## Example

Alice's utility function is `u \left( X, Y \right) = XY`.

Her marginal rate of substitution is the ratio of the marginal utilities `MU_X` and `MU_Y`:

$$ MRS = - \frac{MU_X \left( X, Y \right)}{MU_Y \left( X, Y \right)} = - \frac{Y}{X} $$### Question

Alice's utility function is `u (X, Y) = X^{868} Y^{719}`.

What is the Marginal Rate of Substitution of strawberries for a chocolate in function of X and Y?

Therefore

$$ MRS = - \frac{MU_X \left( X, Y \right)}{MU_Y \left( X, Y \right)} = - \frac{868 X^{867} Y^{719}}{719 X^{868} Y^{718}} = - \frac{868 Y}{719 X} $$