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Equimarginal Principle

At the optimal consumption point, the ratio of marginal utilities must equal the ratio of prices:

\frac{MU_1}{p_1} = \frac{MU_2}{p_2}

. This is the core optimization condition.

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The statement of the theorem

At the optimal consumption point

\mathbf{x}^*

, the ratio of marginal utilities must equal the ratio of prices, ensuring the marginal utility per dollar spent is equal across all goods:

\frac{MU_1}{p_1} = \frac{MU_2}{p_2} = \dots = \frac{MU_N}{p_N}