Answer First
Marshallian demand depends on income because it solves the consumer’s problem of maximizing utility subject to a budget constraint. Income determines which bundles are affordable, so optimal choices change when income changes. Hicksian demand holds utility fixed and therefore does not depend on income.
Problem Setup
Marshallian (uncompensated) demand solves: \[ \max_{x,y} \; U(x,y) \] subject to: \[ p_x x + p_y y = I. \] Hicksian (compensated) demand solves: \[ \min_{x,y} \; p_x x + p_y y \] subject to: \[ U(x,y) = \bar{U}. \]
Step-by-Step Explanation
1. Marshallian demand chooses the best affordable bundle
Income determines the size and position of the budget line. Higher income → more affordable bundles → different optimal choice.
2. Hicksian demand holds utility constant
Hicksian demand asks: “What is the cheapest way to reach a target utility level?” Since utility is fixed, income plays no role.
3. Marshallian demand includes both substitution and income effects
When prices change:
- Marshallian demand changes due to substitution + income effects.
- Hicksian demand changes only due to substitution effects.
4. Marshallian demand is what consumers actually choose
It reflects real-world behavior: people choose the best bundle they can afford given their income.
5. Hicksian demand is a theoretical construct
It is used for:
- compensating variation,
- equivalent variation,
- Slutsky decomposition,
- welfare analysis.
Intuition
Marshallian demand answers: “What do I buy with my income?” Hicksian demand answers: “What would I buy if someone compensated me to keep utility constant?”
Common Exam Mistakes
- Thinking Hicksian demand is “more realistic” (it is not).
- Forgetting that Marshallian demand shifts when income changes.
- Confusing substitution and income effects.
- Using Hicksian demand in consumer surplus problems.
Final Summary
Marshallian demand depends on income because it solves the utility maximization problem under a budget constraint. Hicksian demand holds utility fixed and therefore does not depend on income. Marshallian demand reflects actual consumer choices, while Hicksian demand isolates substitution effects for theoretical analysis.
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