MATHEMATICAL ECONOMICS I

Nature of a Utility Function; properties of an Indifference curve; Maximization of utility; Demand functions- Ordinary and compensated, price and income elasticity, elasticity relations in demand analysis, Restrictions on demand functions; Slutsky Equation - n- commodity case, elasticity form and important results;

Income and Leisure - Derivation of labour supply function and its properties, Linear Expenditure System; properties and derivation of linear demand functions. Homogeneous and Homothetic utility functions; Indirect Utility Functions and Duality in Consumption, properties of indirect utility function, Roy's Identity, duality theorems, derivation of direct and inverse demand functions; Consumer behaviour under conditions of risk and uncertainty.

Production function: Properties of a well behaved and homogeneous production function -Cobb-Douglas and CES Production Functions; product curves; output elasticity of factor input; properties of an isoquant, Elasticity of substitution of a homogeneous production function- linearly homogeneous, Cobb-Douglas and CES Production Functions; Expansion path

Optimization behaviour of a firm- Constrained cost minimization, constrained output maximization and profit maximization; Input Demand- properties and derivation of producer’s input demand functions; Cost functions- properties and derivation of short run and long run cost functions, determination of optimum plant size.

Perfect Competition: short run and long run equilibrium, differential cost conditions and rent; Effects of taxes on optimum output level, supply function and price level. Imperfect Competition: Monopoly- Profit Maximization and sales revenue, price discrimination, Multi-Plant Monopolist, effect of various taxes on output and price of a monopoly firm, bilateral monopoly, Monopolistic competition equilibrium- short run and long run.