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Difficulty: Very hardIncome and Substitution Effects on Demand

When the price of Good X increases, the substitution effect causes a consumer to decrease their consumption of Good X by 77 units. If the net total price effect results in an overall increase of 33 units in the quantity demanded of Good X, which of the following correctly classifies Good X and describes the direction and magnitude of the income effect?

  1. Good X is a Giffen good, and the income effect causes an increase of 1010 units in quantity demanded.Answer
  2. B
    Good X is a standard inferior good, and the income effect causes a decrease of 1010 units in quantity demanded.
  3. C
    Good X is a Giffen good, and the income effect causes an increase of 44 units in quantity demanded.
  4. D
    Good X is a normal good, and the income effect causes an increase of 33 units in quantity demanded.

Answer

Good X is a Giffen good, and the income effect causes an increase of 1010 units in quantity demanded.
The total price effect is the algebraic sum of the substitution effect and the income effect (TE=SE+IETE = SE + IE). When the price of a commodity rises, the substitution effect is strictly negative (−7-7 units). To achieve an overall increase in quantity demanded of +3+3 units, the income effect must equal +10+10 units. Because the income effect acts in the opposite direction of the substitution effect and is powerful enough to outweigh it, the commodity is definitively classified as a Giffen good.

Step-by-Step Solution

1
Set up the fundamental decomposition formula for price effect
Total Effect (TETE) = Substitution Effect (SESE) + Income Effect (IEIE)
According to ordinal utility theory, the total price effect on quantity demanded is decomposed into substitution and income components.
2
Calculate the magnitude and direction of the income effect
+3=−7+IE  ⟹  IE=+10+3 = -7 + IE \implies IE = +10 units
A price increase always produces a negative substitution effect (SE=−7SE = -7). For the overall quantity demanded to increase by 33 units (TE=+3TE = +3), the income effect must be +10+10 units.
3
Determine the economic classification of the good
Good X is a Giffen good
A Giffen good is an extreme case of an inferior good where the positive income effect from a price increase is stronger than the negative substitution effect, resulting in a positively sloped demand curve.

Key Concept

Decomposition of Price Effect into Income and Substitution Effects for Giffen Goods
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Topics

Income and Substitution Effects on Demand

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