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.