Mathematical Economics-I

(The purpose of this unit is to review the mathematical techniques. Their    applications in economics shall be discussed in the subsequent units)
•    Differential Calculus (Functions with one independent variable)-Increasing and decreasing functions, Concavity and convexity, optimization of functions;
•    Differential Calculus (Multivariable Functions)-First-and second-order partial derivatives, total differentials, optimization of multivariable functions, constrained optimization with Lagrange multiplier;
•    Matrix Algebra-Matrices and Determinants, Crammer’s rule, solving linear equations with the inverse matrix, Bordered Hessian determinant for constrained optimization.

•    Nature of the utility function, Indifference curves, Rate of commodity substitution;
•    Maximization of Utility (First-and second-order conditions);
•    Ordinary and Compensated Demand Functions.

•    Price and Income Elasticity of demand;
•     Income and Leisure;
•    The Slutsky Equation- Derivation for two commodity case, its elasticity form, Direct and Cross effects, Substitutes and Complements.

(All the concepts covered under unit IV and unit V shall be illustrated with the help of Cobb-Douglas production function only).
•    Nature of  the production function, isoquants and isocost line;
•    Optimizing Behaviour- constrained output maximization, constrained cost minimization and profit maximization;
•    Elasticity of substitution.

•    Homogeneous Production Functions-Properties, Euler’s theorem, Linearly homogeneous production function as a special case;

• Properties of Cobb-Douglas production Function.