MATHEMATICAL METHODS FOR ECONOMICS - II

MATHEMATICAL METHODS FOR ECONOMICS - II 

Unit - I: Linear Algebra

• Vector and vector space
• Matrix representation and types
• Elementary operations and their properties
• Determinants: Definition and properties
• Solution of linear equations:
  • Matrix inverse method
  • Cramer’s rule
• Rank of a matrix

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Unit - II: Functions of Several Variables and Multi-variable Optimization

• Differentiable functions
• Homogeneous and homothetic functions
• Implicit Function Theorem and application
• Unconstrained Optimization:
  • Solution using calculus
  • Application
• Constrained optimization with equality constraints:
• Lagrange multiplier
• Application

Numerical Problems & Solutions:

• Extreme Values of a Function of Two Variables - Minimum Value and Saddle Point (2 Critical points)
• Extreme Values of a Function of Two Variables - Minimum Value (One Critical Point)
• Extreme Values of a Function of Two Variables - Maximum Value (One Critical Point)
• 
  

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Unit - III: Differential and Difference Equations

• Meaning
• Solutions of first-order equations
• Nature of time path
• Applications:
  • Cost function
  • Dynamic market model
  • Cobweb model

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Unit - IV: Input-output Analysis and Linear Programming

• Concept of input-output (I-O) analysis
• Determination of output (Static Open Model only)
• Hawkins-Simon condition
• Concept of linear programming:
  • Graphical solution only
• Formulation of duals from primals

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Suggested Readings

1. Allen, R.G.D. (2008), Mathematical Analysis for Economists, Macmillan Press, London
2. Chiang, A.C. and K. Wainwright (2013), Fundamental Methods for Mathematical Economics, McGraw Hill, New Delhi
3. Hoy, Livernois, Mckenna, Rees and Stengos (2011), Mathematics for Economics, McGraw Hill
4. Sydsaeter, K., P. J. Hammond and A. Strom (2014), Essential Mathematics for Economic Analysis, Pearson
5. Yamane, Taro (2012), Mathematics for Economists: An Elementary Survey (2e), Prentice Hall of India, New Delhi