Answer First
The Hicksian substitution effect holds utility constant and isolates pure substitution. The Marshallian substitution effect holds real income constant and includes part of the income effect. Hicksian is “compensated”; Marshallian is “uncompensated.”
Problem Setup
Marshallian demand: \[ x(p,I) \] Hicksian demand: \[ h(p,U) \] Slutsky decomposition: \[ \frac{\partial x}{\partial p} = \frac{\partial h}{\partial p} – x \frac{\partial x}{\partial I}. \]
Step-by-Step Explanation
1. Hicksian substitution effect: hold utility fixed
This isolates the pure response to a price change, ignoring income effects.
2. Marshallian substitution effect: hold real income fixed
This includes a small income effect because the consumer must stay on the same budget line.
3. Hicksian is always larger in magnitude
Because it removes the income effect entirely.
4. Hicksian uses expenditure minimization; Marshallian uses utility maximization
Two different optimization problems → two different substitution effects.
5. Slutsky equation links them
The difference between Hicksian and Marshallian is exactly the income effect term.
Intuition
Hicksian asks: “How would you substitute if I compensated you for the price change?” Marshallian asks: “How would you substitute if I didn’t compensate you?”
Common Exam Mistakes
- Thinking Hicksian and Marshallian are the same.
- Forgetting that Hicksian holds utility constant.
- Confusing substitution effect with income effect.
- Misapplying the Slutsky equation.
Final Summary
The Hicksian substitution effect isolates pure substitution by holding utility constant. The Marshallian substitution effect holds real income constant and includes part of the income effect. Hicksian is compensated; Marshallian is uncompensated.
This explanation belongs to the broader Economics Tutoring pillar.
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