Suppose the demand for a certain brand of sandals is given by the equation Q= 1000 - 20P , where Q is the quantity demanded and P is the price. Calculate the own-price elasticity of demand if the price declines from $30 to $25. Please round your answer to 2 decimal places.

To calculate the own-price elasticity of demand (PED) when the price changes, we use the formula:

\[
\text{PED} = \frac{\%\text{ Change in Quantity Demanded}}{\%\text{ Change in Price}}
\]

Given the demand equation:
\[
Q = 1000 - 20P
\]

### Step 1: Find the Initial Quantity Demanded ($Q_1$) and New Quantity Demanded ($Q_2$)

1. **Initial Price $P_1 = 30$:**
   \[
   Q_1 = 1000 - 20 \times 30 = 1000 - 600 = 400
   \]

2. **New Price $P_2 = 25$:**
   \[
   Q_2 = 1000 - 20 \times 25 = 1000 - 500 = 500
   \]

### Step 2: Calculate the Change in Quantity Demanded and Change in Price

1. **Change in Quantity Demanded ($\Delta Q$):**
   \[
   \Delta Q = Q_2 - Q_1 = 500 - 400 = 100
   \]

2. **Change in Price ($\Delta P$):**
   \[
   \Delta P = P_2 - P_1 = 25 - 30 = -5
   \]

### Step 3: Calculate the Percentage Changes

1. **Percentage Change in Quantity Demanded:**
   \[
   \%\text{ Change in Quantity Demanded} = \frac{\Delta Q}{Q_1} \times 100 = \frac{100}{400} \times 100 = 25\%
   \]

2. **Percentage Change in Price:**
   \[
   \%\text{ Change in Price} = \frac{\Delta P}{P_1} \times 100 = \frac{-5}{30} \times 100 \approx -16.67\%
   \]

### Step 4: Calculate the Own-Price Elasticity of Demand

\[
\text{PED} = \frac{25\%}{-16.67\%} \approx -1.5
\]

Rounding this to two decimal places:
\[
\text{PED} \approx -1.50
\]

The own-price elasticity of demand when the price declines from $30 to $25 is approximately **-1.50**.

### Interpretation
Since the absolute value of the elasticity is greater than 1, the demand for this brand of sandals is **elastic** in this price range, meaning that the percentage change in quantity demanded is greater than the percentage change in price.

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### Relative Questions:
1. What happens to total revenue when the price is decreased for an elastic demand?
2. How does this elasticity change if the price drops further, say from $25 to $20?
3. What are the factors that generally affect the elasticity of demand for a product?
4. How would a perfectly inelastic demand curve look compared to this one?
5. How would you interpret the elasticity if the value was less than 1?

### Tip:
Elasticity helps businesses understand how sensitive their consumers are to changes in price, which can be crucial for pricing strategies.

Suppose the demand for a certain brand of sandals is given by the equation Q= 1000 - 20P, where Q is the quantity demanded and P is the price. Calculate the own-price elasticity of demand if the price declines from $30 to $25. Please round your answer to 2 decimal places.

Learn how to calculate the own-price elasticity of demand for sandals using the demand equation Q = 1000 - 20P. This step-by-step solution involves key economic concepts, including percentage change in quantity demanded and price, and is ideal for students in Grades 10-12.

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