Notes-Chapter 9

Notes-Chapter 9 - Chapter 9 OPTIMIZATION A Special Variety...

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Chapter 9: OPTIMIZATION: A Special Variety of Equilibrium Analysis Alpha Chiang, Fundamental Methods of Mathematical Economics 3 rd edition

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Optimum Values and Extreme Values Economics is by and large a science of choice. common criterion of choice among alternative in economic is the goal of maximizing something or minimizing something optimization – means quest for the best maximum and minimum as mathematical concepts – collective term is extremum. Optimization: delineate an objective function independent variables are choice variables eg. π is the object of maximization and Q is the choice variable.
Relative Maximum and Minimum : First Derivative Test: Given ( ), the first derivative ( ) plays a major role in the search for extreme values. y f x f x = We assume that ( ) is continuous and possesses a continuous derivative. y f x = ( ) 0 is a necessary condition for relative extremum. It is necessary but not sufficient to establish a relative extremum. f x =

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First Derivative Test 0 0 0 0 First derivative test for relative extremum: If the first derivative of a function ( ) at is ( ) 0, then the value of the function at
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Notes-Chapter 9 - Chapter 9 OPTIMIZATION A Special Variety...

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