Abstract
A theory or model is the tool by which we organize our thought about a phenomenon and has to have the ability to explain or forecast. Economic processes are the outcome of the interaction of decisions made by many economic agents. It follows that any economic theory has to be based on some model of decision making by economic agents, be it individual, household, firm, or government. Preferably the behavioral assumptions underlying such a model are applicable to a variety of agents and do not vary in an ad hoc manner, because a science worthy of the name cannot consist of a bunch of unrelated models, each of which is applicable to only a special case. Indeed, it is quite easy to find a rationalization for any event or phenomenon after the fact.
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Notes
- 1.
If \(f(x) < f(x^* )\), then \(f(x^* )\) is referred to as the strict maximum and if \(f(x) > f(x^* )\), then it is the strict minimum.
- 2.
The case where the second and higher derivatives are zero is taken up later.
- 3.
Extremum is a generic word for any point on the function where the first derivative is equal to zero and includes maximum, minimum, and as will be seen later, the inflection point.
- 4.
Procedures for maximizing a function are similar to minimization discussed in this section. Note that minimizing \(- f\left( {\textbf{x}} \right)\) results in maximizing \(f\left( {\textbf{x}} \right)\).
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© 2011 Springer-Verlag Berlin Heidelberg
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Dadkhah, K. (2011). Static Optimization. In: Foundations of Mathematical and Computational Economics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13748-8_12
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DOI: https://doi.org/10.1007/978-3-642-13748-8_12
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