Marginal Utility

The marginal utility tells 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

$$u \left( X, Y \right) = X^2 \times Y$$

Her marginal utility for chocolate is

$$ \begin{equation*} MU_X = \frac{du \left( X, Y \right)}{dX} = \frac{d X^2 Y}{dX} = 2 X Y \end{equation*} $$

Her marginal utility for strawberries is

$$ \begin{equation*} MU_Y = \frac{du \left( X, Y \right)}{dY} = \frac{d X^2 Y}{dY} = X^2 \end{equation*} $$

Question

Now Alice's utility is `u (X, Y) = X^{318} Y^{121}`. Compute her marginal utility for strawberries?

Her marginal utility for strawberries is the derivative of `u (X, Y) = X^{318} Y^{121}` with regards to `Y`.

$$ \begin{align*} MU_Y = \frac{du(X, Y)}{dY} = 121 X^{318} Y^{121 - 1} = 121 X^{318} Y^{120} \end{align*} $$