A good is a Giffen good: when its price rises, quantity demanded actually increases because the positive income effect (consumers feel poorer, so they buy more of this inferior staple) overwhelms the negative substitution effect. What does the Hicksian demand curve for this good look like?
AUpward-sloping, because the good is a Giffen good and quantity demanded rises with price
BDownward-sloping, because the Hicksian curve removes the income effect entirely and shows only the substitution effect, which is always negative regardless of good type
CUpward-sloping, because holding utility constant requires the consumer to buy more when price rises to remain on the same indifference curve
DVertical, because for a Giffen good the substitution and income effects exactly offset, producing zero net response
This is the core theoretical point of Hicksian demand. The Marshallian demand curve for a Giffen good slopes upward because the income effect dominates. But the Hicksian curve strips away the income effect and shows only the substitution effect — which is always negative by definition (when price rises, the consumer substitutes away from the relatively more expensive good). The Slutsky matrix has a negative semidefinite substitution effect block, meaning the own-price substitution effect is always ≤ 0. Giffen behavior is an income-effect phenomenon, invisible in Hicksian demand.
Question 2 Multiple Choice
A government imposes a large excise tax on cigarettes, nearly doubling the price. A health economist wants to calculate the exact welfare cost to consumers. She should:
ACalculate the area under the Marshallian demand curve between the old and new price — this is the compensating variation by definition
BIntegrate under the Hicksian (compensated) demand curve between the old and new price — this gives the compensating variation, the theoretically exact welfare measure
CUse only the expenditure function directly; no demand curve can give an exact welfare measure because they are approximations
DAverage the Marshallian consumer surplus loss and the Hicksian compensating variation to eliminate directional bias
The area under the Marshallian demand curve gives consumer surplus — which approximates, but does not exactly equal, the welfare change. The approximation error arises because Marshallian demand includes income effects, which distort the willingness-to-pay interpretation. The Hicksian curve, by holding utility constant, gives the exact compensating variation: the lump-sum income adjustment needed to restore the consumer to original utility after the price change. For large price changes on major expenditure categories like cigarettes, the difference between Marshallian surplus and Hicksian compensating variation can be substantial.
Question 3 True / False
The Hicksian demand curve is always downward-sloping because it captures only the substitution effect, which is always non-positive — the consumer always substitutes away from a good that has become relatively more expensive.
TTrue
FFalse
Answer: True
This follows directly from the theory of consumer choice and the Slutsky equation. The own-price substitution effect, ∂h_i/∂p_i (where h is Hicksian demand), is guaranteed to be non-positive by the second-order conditions of expenditure minimization — equivalently, by the negative semidefiniteness of the Slutsky matrix. Unlike Marshallian demand, which can exhibit Giffen behavior when income effects dominate, Hicksian demand has an unambiguous sign. This is one reason Hicksian demand is a cleaner theoretical object for welfare and comparative statics analysis.
Question 4 True / False
For a normal good, the Hicksian demand curve is flatter (more elastic) than the Marshallian demand curve, because holding utility constant amplifies the consumer's price response.
TTrue
FFalse
Answer: False
For a normal good, the Hicksian curve is steeper (less elastic) than the Marshallian curve. Here is why: when price falls, the Marshallian consumer gets both a substitution effect (buys more because it's cheaper) and a positive income effect (feels richer, buys even more of the normal good). These two effects reinforce each other, making Marshallian demand more elastic. The Hicksian curve removes the income effect, leaving only the smaller substitution effect — so the quantity response is smaller at each price, making the Hicksian curve steeper. The relationship reverses for inferior goods.
Question 5 Short Answer
What is the fundamental difference between Marshallian and Hicksian demand, and why does this make Hicksian demand the theoretically correct tool for welfare analysis?
Think about your answer, then reveal below.
Model answer: Marshallian demand holds income constant as price varies, so both the substitution effect and the income effect are present. Hicksian demand holds utility constant (compensating the consumer's income at each price to keep them on the same indifference curve), so only the substitution effect remains. For welfare analysis, what matters is how the consumer's utility changes — the income effect contaminates the Marshallian measure by conflating real price-responsiveness with purchasing-power effects. Integrating under the Hicksian curve gives the compensating variation, the exact income adjustment needed to restore original utility, which is the correct welfare metric.
The practical implication: for small price changes on goods that are a small share of the budget, Marshallian consumer surplus and Hicksian compensating variation are nearly identical (the income effect is small). For large price changes on necessities like housing, healthcare, or food — where income effects are large — the two measures diverge significantly. Using Marshallian surplus to evaluate housing subsidy programs, for instance, can substantially overstate consumer welfare gains.