Income Elasticity of Demand and Cross Price Elasticity of Demand

Income Elasticity of Demand and Cross-Price Elasticity of Demand

Income Elasticity of Demand

Definition: The Income Elasticity of Demand measures how much the quantity demanded of a good responds to a change in consumers' income.
Formula: It is calculated as the percentage change in quantity demanded divided by the percentage change in income.
- E{d,I} = \frac{\text{percentage change in } Qd}{\text{percentage change in income}}
Types of Goods Based on Income Elasticity:
- Normal Goods:
  - Have a positive income elasticity ( \text{i.e., } E_{d,I} > 0).
  - As income increases, the quantity demanded of these goods increases.
  - Further categorized into:
    - Necessities: Tend to have smaller income elasticities (positive but close to zero, \text{e.g., between 0 and 1}), meaning demand changes less proportionally to income changes (e.g., water, housing). People need them regardless of income.
    - Luxuries: Tend to have large income elasticities (positive and greater than 1, \text{e.g., } E_{d,I} > 1), meaning demand changes more than proportionally to income changes (e.g., diamonds, yachts). These are purchased more significantly as income rises.
- Inferior Goods:
  - Have a negative income elasticity ( \text{i.e., } E_{d,I} < 0).
  - As income increases, the quantity demanded of these goods decreases. Consumers buy less of them, often switching to higher-quality alternatives (e.g., generic brands, bus rides vs. car ownership).

Practice Questions - Income Elasticity of Demand

Question: Last year, Carolyn bought 6 pairs of earrings when her income was 40,000$. This year, her income is 52,000$, and she purchased 7 pairs of earrings. Holding other factors constant, it follows that Carolyn’s income elasticity of demand is about
- Calculation:
  - Percentage change in quantity demanded (Q_d): \frac{7-6}{(7+6)/2} \times 100\% = \frac{1}{6.5} \times 100\% \approx 15.38\%
  - Percentage change in income (I): \frac{52,000-40,000}{(52,000+40,000)/2} \times 100\% = \frac{12,000}{46,000} \times 100\% \approx 26.09\%
  - Income Elasticity of Demand (E_{d,I}): \frac{15.38\%}{26.09\%} \approx 0.59
- Classification: Since the income elasticity is positive (0.59 > 0), earrings are a normal good for Carolyn.
- Answer: b. \text{0.59}, and Carolyn regards earrings as a normal good.
Question: Income elasticity of demand measures how
- Answer: a. the quantity demanded changes as consumer income changes.
Question: For which of the following goods is the income elasticity of demand likely highest?
- Explanation: Luxuries have the highest income elasticity. Among the choices, diamonds are typically considered a luxury.
- Answer: b. diamonds
Question: For which of the following goods is the income elasticity of demand likely lowest?
- Explanation: Necessities have the lowest (though still positive) income elasticity. Water is a fundamental necessity.
- Answer: a. water
Question: Assume that a 4 percent increase in income results in a 2 percent increase in the quantity demanded of a good. The income elasticity of demand for the good is
- Calculation: \text{Income Elasticity} = \frac{+2\%}{+4\%} = +0.5
- Classification: Since the elasticity is positive (+0.5 > 0), the good is a normal good.
- Answer: c. positive, and the good is a normal good.

Cross-Price Elasticity of Demand

Definition: The Cross-Price Elasticity of Demand measures how much the quantity demanded of one good responds to a change in the price of another good.
Formula: It is calculated as the percentage change in quantity demanded of the first good divided by the percentage change in price of the second good.
- E{d,XP} = \frac{\text{percentage change in } Q{d1}}{\text{percentage change in } P_2}
Significance of the Coefficient's Sign: The sign (positive or negative) of the cross-price elasticity coefficient indicates the relationship between the two goods.
- Substitutes:
  - Goods typically used in place of one another (e.g., coffee and tea).
  - Have a positive cross-price elasticity ( \text{i.e., } E_{d,XP} > 0).
  - If the price of one good increases, the quantity demanded of its substitute increases.
- Complements:
  - Goods that are typically used together (e.g., peanut butter and jelly, cars and gasoline).
  - Have a negative cross-price elasticity ( \text{i.e., } E_{d,XP} < 0).
  - If the price of one good increases, the quantity demanded of its complement decreases.

Practice Questions - Cross-Price Elasticity of Demand

Question: Cross-price elasticity of demand measures how
- Answer: c. the quantity demanded of one good changes in response to a change in the price of another good.
Question: Which of the following could be the cross-price elasticity of demand for two goods that are complements?
- Explanation: Complements have a negative cross-price elasticity.
- Answer: a. \text{-1.3}
Question: The cross-price elasticity of demand can tell us whether goods are
- Explanation: The sign of the cross-price elasticity indicates if goods are substitutes or complements.
- Answer: d. complements or substitutes.
Question: For which pairs of goods is the cross-price elasticity most likely to be positive?
- Explanation: A positive cross-price elasticity indicates substitutes. Pens and pencils are commonly used as substitutes for writing.
- Answer: c. pens and pencils
Question: If the cross-price elasticity of demand for two goods is 1.25, then
- Explanation: A positive cross-price elasticity (like \text{1.25}) indicates that the two goods are substitutes.
- Answer: b. the two goods are substitutes.