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Utility Maximization Problem

The core optimization problem: maximizing utility subject to a budget constraint. \text{Maximize } U(x, y) \text{ subject to } P_x x + P_y y \text{ } \binom{=} \text{ } M.

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The statement of the theorem

The utility maximization problem is formulated as a constrained optimization:

\text{Maximize } U(x, y) \text{ subject to } P_x x + P_y y = M

where

P_x

and

P_y

are the prices of goods

x

and

y

, and

M

is the consumer's fixed income (budget constraint). The solution requires the Lagrangian method or the tangency condition.