Comparison and Contrast: Slutsky’s Method for Normal Goods

and Hicksian Compensating Variation Method for Inferior Goods

Slutsky’s Method for Normal Goods
Purpose: Slutsky’s method decomposes the effect of a price change on the demand for a normal good into
substitution and income effects. Normal goods are those for which demand increases as income rises.
Mechanics:
• Substitution Effect: Measures the change in quantity demanded due to a change in relative prices,
holding utility constant (movement along the same indifference curve).
• Income Effect: Measures the change in quantity demanded due to the change in real income caused
by the price change, holding prices constant (movement to a new indifference curve).

• Slutsky Equation: The total effect of a price change on demand is given by:
∂x ∂xc ∂x
= −x
∂p ∂p ∂I

where x is the quantity demanded, p is the price, xc is the compensated (Hicksian) demand, and I is
income.
• For normal goods, the income effect reinforces the substitution effect when the price decreases (both
increase quantity demanded), or works in the same direction when the price increases (both decrease
quantity demanded).
• Compensation: The consumer is compensated to maintain the same purchasing power at new prices
(Slutsky compensation).

Application to Normal Goods:

• Normal goods have a positive income effect ( ∂x
∂I > 0).

• Example: If the price of a normal good like coffee decreases, the substitution effect encourages more
coffee consumption (as it is relatively cheaper), and the income effect further increases demand because
the consumer’s real income rises.

Hicksian Compensating Variation Method for Inferior Goods

Purpose: The Hicksian compensating variation (CV) measures the amount of money needed to restore the
consumer to their original utility level after a price change, particularly useful for inferior goods (demand
decreases as income rises).
Mechanics:
• Compensating Variation: CV is the income adjustment required to keep the consumer on the same
indifference curve (same utility level) after a price change.
– If the price increases, CV is the additional income needed to afford the original utility level.
– If the price decreases, CV is the income reduction that keeps utility constant.
• Hicksian Demand: Uses compensated demand functions, which hold utility constant and adjust
income to reflect the price change.
• Mathematical Representation: For a price change from p0 to p1 , CV is derived from the expenditure
function:
CV = e(p1 , U0 ) − e(p0 , U0 )
where e(p, U0 ) is the minimum expenditure required to achieve utility U0 at prices p.

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 • For inferior goods, the income effect opposes the substitution effect because an increase in income
reduces demand for the good.
Application to Inferior Goods:
• Inferior goods have a negative income effect ( ∂x
∂I < 0).

• Example: If the price of an inferior good like generic canned food decreases, the substitution effect
increases demand (it is cheaper relative to substitutes), but the income effect reduces demand because
the consumer’s increased real income leads them to buy less of the inferior good in favor of higher-
quality alternatives.

Comparison
Aspect Slutsky’s Method (Normal Hicksian CV Method (Inferior
Goods) Goods)
Purpose Decomposes price effect into substitu- Measures income adjustment to main-
tion and income effects. tain utility after price change.
Compensation Basis Compensates to maintain purchasing Compensates to maintain original util-
power at new prices. ity level.
Income Effect Positive for normal goods (reinforces Negative for inferior goods (opposes
substitution effect). substitution effect).
Utility Level Utility changes after income effect (new Utility remains constant (same indiffer-
indifference curve). ence curve).
Focus Analyzes demand changes due to price Measures welfare impact (monetary
and income effects. compensation needed).
Mathematical Approach Uses Slutsky equation to separate ef- Uses expenditure function to calculate
fects. CV.
Application Best for understanding demand re- Useful for welfare analysis, especially
sponses for normal goods. for inferior goods.

Contrast
1. Type of Good:
• Slutsky’s method applies to normal goods, where the income effect amplifies the substitution
effect.
• Hicksian CV is applied to inferior goods, where the income effect counteracts the substitution
effect, potentially leading to complex demand responses (e.g., Giffen goods).
2. Objective:
• Slutsky’s method focuses on decomposing the total effect of a price change to understand consumer
behavior.
• Hicksian CV focuses on welfare, quantifying the monetary compensation needed to offset the
utility impact.
3. Compensation Approach:
• Slutsky compensates to afford the original bundle at new prices, which may result in a different
utility level.
• Hicksian CV compensates to maintain the original utility level, addressing welfare changes.
4. Outcome:
• For normal goods (Slutsky), a price decrease leads to a clear increase in demand due to aligned
effects.
• For inferior goods (Hicksian CV), a price decrease may result in a smaller demand increase (or
decrease in Giffen cases) due to the opposing income effect.

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Example for Clarity
• Normal Good (Slutsky): If the price of steak (a normal good) drops, the substitution effect encour-
ages more steak consumption over chicken, and the income effect further boosts steak demand as the
consumer feels richer.

• Inferior Good (Hicksian CV): If the price of instant noodles (an inferior good) drops, the sub-
stitution effect increases noodle consumption, but the income effect reduces it as the consumer, with
higher real income, switches to better alternatives. CV calculates the income adjustment to keep the
consumer at the same utility level.

Conclusion
Slutsky’s method is ideal for analyzing demand changes for normal goods by separating substitution and
income effects, with both effects typically aligning. The Hicksian CV method, applied to inferior goods,
focuses on welfare by calculating the income needed to maintain utility, accounting for the opposing income
effect. While Slutsky emphasizes demand dynamics, Hicksian CV prioritizes welfare measurement, making
them complementary tools in consumer theory.