Valerie is a retired teacher who lives in Miami and provides math tutoring for extra cash. At a wage of $25 per hour, she is willing to tutor 4 hours per week. At $40 per hour, she is willing to tutor 10 hours per week.
Using the midpoint method, the elasticity of Valerie's labor supply between the wages of $25 and $40 per hour is approximately    , which means that Valerie's supply of labor over this wage range is    .

To determine the elasticity of Valerie's labor supply between the wages of $25 and $40, we can use the **midpoint method**. The formula for the elasticity of labor supply (or any elasticity) using the midpoint method is:

\[
\text{Elasticity} = \frac{\left( \frac{Q_2 - Q_1}{(Q_2 + Q_1)/2} \right)}{\left( \frac{P_2 - P_1}{(P_2 + P_1)/2} \right)}
\]

Where:
- $ Q_1 $ and $ Q_2 $ are the quantities of labor supplied at the two wage levels.
- $ P_1 $ and $ P_2 $ are the wage rates.

### Step 1: Identify the values
- $ Q_1 = 4 $ hours at $ P_1 = 25 $ dollars.
- $ Q_2 = 10 $ hours at $ P_2 = 40 $ dollars.

### Step 2: Apply the formula
We will calculate the percentage change in quantity of labor and percentage change in wages.

\[
\text{Percentage change in quantity} = \frac{10 - 4}{\frac{10 + 4}{2}} = \frac{6}{7} \approx 0.857
\]

\[
\text{Percentage change in price (wages)} = \frac{40 - 25}{\frac{40 + 25}{2}} = \frac{15}{32.5} \approx 0.462
\]

### Step 3: Calculate the elasticity
\[
\text{Elasticity} = \frac{0.857}{0.462} \approx 1.855
\]

### Conclusion:
The elasticity of Valerie's labor supply between the wages of $25 and $40 per hour is approximately **1.86**, which means that her labor supply is **elastic** over this wage range. This implies that her willingness to supply labor is highly responsive to changes in wages within this range.

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Would you like further explanation or have any questions? Here are five related questions that might interest you:

1. How is labor supply elasticity typically interpreted in economics?
2. What factors influence a person’s elasticity of labor supply?
3. How does Valerie’s labor supply change if the wage increases beyond $40?
4. What are some examples of elastic and inelastic labor supplies?
5. Can elasticity of labor supply vary depending on the profession?

**Tip:** Elasticity greater than 1 means the quantity supplied changes by a larger percentage than the price change.

Valerie is a retired teacher who lives in Miami and provides math tutoring for extra cash. At a wage of $25 per hour, she is willing to tutor 4 hours per week. At $40 per hour, she is willing to tutor 10 hours per week. Using the midpoint method, the elasticity of Valerie's labor supply between the wages of $25 and $40 per hour is approximately    , which means that Valerie's supply of labor over this wage range is    .

Learn how to calculate the elasticity of labor supply using the midpoint method for Valerie's tutoring hours. This problem demonstrates key economic concepts such as labor supply elasticity, percentage change, and responsiveness to wage changes. Suitable for students studying economics or advanced math.

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