Marginal Utility

The marginal utility tells us how much more utility the consumer gets for a tiny bit more of a good. $$MU_X = \frac{d u\left( X, Y \right)}{dX}$$ $$MU_Y = \frac{d u\left( X, Y \right)}{dY}$$

Example

Alice's utility for chocolate and strawberries is $$u \left( X, Y \right) = X \times Y$$

Her marginal utility for chocolate is $$ \begin{equation*} MU_X = \frac{du \left( X, Y \right)}{dX} = \frac{d X \times Y}{dX} = Y \end{equation*} $$

Her marginal utility for strawberries is $$ \begin{equation*} MU_Y = \frac{du \left( X, Y \right)}{dY} = \frac{d X \times Y}{dY} = X \end{equation*} $$

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