Editing Implicit function (section)

===Optimization===
{{Main|Mathematical economics#Mathematical optimization}}

Often in [[economic theory]], some function such as a [[utility function]] or a [[Profit (economics)|profit]] function is to be maximized with respect to a choice vector {{mvar|x}} even though the objective function has not been restricted to any specific functional form. The [[implicit function theorem]] guarantees that the [[first-order condition]]s of the optimization define an implicit function for each element of the optimal vector {{math|''x''*}} of the choice vector {{mvar|x}}. When profit is being maximized, typically the resulting implicit functions are the [[labor demand]] function and the [[supply function]]s of various goods. When utility is being maximized, typically the resulting implicit functions are the [[labor supply]] function and the [[demand function]]s for various goods.

Moreover, the influence of the problem's [[Parameter#Mathematical functions|parameters]] on {{math|''x''*}} — the partial derivatives of the implicit function — can be expressed as [[total derivative]]s of the system of first-order conditions found using [[Differential of a function#Differentials in several variables|total differentiation]].
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