Correct Option: C. an inferior good
Step-by-Step Explanation:
- Understanding the Concepts:
- Normal Goods: These are goods for which demand increases as income increases. When consumers have more income, they tend to buy more of these goods.
- Inferior Goods: These are goods for which demand decreases as income increases. When consumers have more income, they tend to buy less of these goods, opting for higher-quality alternatives.
-
Income Elasticity of Demand: This measures how the quantity demanded of a good responds to a change in income. It is calculated using the formula:
[
\text{Income Elasticity of Demand (E)} = \frac{\%\text{ Change in Quantity Demanded}}{\%\text{ Change in Income}}
]
-
Calculating Changes:
- Initial Income: N200.00
- New Income: N250.00
- Change in Income: N250.00 - N200.00 = N50.00
-
Percentage Change in Income:
[
\frac{50}{200} \times 100 = 25\%
]
-
Initial Spending on Good X: N30.00
- New Spending on Good X: N28.00
- Change in Spending: N28.00 - N30.00 = -N2.00
-
Percentage Change in Quantity Demanded:
[
\frac{-2}{30} \times 100 \approx -6.67\%
]
-
Calculating Income Elasticity:
- Now, we can calculate the income elasticity of demand for good X:
[
E = \frac{-6.67\%}{25\%} \approx -0.267
]
-
Since the elasticity is negative, this indicates that good X is an inferior good. In general, for inferior goods, the income elasticity of demand is negative.
-
Conclusion:
- Since the demand for good X decreased as income increased, we conclude that good X is an inferior good.
Why Other Options Are Incorrect:
- Option A: An income elastic good:
-
Income elastic goods have an elasticity greater than 1 (in absolute value), meaning demand increases significantly with income. Since we found a negative elasticity, this option is incorrect.
-
Option B: A normal good:
-
Normal goods have a positive elasticity, meaning demand increases with income. Since the demand for good X decreased as income increased, this option is also incorrect.
-
Option D: Demand elastic:
- Demand elasticity refers to how sensitive the quantity demanded is to changes in price, not income. The question is about income changes, not price changes, making this option irrelevant.
Revision Summary:
- Inferior goods: Demand decreases as income increases.
- Normal goods: Demand increases as income increases.
- Income elasticity of demand: Calculated as the percentage change in quantity demanded divided by the percentage change in income.
- Negative elasticity indicates an inferior good, while positive elasticity indicates a normal good.