Mathematics for Economists

Introduction of Real Analysis   
Linear Algebra 

  • Introduction
  • Application in Input Output System
  • Application in the Complete Keynesian Model
  • Optimization using Linear Programming

Simplex Method

  • Concept of Duality problem and application of cost minimization problem
  • Concept of shadow prices
  • Single and Multi-variable Optimization

Total differential

  • Concavity, convexity, quasi-concavity, quasi-convexity
  • Unconstrained optimization
  • Constrained optimization: Equality constraints
  • Constrained optimization: Inequality constraints
  • Concave programming, Kuhn-Tucker conditions
  • Application in Consumer Optimization, Production Optimization, Overlapping Generation Models etc.   

Comparative static analysis 

  • Value function
  • Envelope Theorem
  • Implicit function theorem
  • Application inSlutsky equation, Roy’s identity, input demand function, Le-Chatelier Principle   

Dynamic analysis 

Differential Equations 

  • First order linear differential equations with constant term and constant coefficient (Dynamics of market price)
  • Second order linear differential equations with constant term and constant coefficient (Expectation augmented Phillips curve)
  • Simultaneous differential equations (Dynamic Input Output model)

Difference Equations 

  • First order linear difference equations with constant term and constant coefficient (Cobweb Model)
  • Second order linear difference equations with constant term and constant coefficient (Samuelson Multiplier Acceleration Interaction model)
  • Simultaneous difference equation (Inflation Unemployment model)

Text

  1. Fundamental Methods of Mathematical Economics, Alpha C Chiang and Kevin Wainwright, McGraw-Hill, 2005
  2. Mathematics for Economist, Carl P. Simon and Lawrence E. Blume, W. W. Norton, Incorporated, 1994
  3. The Structure of Economics: A Mathematical Analysis, Eugene Silberberg and Wing Suen, McGraw-Hill, 2001
  4. Real Analysis with Economic Applications, EfeA.Ok, Princeton University Press, 2007
  5. Introduction to Linear Algebra, Gilbert Strang,Wellesley-Cambridge Press, 2005