Slutsky Method

The Slutsky method provides a framework to separately measure the substitution effect and the income effect resulting from a price change. Considering two goods, X₁ and X₂, an increase in the price of X₁ alters their relative prices. As we know, the overall price effect reflects changes in the consumer’s choice basket driven by both shifts in relative prices and variations in purchasing power (income). This price effect shifts the consumer’s optimal choice from basket A to basket B.

To isolate these two effects, Slutsky suggests introducing a subsidy that enables the consumer to afford the original basket A. Graphically, this involves shifting the new budget line, adjusted for the updated relative prices, until it passes through point A. Under these conditions, the consumer identifies the optimal choice at basket C, which lies tangent to a higher indifference curve. At point C, the consumer is compensated for the loss of real income, allowing only the substitution effect to be observed. The Slutsky method can be understood as follows:

• Substitution Effect. The shift from basket A to basket C measures changes in the quantity demanded while keeping real income constant. This isolates the substitution effect.
• Income Effect. The shift from basket C to basket B measures changes in the quantity demanded while keeping relative prices constant. This isolates the income effect.

In summary, the Slutsky method provides a systematic approach to analyzing the price effect, enabling the separate measurement of the income and substitution effects following a price change. It identifies a theoretical third basket on the graph, representing the consumer’s constant purchasing power (real income).

Hicks Method. The Hicks method is another way to separate the income and substitution effects. Both methods identify a third theoretical basket: the Slutsky method does so under constant real income, while the Hicks method focuses on constant utility (welfare).