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Income Effect and Substitution Effect

Decomposes the total change in demand (total effect) into two components: the change due to income (income effect) and the change due to relative prices (substitution effect).
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The statement of the theorem

The total effect of a change in a parameter (e.g., price p1p_1) on the optimal demand x1∗x_1^* is decomposed into two parts: the Substitution Effect (SE) and the Income Effect (IE). Mathematically, this is often represented as: ∂x1∗∂p1=∂x1∗∂p1∣SE+∂x1∗∂M∣SE\frac{\partial x_1^*}{\partial p_1} = \frac{\partial x_1^*}{\partial p_1} \bigg|_{\text{SE}} + \frac{\partial x_1^*}{\partial M} \bigg|_{\text{SE}} (where the SE component is calculated by holding real income constant).