Slutsky Equation & Hicksian Demand
Decomposing a price change into substitution and income effects. Marshallian vs. compensated demand.
Definition
The decomposition of a price change's effect on demand into a substitution effect (relative-price change, utility held constant) and an income effect (purchasing-power change).
Key equation
∂x/∂p = ∂h/∂p − x·(∂x/∂m) (Slutsky equation)
The intuition
When petrol gets dearer you buy less both because alternatives look relatively cheaper (substitution, always negative) and because you're effectively poorer (income, direction depends on the good). A Giffen good needs an income effect so perverse it swamps substitution.
Exam tip
Substitution effects are ALWAYS negative; only the income effect can flip signs, that's the wedge between Marshallian and Hicksian demand.
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