The equation showing how the effect on demand for a good of a change in a price can be decomposed into a substitution effect, which is the effect of a change in relative prices at an unchanged level of utility, and an income effect, which is the effect of a change in real income holding prices constant. Denote the demand for good i by x_i, the price of good j by p_j, income by M, and utility by U. The Slutsky equation is

where $\frac{\partial x_i}{\partial p_j}{|}_U$ is the substitution effect and $-x_j\frac{\partial x_i}{\partial M}$ the income effect.