participants, after the completion of this course, are expected to understand and analyze economic models and their multivariate relationship, encompassing the economics theories.

*Prerequisite for this course is a basic knowledge of introductory-level algebra*.

**Topic 1: The Nature of Mathematical Economics**

Ingredients of mathematical models. Derivations: Equation of a straight line and its forms: Two point, intercept, point slope and slop intercept. Types of functions: constant, polynomial, rational, non-algebraic. Relationships and functions. Indices & their rules. Functions of more than two independent variables. Logarithms & the rules of logarithms.

**Topic 2: Equilibrium Analysis in Economics**

A linear partial equilibrium market model. The effect of an excise tax in a competitive market. Non linear market model. General Market Equilibrium. Equilibrium in a linear National Income Model.

**Topic 3: Linear Models and Matrix Algebra**

Theory of matrix multiplication. Laws of matrix operations. Types of matrices: Square, identity, null, idempotent, diagonal, transpose and their properties. Conditions for non singularity of a matrix. Minors and cofactors. Determinant & its properties. Solution of linear equations through Gaussian method, Cramer’s rule and Inverse of a matrix method. Properties of inverse of a matrix. Use of matrix approach in market & national income models.

**Topic 4: Input-Output Analysis**

Input-output model, its structure and its derivation. The use of input output model in Economics.

**Topic 5: Differentiation**

Rules of differentiation. Differentiation of a function of one variable. Sum- difference, product, quotient, chain, power, inverse, logarithmic & exponential functions Combinations of rules. Higher order derivatives. Economic applications of derivative. Concept of maxima & minima, elasticity and point of inflection. Profit & revenue maximization under perfect competition, under monopoly. Maximizing excise tax revenue in monopolistic competitive market, Minimization of cost etc.

**Topic 6: Partial & Total Differentiation**

Partial differentiation & its rules. Higher order & cross partial derivatives (young’s theorem). Total differential & total derivatives. Implicit functions rule of differentiation. Optimizing cubic functions & their economic application.

**Topic 7: Economic Applications of Partial & Total Differentiation**

Comparative static analysis: a linear Partial equilibrium market model, a linear National Income model. Partial elasticities. Production functions Analysis. Maximization & Minimization of unconstrained functions & their economic applications: Profit maximization by a multi-product firm under perfect Competition & monopoly, Price discrimination, Multi-plant monopoly, input decisions etc.

**Topic 8: Optimization: Constrained & Extrema**

Free and constrained optimization, extrema of a function of two variables: graphical analysis, Lagrange method. Utility maximization & Cost minimization. Homogenous Production function, Cobb Douglas Production function. Jaccobian determinants. CES Production Function. Translof Function.

**Topic 9: Linear Programming**

Ingredients of linear Programming. Graphical approach, simplex method, economic application of linear programming. Concept of primal & dual. Duality theorems. Solving of Primal via dual. Economic interpretation of a dual.

### Recommended Books:

- Chiang, C., Fundamental Methods of Mathematical Economics, McGraw Hills,
*(Latest Edition).* - Baumol W. J., Economic Dynamics, Macmillan,
*(Latest edition).* - Budnick, Frank, Applied Mathematics for Business, Economics and Social Sciences.
- Dowling E. T., Mathematics for economists, Schum Series (latest edition).
- Weber E. Jean, Mathematical Analysis, Business and Economic Applications (Latest Edition) Harper and Row Publishers, New

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