4. If Cassandra bought 16 cotton blouses last year when her income was $40,000 and she buys 24 cotton blouses this year when her income is $50,000, then what is her income elasticity of demand? Interpret what the income elasticity of demand you just calculated means to you. Also, are cotton blouses normal goods or inferior goods? Why? Will the demand curve shift rightward or leftward if cotton blouses are normal goods or inferior goods? Are cotton blouses income elastic, income inelastic or unit elastic? Why?
Income elasticity of demand = (24-16)/(50,000-40,000) = 0.4
The income elasticity of demand of 0.4 means that Cassandra's demand for cotton blouses increases by 0.4 for every 1% increase in her income.
Cotton blouses are normal goods, as an increase in income leads to an increase in demand for them. The demand curve will shift rightward if cotton blouses are normal goods.
Cotton blouses are income elastic, as an increase in income leads to an increase in demand for them.
To calculate the income elasticity of demand for cotton blouses, we can use the following formula:
Income Elasticity of Demand = ((Q2 - Q1) / Q1) / ((Y2 - Y1) / Y1)
Where:
Q1 = quantity of cotton blouses bought last year = 16
Q2 = quantity of cotton blouses bought this year = 24
Y1 = income last year = $40,000
Y2 = income this year = $50,000
Plugging the values into the formula, we get:
Income Elasticity of Demand = ((24 - 16) / 16) / (($50,000 - $40,000) / $40,000)
Simplifying, we have:
Income Elasticity of Demand = (8 / 16) / (10,000 / 40,000)
Income Elasticity of Demand = 0.5 / 0.25
Income Elasticity of Demand = 2
The income elasticity of demand for cotton blouses is 2.
Interpretation:
A positive income elasticity of demand value indicates that cotton blouses are a normal good. Since the calculated value is 2, it suggests that a 1% increase in income leads to a 2% increase in the quantity of cotton blouses bought. This means that cotton blouses are income-elastic, meaning they are sensitive to changes in income.
Since cotton blouses are normal goods, if there is an increase in income, the demand curve for cotton blouses will shift rightward, indicating a higher quantity demanded. Conversely, if there is a decrease in income, the demand curve will shift leftward, indicating a lower quantity demanded.
Therefore, cotton blouses are income elastic due to the positive income elasticity value of 2.
To calculate the income elasticity of demand for cotton blouses, we will use the following formula:
Income Elasticity of Demand = [(Q2 - Q1) / Q1] / [(Y2 - Y1) / Y1]
Where:
- Q1 is the quantity of cotton blouses bought last year (16)
- Q2 is the quantity of cotton blouses bought this year (24)
- Y1 is the income last year ($40,000)
- Y2 is the income this year ($50,000)
Substituting the values into the formula:
Income Elasticity of Demand = [(24 - 16) / 16] / [(50,000 - 40,000) / 40,000]
Simplifying:
Income Elasticity of Demand = [8 / 16] / [10,000 / 40,000]
= 0.5
Interpreting the income elasticity of demand value:
The income elasticity of demand is 0.5, indicating that the demand for cotton blouses is income inelastic. This means that a 1% increase in income will result in less than a 0.5% increase in the quantity bought of cotton blouses. Cotton blouses are considered a necessity rather than a luxury, as their demand is not strongly influenced by changes in income.
Next, let's determine if cotton blouses are normal goods or inferior goods:
Normal goods are characterized by a positive income elasticity of demand, while inferior goods have a negative income elasticity of demand.
Since the income elasticity of demand for cotton blouses is positive (0.5), it means that they are normal goods. This implies that as income increases, the demand for cotton blouses also increases.
Regarding the demand curve, when a good is a normal good, an increase in income shifts the demand curve rightward, indicating a higher quantity demanded at each price level. Therefore, if cotton blouses are normal goods, an increase in income would cause the demand curve for cotton blouses to shift rightward.
In summary, the income elasticity of demand for cotton blouses is 0.5, indicating that they are income inelastic. Cotton blouses are normal goods since their income elasticity of demand is positive. If income increases, the demand for cotton blouses will shift rightward.