Roy's Identity

thm. Roy’s Identity. Relates income, price, and Indirect Utility Function to a own-price demand function.

$$\begin{array}{r}{x}_1(p_1,p_2,I)\equiv -\frac{\partial v/\partial p_1}{\partial v/\partial I}\\ x_2(p_1,p_2,I)\equiv -\frac{\partial v/\partial p_2}{\partial v/\partial I}\end{array}$$