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Utility Function Formalization

A mathematical mapping

U: X \to \mathbb{R}

that assigns a scalar utility value to every consumption bundle

X

. The consumer's goal is to maximize this function:

\max U(x_1, x_2, \dots)

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The statement of the theorem

Define the utility function

U: X \to \mathbb{R}

as a scalar mapping that assigns a utility value to every consumption bundle

\mathbf{x} = (x_1, x_2, \dots, x_N)

. The consumer's objective is to find the bundle

\mathbf{x}^*

that maximizes this function:

\max_{\mathbf{x} \in X} U(\mathbf{x})

Source: Wikipedia