Optimization In Mathematical Economics

Definition of Optimization

Optimization is process of obtaining either maximization or minimization.  It helps in finding minimum or maximum value of function of several variables subject to a set o constraint.

Types of Optimization:

There are two types of optimization on the basis of restriction provided to objective function.

  1. Unconstraint optimization
  2. Constraints optimization

Unconstraint optimization 

The optimization (maximization or minimization) without any restriction is defined as unconstraint optimization. it deals with only objective  function you are trying to optimize. It involves without any condition.

For unconstraint optimization, following three conditions should be fulfilled.

Let z=f(x,y) be function define then,

  1.  For maximization or minimization first order derivative   must be zero .ie.

Fx or zx=0

2. Fy or zy =0 Second order partial derivation at crictical  point (a,b) must be (+ve) for minimum and must be (-ve) for maximum

Fxx <0  (-ve)

Fyy <0  (-ve) for maximum

Fxx  > (+ve) for  minimum

Fyy  > (+ve)

3. The product of second or partial derivation must exceed the product of the cross partial derivative at the optimum point ie.

Fxx.fyy _ fxx. Fyx > 0

Or fxx.fyy – (FXY) 2 > 0, ( ve)

If there is zero or negative ,there is saddle point or inflection .

Leave a Reply

Your email address will not be published. Required fields are marked *