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Introduction: A special variety of equilibrium state is defined as the optimum position for a giveneconomic unit(a household, a business firm or even an entire economy)and in which the said
economic unit will be deliberately striving for attainment of that equilibrium.
Optimum Values and Extreme Values
Economics is usually a science of choice. When an economic project is to be carried out,
such as the production of a specific level of output, there are normally a number of alternative
ways of accomplishing it. One or more of these alternatives will, however, be more desirable
than other from standpoint of some creation and it is essence of optimization problem to
choose, on the basic off that specified criterion the best alternative available.
The most common criterion of choice among alternatives in economics is the goals ofmaximizing something(such as maximizing a firms profits, a consumers utility or a rate of
growth of a firm or of a countrys economy or of minimizing something (such as minimizing
the cost of producing a given output).Economically we may categorize such maximization
and minimization problem under the general heading of optimization meaning the quest for
the best
This equation constitute the relevant objective function with as the objective of
maximization and Q as the choice variable . The optimization probleme is then that of
choosing the level of Q that maximizes .Note that while the optimal level of is by
definition is maximal level, the optimal level of choice variable Q is itself not required to be
either a maximum of a minimum.
To cast the problem into more general mold for the farther discussion (though still confining
ourselves to objective function of one variable
let us consider the general function
=(x)
and attempt to develop a procedure for finding the level of x that will maximize or minimize
the valu of y. It will be assumed in our discussion that the function is continuouslydifferentiable .
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Figure 9.1
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Figure 9.2
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First Derivative Test:
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Figure 9.3
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Example 1
Second and Higher Derivatives
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Condition of Profit Maximization
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Second Derivative Test
Example 2
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Necessary versus Sufficient Condition
Maclaurin and Taylor Series
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Example 1
References:
1. Alpha C.Chiang & Kevin Wainwright(Fundamental Methods Of
Mathematical Economics)
2. Class Lecture
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Contents:
Introduction
Optimum values and Extreme values
Relative Maximum and Minimum: First Derivative Test
Second and Higher Derivatives
Attitudes toward Risk
Maclaurin and Taylor series
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Optimization: A Special Variety of Equilibrium Analysis
Course Title: Introduction to Mathematics-B
Course Code:122
Submitted TO Submitted By
MD:Mohiuddin Hossain
Lecturer
Dept.of Economics
Name
Fahima siddiqua
Farzana Habib
Mozia Showkhin
Most.Kamrun NaharNaznin Naher
Rawshan Aktar
Md.Bodiul Islam
Md.Salim Reza
ID
1003013
1003024
1003030
10030071003025
1003047
1003003
1003055
Date of Submission: 07-12-2012
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