When the Shaffers have a monthly income of $4,000, they would usually eat out 8 times a month. Now
that the couple makes $4,500 a month, they eat out 10 times a month. Compute the couple’s income
elasticity of demand using the midpoint method. Explain your answer. (Is a restaurant meal a normal or
inferior good to the couple?
To compute the couple's income elasticity of demand using the midpoint method, we need to calculate the percentage change in quantity demanded and the percentage change in income.
First, let's find the percentage change in quantity demanded:
Old quantity demanded = 8 times a month
New quantity demanded = 10 times a month
Using the midpoint method formula to calculate the percentage change:
Percentage change in quantity demanded = [(New quantity - Old quantity) / ((New quantity + Old quantity) / 2)] * 100
= [(10 - 8) / ((10 + 8) / 2)] * 100
= (2 / 9) * 100
≈ 22.22%
Next, let's find the percentage change in income:
Old income = $4,000
New income = $4,500
Percentage change in income = [(New income - Old income) / ((New income + Old income) / 2)] * 100
= [(4,500 - 4,000) / ((4,500 + 4,000) / 2)] * 100
= (500 / 4,250) * 100
≈ 11.76%
Now, we can calculate the income elasticity of demand using the formula:
Income elasticity of demand = (Percentage change in quantity demanded) / (Percentage change in income)
Income elasticity of demand = 22.22% / 11.76%
≈ 1.89
To interpret the income elasticity of demand, we look at the absolute value of the elasticity. In this case, the income elasticity of demand is positive (1.89), indicating that restaurant meals are a normal good for the Shaffers. A positive income elasticity greater than 1 suggests that as the couple's income increases by 1%, the quantity of restaurant meals they consume increases by approximately 1.89%. Therefore, we can conclude that restaurant meals are a normal good for the Shaffers.