The following graph plots a supply curve for some hypothetical good.

A graph with price in dollars per unit on the y-axis and quantity of units on the x-axis plots a convex upward-sloping supply curve through points V (7, 37.5), W (17.5, 50), X (56, 225) and Y (63, 450).

PRICE (Dollars per unit)QUANTITY (Units)Supply0V37.57W5017.5X22556Y45063

For each of the regions, use the midpoint method to identify whether the supply of this good is elastic or inelastic.

Region

Elastic

Inelastic

Between V and W

Between X and Y

True or False: As firms reach near maximum capacity at high levels of quantity supplied, supply becomes more elastic because firms may need to invest in additional capital in order to further increase production.

True

False

To determine whether the supply of this good is elastic or inelastic in each region using the **midpoint method**, we must calculate the **price elasticity of supply (PES)** for the two regions (V to W and X to Y).

### **Midpoint Method for Price Elasticity of Supply**
The formula for price elasticity of supply using the midpoint method is:

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

Where:
- \( Q_1 \) and \( Q_2 \) are the quantities at the two points.
- \( P_1 \) and \( P_2 \) are the prices at the two points.

The interpretation of the price elasticity of supply:
- If \( PES > 1 \), supply is **elastic**.
- If \( PES < 1 \), supply is **inelastic**.

### 1. **Between Points V (7, 37.5) and W (17.5, 50)**

- \( Q_1 = 37.5 \), \( Q_2 = 50 \)
- \( P_1 = 7 \), \( P_2 = 17.5 \)

Using the midpoint method formula:

\[
\text{PES} = \frac{\left(\frac{50 - 37.5}{\frac{50 + 37.5}{2}}\right)}{\left(\frac{17.5 - 7}{\frac{17.5 + 7}{2}}\right)}
\]

Let's calculate the PES for this region.

### 2. **Between Points X (56, 225) and Y (63, 450)**

- \( Q_1 = 225 \), \( Q_2 = 450 \)
- \( P_1 = 56 \), \( P_2 = 63 \)

Using the midpoint method formula:

\[
\text{PES} = \frac{\left(\frac{450 - 225}{\frac{450 + 225}{2}}\right)}{\left(\frac{63 - 56}{\frac{63 + 56}{2}}\right)}
\]

Let's calculate the PES for this region as well.

### **True or False: Elasticity at High Levels of Supply**

The statement:

> "As firms reach near maximum capacity at high levels of quantity supplied, supply becomes more elastic because firms may need to invest in additional capital in order to further increase production."

This statement is **False**. As firms approach maximum capacity, it becomes more difficult to increase production without significant investments in new capacity. In this situation, supply tends to become **inelastic**, not more elastic, because firms cannot easily respond to price increases by significantly increasing quantity supplied without incurring additional costs.

Let me calculate the exact values of PES for both regions next.### **Elasticity Results:**

1. **Between Points V (7, 37.5) and W (17.5, 50)**:
   - The **PES** is approximately **0.33**, which is **inelastic** since the value is less than 1.

2. **Between Points X (56, 225) and Y (63, 450)**:
   - The **PES** is approximately **5.67**, which is **elastic** since the value is greater than 1.

### **Conclusion:**
- **Between V and W**, supply is **inelastic**.
- **Between X and Y**, supply is **elastic**.

### The Statement:
> "As firms reach near maximum capacity at high levels of quantity supplied, supply becomes more elastic..."

This is **False**. As firms approach capacity, supply typically becomes **inelastic**.

---

Would you like more details on these calculations or have any further questions? Here are some related questions you might explore:

1. What are the key factors influencing price elasticity of supply?
2. How does elasticity change in the short run versus the long run for firms?
3. Can PES ever be negative, and if so, under what conditions?
4. How do technological advancements affect the elasticity of supply?
5. What role does supply chain management play in improving supply elasticity?

**Tip:** The closer a firm is to its production capacity, the less responsive it is to price changes, leading to more inelastic supply behavior.

The following graph plots a supply curve for some hypothetical good. A graph with price in dollars per unit on the y-axis and quantity of units on the x-axis plots a convex upward-sloping supply curve through points V (7, 37.5), W (17.5, 50), X (56, 225) and Y (63, 450). For each of the regions, use the midpoint method to identify whether the supply of this good is elastic or inelastic.

Analyze the price elasticity of supply using the midpoint method for a convex supply curve through points V (7, 37.5), W (17.5, 50), X (56, 225), and Y (63, 450). This problem involves calculating the PES and determining if the supply is elastic or inelastic between key points. Suitable for advanced high school or college-level economics students.

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