The following graph shows the demand for a good.
PRICE (Dollars per unit)
QUANTITY (Units)
Demand
0
W
140
10
X
70
25
Y
50
35
Z
20
70
For each region on the graph given in the following table, use the midpoint method to identify whether the demand for this good is elastic, (approximately) unit elastic, or inelastic.
Region
Elastic
Inelastic
Unit Elastic
Between X and Y

Between Y and Z

Between W and X

True or False: The value of the price elasticity of demand is not equal to the slope of the demand curve.

True
False

Let's address each part of your question step-by-step:

### Midpoint Method Formula
To calculate the price elasticity of demand (PED) using the midpoint method, we use the following formula:

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

Where:
- \( Q_1 \) and \( Q_2 \) are the initial and final quantities demanded.
- \( P_1 \) and \( P_2 \) are the initial and final prices.

After calculating the PED, we interpret it as follows:
- If \( \text{PED} > 1 \), demand is **elastic** (price-sensitive).
- If \( \text{PED} < 1 \), demand is **inelastic** (price-insensitive).
- If \( \text{PED} = 1 \), demand is **unit elastic** (proportional response).

### 1. Region Between X and Y
Here:
- \( P_1 = 10 \) and \( P_2 = 25 \)
- \( Q_1 = 70 \) and \( Q_2 = 50 \)

Using the midpoint method formula, let’s calculate the PED.

### 2. Region Between Y and Z
Here:
- \( P_1 = 25 \) and \( P_2 = 35 \)
- \( Q_1 = 50 \) and \( Q_2 = 20 \)

We will follow the same steps to calculate the PED using the midpoint method.

### 3. Region Between W and X
Here:
- \( P_1 = 0 \) and \( P_2 = 10 \)
- \( Q_1 = 140 \) and \( Q_2 = 70 \)

Similarly, we apply the midpoint method formula.

### True or False: The value of the price elasticity of demand is not equal to the slope of the demand curve.
**True.**
The price elasticity of demand (PED) measures the percentage change in quantity demanded in response to a percentage change in price. In contrast, the slope of the demand curve measures the absolute change in quantity divided by the absolute change in price. Elasticity adjusts for proportional changes, while slope does not.

Let me compute the elasticity for each region.

### Elasticity Results for Each Region:

1. **Between X and Y**: The price elasticity of demand (PED) is approximately 0.39, which indicates that the demand is **inelastic**.
2. **Between Y and Z**: The PED is approximately 2.57, meaning the demand is **elastic**.
3. **Between W and X**: The PED is approximately 0.33, showing that the demand is **inelastic**.

### True or False Question:
The statement, **"The value of the price elasticity of demand is not equal to the slope of the demand curve"**, is **True**, as elasticity measures relative changes, while slope measures absolute changes.

Would you like more details or have any questions? Here are 5 related questions to deepen your understanding:

1. How does elasticity affect total revenue for a firm?
2. What factors determine whether a good has elastic or inelastic demand?
3. Can demand become more elastic over time, and why?
4. How does elasticity differ along a straight-line demand curve?
5. What is the significance of unit elastic demand for pricing decisions?

**Tip**: Elasticity changes along a demand curve—it's often more elastic at higher prices and less elastic at lower prices.

The following graph shows the demand for a good. PRICE (Dollars per unit) QUANTITY (Units) Demand 0 W 140 10 X 70 25 Y 50 35 Z 20 70 For each region on the graph given in the following table, use the midpoint method to identify whether the demand for this good is elastic, (approximately) unit elastic, or inelastic. Region Elastic Inelastic Unit Elastic Between X and Y Between Y and Z Between W and X True or False: The value of the price elasticity of demand is not equal to the slope of the demand curve. True False

Learn how to calculate the elasticity of demand using the midpoint method with a step-by-step approach. Analyze demand elasticity between different price points on a graph and understand when demand is elastic, inelastic, or unit elastic. Suitable for high school economics and advanced mathematics students.

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