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Utility Maximization Problem

The formal problem of finding the bundle

X^*

that maximizes utility subject to the budget constraint:

\max U(X)

s.t.

\sum p_i x_i \le M

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The statement of the theorem

The formal utility maximization problem is to find the optimal bundle

\mathbf{x}^*

that maximizes the utility function

U(\mathbf{x})

subject to the budget constraint:

\max U(\mathbf{x}) \quad \text{s.t.} \quad \sum_{i=1}^{N} p_i x_i \le M