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.