matrix form is: Although strictly speaking the Slutsky equation only applies to infinitesimal changes in prices, it is standardly used a linear approximation for finite changes. If the prices of the two goods change by and , the effect on the demands for the two goods are: Multiplying out the matrices, the effect on good 1, for example, would be The first term is the substitution effect. The second term is the income effect, composed of the consumer's response to income loss times the size of the income loss from each price's increase. Giffen goods A Giffen good is a product that is in greater demand when the price increases, which are also special cases of inferior goods. In the extreme case of income inferiority, the size of income effect overpowers the size of the substitution effect, leading to a positive overall change in demand responding to an increase in the price. Slutsky's decomposition of the change in demand into a pure substitution effect and income effect explains why the law of demand doesn't hold for Giffen goods. See also Consumer choice Hotelling's lemma Hicksian demand function Marshallian demand function Cobb-Douglas production function Giffen Goods Purchasing power Normal good Substitute goods Inferior goods Complementary goods References Demand Equations Microeconomics Mathematical economics References Varian, H. R. (2020). Intermediate microeconomics : a modern approach (Ninth edition.). W.W. Norton & Company.