Informatica Grafica

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University of Cagliari
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Mathematics in Economics
Prof. Beatrice Venturi

• Lesson 1

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Mathematics in Economics

• In economics we consider mathematics problems
  as
• Static Optimization
• Dinamic Optimization

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Preliminary topics

• One variable functions.
• Limits.
• Derivatives.
• Optimization.
• Integrals.
• Linear algebra. Matrices. Determinants. Linear
  systems.

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Functions of several variables

• Partial and total derivatives.
• Differential.
• Implicit functions theorem
• (for equations and systems).

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Static optimization

• Unconstrained problems.
• Necessary and sufficient conditions. Constrained
  problems.
• Equality constraints.
• The Lagrange multipliers method.
• Inequality constrained Karush-Kuhn-Tucker
  condition.

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Optimum Values and Extreme Values of a Function
of two Variables

• Local maximum

• Local minimum

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Extreme Values of a Function of two Variables

• Saddle point

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Extreme Values of a Function of two Variables

• The method of Lagrange multipliers provides a
  strategy for finding the maxima and minima of a
  function
• subject to constraints

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First Order Conditions(The necessary conditions)
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Dynamic optimization

• Calculus of variations.
• Euler equations.
• Sufficient condition.
• Optimal control.
• Hamiltonian function.
• Sufficient conditions.

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The Time Path of the Market Price

• The equilibrium price P is asymptotically stable
  equilibrium

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Tabel Time

• Prof.ssa Beatrice Venturi
• Lessons
• Monday from 1000 to 1200 a.m. Lab
• Thursday from 1000 to 1200 a.m. Lab
• Tutorials
• Wedsnesday from 1000 to 1200 a.m. Lab

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First semester A.A. 2012-13

• Start 1 October
• End 13 December
• January-February (tests)

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Instructor

• Prof.ssa Beatrice Venturi
• Room N 22
• Faculty of Economics.
• Phone number 070 6753333
• E-mail venturi_at_unica.it
• Info http//poloeco.unica.it/

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Bibliography

• Books
•  
• CHIANG A. C.,Advances Methods in Mathematics,
  McGraw-Hill, 1984.
• CHIANG A. C., Dynamic optimization, McGraw-Hill,
  1992.
• .

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Questions
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• Thank