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The Slutsky Equation, named for Russian mathematician Eugen Slutsky, is a concept in microeconomics detailing how a change in the price of a good affects the quantity demanded of the good.
It breaks the net effect of a price change into two parts: the income effect and the substitution effect, as follows:
Total Effect = Substitution Effect + Income Effect (Te = Se + Ie)
The substitution effect is the change in quantity demanded (Q) due to changes in the relative prices of goods, given that consumer’s utility functions is constant. Logically, consider two substitute products: if one becomes more expensive, the other relatively becomes cheaper and thus more attractive to purchase if the derived utility is otherwise a constant.
Meanwhile, the income effect is the change in quantity demanded (Q) as a result of the change in the consumer’s purchasing power. This basically says that consumers who can afford fewer items will change their spending habits.
Mathematical Representation of the Slutsky Equation
The Slutsky Equation can be expressed mathematically as:
∂xᵢ/∂pⱼ = ∂hᵢ/∂pⱼ- xⱼ(∂xᵢ/∂I)
The Slutsky Equation
Let’s break that down:
I is the consumer’s income.xⱼis the quantity consumed of good j and vice versa for good i (xᵢ).∂xᵢ/∂pⱼis the total change in quantity demanded for good “i” due to change in the price of good “j”.∂hᵢ/∂pⱼ is the substitution effect. This reflects how consumers will substitute toward goods that are relatively cheaper, and is calculated by keeping the consumer’s utility constant (think compensated demand).∂xᵢ/∂I is one’s marginal propensity to consume good i with respect to income (the income effect). For normal goods, the income effect reinforces the substitution effect, while for inferior goods, the income effect works in the opposite direction to the substitution effect.
Applications of the Slutsky Equation
The Slutsky equation has applications across policy analysis when, say, exploring the impact of taxation or subsidies on behavior, and when calculating price elasticities in order to separate the effects.
Note the special case of Giffen Goods, which are inferior goods where the income effect is so strong that it outweighs the substitution effect, thus leading to an increase in quantity demanded when prices rise.
So, hope you found that helpful! Here’s another article detailing nominal and real GDP (here), and one more about how to calculate inflation using multiple GDP deflators (here). Also:
Read about the Income Approach to GDP here.Read more economics stories here.To learn more about the oil market, consider reading about PADD Districts, the Why WTI and Brent are Crude Oils, and Why There are Price Differences Among Crude Oils, and my Oil & Gas Terms Guide.