Becky only eats out at Macaroni Grill and eats out 3 times per month. She receives a raise from $31,900 to $33,500 and decides to eat out 5 times per month. Use the midpoint method to calculate the monthly income elasticity of demand for eating out.

Round your answer to two decimal places.

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."

Becky only eats out at Macaroni Grill and eats out 3 times per month. She receives a raise from $31,900 to $33,500 and decides to eat out 5 times per month. Use the midpoint method to calculate the monthly income elasticity of demand for eating out. Round your answer to two decimal places.

Learn how to calculate the income elasticity of demand using the midpoint method. Becky’s income increases from $31,900 to $33,500, leading her to eat out more frequently. Discover how to apply the elasticity formula and calculate a value of 10.22 for Becky's dining habits. Suitable for Grades 10-12.

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