To calculate the income elasticity of demand using the midpoint method, we use the following formula:

$\text{Income Elasticity of Demand} = \frac{\%\text{ change in quantity demanded}}{\%\text{ change in income}}$

The percentage change in quantity demanded ($Q$) and income ($I$) using the midpoint method is given by:

$\%\text{ change in quantity demanded} = \frac{Q_2 - Q_1}{\left( \frac{Q_2 + Q_1}{2} \right)}$ $\%\text{ change in income} = \frac{I_2 - I_1}{\left( \frac{I_2 + I_1}{2} \right)}$

Where:

• $Q_1 = 3$ (initial quantity of meals per month),
• $Q_2 = 5$ (new quantity of meals per month),
• $I_1 = 31,900$ (initial income),
• $I_2 = 33,500$ (new income).

Step 1: Calculate the percentage change in quantity demanded

$\%\text{ change in quantity demanded} = \frac{5 - 3}{\left( \frac{5 + 3}{2} \right)} = \frac{2}{4} = 0.5$

Step 2: Calculate the percentage change in income

$\%\text{ change in income} = \frac{33,500 - 31,900}{\left( \frac{33,500 + 31,900}{2} \right)} = \frac{1,600}{32,700} \approx 0.04893$

Step 3: Calculate the income elasticity of demand

$\text{Income Elasticity of Demand} = \frac{0.5}{0.04893} \approx 10.22$

Therefore, the income elasticity of demand for eating out is approximately 10.22.

This high value suggests that eating out at Macaroni Grill is a luxury good for Becky, as her demand for it increases significantly with an increase in income.

Would you like more details or have any questions?

Here are 5 related questions to consider:

1. How does income elasticity help in understanding consumer behavior?
2. What does a high income elasticity imply about a good's necessity or luxury status?
3. What is the midpoint method, and why is it used?
4. Can income elasticity be negative? If so, what does that mean?
5. How would a different percentage change in income affect Becky's demand for eating out?

Tip: Goods with high-income elasticity are often referred to as "luxury goods," while those with low or negative elasticity are considered "necessities" or "inferior goods."